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LIFE

JOHN DOLLOND, F.R.S.

With a copious Appendix of alJ the Papers referred to.

Author of the Triglott Celtic Dictionary, and a Translator of the Bible into the Manks Gaelic.

1808.

An Account of some Experiments concerning the different Refranglbility of Light. By Mr. John Dollond. With a Letter from Jamesnbsp;Short, M.A. F.R.S. Acad. Reg. Suec. Soc. .....50

Some Account of the Discovery, made by the late Mr. John Dollond, R. S. ivhich led to the grand Improvement of Refracting Telescopes, in order to correct some Misrepresentations, in Foreignnbsp;Publications, of that Discovery: with an Attempt to account for thenbsp;Mistake in an Experiment made by Sir Isaac Newton; on ivhichnbsp;Experiment, the Improvement of the Refracting Telescope intirelynbsp;depended. By Peter Dollond, Member of the American Philosophical Society at Philadelphianbsp;nbsp;nbsp;nbsp;6l

An Attempt to explain a Difficulty in the Theory of Vision, depending on the different Refrangihility of Light. By the Rev. Nevil Maske-lyne, D.D. F.R.S. and Astronomer Royal .nbsp;nbsp;nbsp;nbsp;.nbsp;nbsp;nbsp;nbsp;.nbsp;nbsp;nbsp;nbsp;�nbsp;nbsp;nbsp;nbsp;�nbsp;nbsp;nbsp;nbsp;.nbsp;nbsp;nbsp;nbsp;78

An Account of an Improvement made by Mr. Peter Dollond in his New Telescopes.- In a Letter ?o James Short, M.A. F.R-S. with anbsp;Letter of Mr. Short to the i2ev. Thomas Birch, D.D. Sec.B.S. 8 8

A Letter from Mr. Peter Dollond, to Nevil Maskelyne, F.R.S. and Astronomer Royal; describing some Additions and Alterations madenbsp;to Hadley�s Quadrant, to render it more serviceable at Sea . Q2

Remarks on the Hadley�s Quadrant, tending principally to remove the Difficulties which have hitherto attended the Use of the Back-observa-

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LIFE

JOHN DOLLOND, F.R.S.

In modern times the attention of men has been employed rather in improving what they know than in attempting to make new discoveries. When a man, therefore, has been fortunate enough, bynbsp;extraordinary research, or by a strong effort of genius, to surprisenbsp;the world with a new invention, a lively interest is immediately excitednbsp;in every mind to trace the steps, investigate the means, and collect

every incident which led to the result:�and to the honour of human nature be it said, while curiosity exerts itself in this manner on thenbsp;invention, the inventor is not less the object of regard and consideration; we wish to learn the history, the life, the character of thenbsp;man, and, as far as it is possible, to be acquainted with him. Thenbsp;subject of the following memoir is entitled to this introduction, andnbsp;the public will receive with satisfaction the following account of thenbsp;inventor of the achromatic telescope.

John Dollond, fellow of the Royal Society, was born in Spitalfields, on the tenth day of June in the year 1706: his parents were Frenchnbsp;protestants, and at the time of the revocation of the edict of Nantz,nbsp;which happened in the year 1085, resided in Normandy; hut in whatnbsp;particular part of it is not at present precisely known: M- de Lalandenbsp;does not believe the name to be of French origin; but however this maynbsp;be, the family were compelled soon after this period to seek refuge innbsp;England, in order to avoid persecution and to preserve their religion.

The fate of this family was not a solitary case; fifty thousand persons pursued the same measures, and we may date from this period the rise of several arts and manufactures, which have become highlynbsp;beneficial to this country. An establishment was given to thesenbsp;refugees, by the wise policy of our government, in Spitalfields, andnbsp;particular encouragement granted to the silk manufactory.

The first years of Mr. Dollond�s life were employed at the loom; but, being of a very studious and philosophic turn of mind, his leisurenbsp;hours were engaged in mathematical pursuits; and though by thenbsp;death of his father, which hippened in his infancy, his educationnbsp;gave way to the necessities of I �s family, yet at the age of fifteen,

before he had an opportunity of seeing works of science or elementary treatises, he amused himself by constructing sun-dials, drawing geometrical schemes, and solving problems.

An early marriage and an increasing family afforded him little opportunity of pursuing his favourite studies; but such are the powersnbsp;of the human mind when called into action, that difficulties, whichnbsp;appear to the casual observer insurmountable, yield and retire beforenbsp;perseverance and genius: even under the pressure of a close application to business for the support of his family, he found time, bynbsp;abridging the hours of his rest, to extend his mathematical knowledge,nbsp;and made a considerable proficiency in optics and astronomy, to whichnbsp;he now principally devoted his attention, having in the earlier stagesnbsp;of his life prepared himself for the higher parts of those subjects bynbsp;a perfect knowledge of algebra and geometry.

Soon after this, without abating from the ardour of his other literary pursuits, or relaxing from the labours of his profession, he began to study anatomy, and likewise to read divinity; and finding thenbsp;knowledge of Latin and Greek indispensably necessary towards attaining those ends, he applied himself diligently, and was soon ablenbsp;to translate the Greek Testament into Latin; and as he admired thenbsp;power and the wisdom of the Creator in the mechanism of thenbsp;human frame, so he adored his goodness displayed in his revealednbsp;word.

It might from hence be concluded that his sabbath was devoted to retired reading and philosophical objects; but he was not content withnbsp;private devotion, as he was always an advocate for social worship, andnbsp;with his family regularly attended the public service of the French

protestant church, and occasionally heard Benson and Lardner, whom he respected as men and admired as preachers. In his appearance henbsp;was grave, and the strong lines of his face were marked with deepnbsp;thought and reflection; but in his intercourse with his family andnbsp;friends, he was cheerful and affectionate; and his language and sentiments are distinctly recollected as always making a strong impressionnbsp;on the minds of those with whom he conversed. His memory wasnbsp;extraordinarily retentive, and, amidst the variety of his reading, henbsp;could recollect and quote the most important passages of every booknbsp;which he had at any time perused.

He designed his eldest son, Peter Dollond, for the same business with himself; and for several years they carried on their manufacturesnbsp;together in Spitalfields; but the employment neither suited the expectations nor disposition of the son, who, having received muchnbsp;information upon mathematical and philosophical subjects from thenbsp;instruction of his father, and observing the great value which was setnbsp;upon his father�s knowledge in the theory of optics by professionalnbsp;men, determined to apply that knowledge to the benefit of himselfnbsp;and his family; and accordingly, under the directions of his father,nbsp;commenced optician. Success, though under the most unfavourablenbsp;circumstances, attended every effort; and in the year 1752 John Dollond, embracing the opportunity of pursuing a profession congenialnbsp;with his mind, and without neglecting the rules of prudence towardsnbsp;his family, joined his son, and in consequence of his theoreticalnbsp;knowledge, soon became a proficient in the practical parts of optics.

His first attention was directed to improve the combination of the eye-glasses of refracting telescopes; and having succeeded in his sys-

tern of four eye-glasses, he proceeded one step further, and produced telescopes furnished with five eye-glasses, which considerably surpassednbsp;the former; and of which he gave a particular account in a papernbsp;presented to the Royal Society, and which was read on the 1st ofnbsp;March 1753, and printed in the Philosophical Transactions, vol.nbsp;xlviii. page 108.�See appendix, pp. 17�20.

Soon after this he made a very useful improvement in Mr, Savery�s micrometer: for instead of employing two entire object-glasses, asnbsp;Mr. Savery and M. Bouguer had done, he used only one glass cutnbsp;into two equal parts, one of them sliding or moving laterally by thenbsp;other. This was considered to be a great improvement, as the micrometer could now be applied to the reflecting telescope with muchnbsp;advantage, and which Mr. James Short immediately did. An accountnbsp;of the same was given to the Royal Society, in a paper which wasnbsp;afterwards printed in the Philosophical Transactions, vol. xlviii. pagenbsp;178; and in another paper, part ii. page 55l.-^See Appendix, pp,nbsp;33�49.¹

Mr. Dollond�s celebrity in optics became now universal; and the friendship and protection of the most eminent men of science flatterednbsp;and encouraged his pursuits. To enumerate the persons, both atnbsp;home and abroad, who distinguished him by their correspondence ornbsp;cultivated his acquaintance, however honourable to his memory,nbsp;would only be an empty praise. We cannot, however, forbear men-

This kind of micrometer was afterwards applied by Mr. P, Dollond to the achromatic telescope.�See Appendix, pp. 88�91.

tioning the names of a few persons, who held the highest place in his esteem as men of worth and learning:�Mr. Thomas Simpson,nbsp;master of the Royal Academy at Woolwich; Mr. Harris, assay-master at the Tower, who was at that time engaged in writing andnbsp;publishing his Treatise on Optics; the Rev. Dr. Bradley, then astronomer royal; the Rev. William Ludlam, of St. John�s college, Cambridge; Mr. John Canton, a most ingenious man, and celebratednbsp;not less for his knowledge in natural philosophy, than for his neatnbsp;and accurate manner of making philosophical experiments. To thisnbsp;catalogue of the philosophical names of those days, we must add thatnbsp;of the present astronomer royal, the Rev. Dr. Maskelyne, whosenbsp;labours have so eminently benefited the science of astronomy.

Surrounded by these enlightened men, in a state of mind prepared for the severest investigation of philosophic truths, and in circumstances favourable to liberal inquiry, Mr. Dollond engaged in thenbsp;discussion of a subject, which at that time not only interested thisnbsp;country, but all Europe. Sir Isaac Newton had declared, in his Treatise on Optics, page 112, � That all refracting substances divergednbsp;the prismatic colours in a constant proportion to their mean refraction and drew this conclusion, � that refraction could not benbsp;produced without colour;� and consequently, � that no improvementnbsp;could he expected in the refracting telescope'^ No one doubted thenbsp;accuracy with which Sir Isaac Newton had made the experiment; yetnbsp;some men, particularly M. Euler and others, w'ere of opinion thatnbsp;the conclusion which Newton had drawn from it went too far, andnbsp;maintained that in very small angles refraction might be obtainednbsp;without colour. Mr. Dollond was not of that opinion, but defended

Newton�s doctrine with much learning and ingenuity, as may be seen by a reference to the letters which passed between Euler and Dollondnbsp;upon that occasion, and which were published in the Philosophicalnbsp;Transactions, vol. xlviii. page 287�Appendix, pp. 21�32; andnbsp;contended that, � If the result of the experiment -had been as described by Sir Isaac Newton, there could not be refraction withoutnbsp;colour.�

A mind constituted like Mr. Dollond�s could not remain satisfied with arguing in this manner from an experiment made by another,nbsp;but determined to try it himself, and accordingly, in the year I757jnbsp;began the examination; and, to use his own words, with, quot; a resolutenbsp;perseverance,� continued during that year, and a great part of thenbsp;next, to bestow his whole mind on the subject, until in the monthnbsp;of June 1758 he found, after a complete course of experiment, thenbsp;result to be very different from that which he expected, and from thatnbsp;which Sir Isaac Newton had'related. He discovered � the differencenbsp;in the dispersiori of the colours of light, when the mean rays are equallynbsp;refracted hy different mediums.quot; The discovery was complete, and henbsp;immediately drew from it this practical conclusion, � That the object-glasses of refracting telescopes were capable of being made withoutnbsp;the images formed by them being affected by the different refrangi-bility of the rays of light.� His account of this experiment, and ofnbsp;others connected with it, was given to the Royal Society, and printednbsp;in their Transactions, vol. 1. page 743�see Appeiidix, pp. 50�60;nbsp;and he was presented in the same year, by that learned body, withnbsp;Sir Godfrey Copley�s medal, as a reward of his merit, and a memorialnbsp;of the discovery, though not at that time a member of the society.

This discovery no way affected the points in dispute between Euler and Dollond, respecting the doctrine advanced by Sir Isaac Newton.¹nbsp;A new principle was in a manner found out, which had no part innbsp;their former reasonings, and it was reserved for the accuracy of Dol-lond to have the honour of making a discovery which had eluded thenbsp;observation of the immortal Newton.-I-

This new principle being now established, he was soon able to construct object-glasses, in which the different refrangibility of the rays of light was corrected,, and the name of achromatic given to them bynbsp;the late Dr. Bevis, on account of their being free from the prismaticnbsp;colours. Dr. Hutton, in his Mathematical Dictionary, has said thatnbsp;this name was given to them by M. de Lalande; but that is a mistake.

As usually happens on such occasions, no sooner was the achromatic telescope made public, than the rivalship of foreigners, and the jealousy of philosophers at home, led them to doubt of itsnbsp;reality;, and Euler himself, in his paper read before the Academy ofnbsp;Sciences at Berlin, in the year 1704, says, � I am not ashamednbsp;frankly to avow, that the first accounts, which were published of it,nbsp;appeared so suspicious, and even so contrary to the best establishednbsp;principles, that I could not prevail upon myself to give credit to them;�

�j- The cause of this difference of the results of the 8th experiment of the 2nd part of the first book of Newton�s'Optics, as related by himself, and as it was found whennbsp;tried by Dollond in the years 1757 and 1758, is fully and ingeniously accounted for bynbsp;Mr. Peter Dollond in a paper read at the Royal Society on the 21st of May 1789, andnbsp;afterwards published for J. Johnson in St. Paul�s Church Yard�see Appendix, pp. 6) �nbsp;77; also in button�s Dictionary�Article, Chromatic.

and he adds, � I should never have submitted to the proofs which Mr. Dollond produced to support this strange phenomenon, if M.nbsp;Clairaut, who must at first have been equally surprized at it, had notnbsp;most positively assured me that Dollond�s experiments were but toonbsp;well founded.� And when the fact could no longer be disputed, theynbsp;endeavoured to find a prior inventor, to whom it might be ascribed,nbsp;and several conjecturers were honoured with the title of discoverers.

Mr. Dollond�s improvement in refracting telescopes was of the greatest advantage in astronomy, as they have been applied to fixednbsp;instruments; by which the motions of the heavenly bodies are determined to a much greater exactness than by the means of the old.nbsp;telescope. Navigation has also been much benefited by applying:nbsp;achromatic telescopes to the � Hadley�s sextant:� and from the improved state of the lunar tables, and of that instrument, the longitudenbsp;at sea may now be determined by good observers to a great degree ofnbsp;accuracy; and their universal adoption by the navy and army, as wellnbsp;as by the public in general, is the best proof of the great utility of.nbsp;the discovery.

In the beginning of the year 1761, Mr. Dollond was elected fellow of the Royal Society, and appointed optician to his majesty, but didnbsp;not live to enjoy those honours long; for on the 30th of November,nbsp;in the same year, as he was reading a new publication of M. Clairaut,nbsp;on the theory of the moon, and on which he had been intently engaged for several hours, he was seized with apoplexy, which renderednbsp;him immediately speechless, and occasioned his death in a few hoursnbsp;afterwards. Besides Mr. Peter Dollond, whom we had occasion tonbsp;mention in this memoir, his family, at his death, consisted of three

daughters and a son, who, possessing the name of his father, and we may add, a portion of the family abilities, carried on the opticalnbsp;business in partnership with his elder brother.

Since the last edition of this Life, we have to mention the death of Mr. John Dollond, the partner of his elder brother Mr. Peternbsp;Dollond, which has occasioned the latter to take into partnership hisnbsp;nephew, the son of his eldest sister, Mr. George Huggins, who has,nbsp;by the King�s permission, taken the name of Dollond.

APPENDIX.

A Letter J^rom Mr. John Dollond to Mr. James Short, F.R S. concerning an Improvement ofnbsp;Refracting Telescopes.

SIR,

It is well known, that the perfection of refracting telescopes is very much limited by the aberration of the rays of lightnbsp;from the geometrical focus; which arises from two very different causes;nbsp;that is, from different degrees of refrangibility of light, and from thenbsp;figure of the sphere, which is not of a proper curvature for collectingnbsp;the rays in a single point. The object-glass is chiefly affected by thenbsp;first of these; nor has there been yet any method discovered for rectifying that aberration so, as in the least to remove the indistinctness ofnbsp;the image arising from it. We are therefore reduced to the necessitynbsp;of contracting their apertures, which renders it impossible to magnifynbsp;much without very long glasses.

But the case is widely different with regard to the eye-glasses; for^ though they are very much affected by both the aberrations before-mentioned, yet, by a proper combination of several together, theirnbsp;errors may be in a great measure corrected. If any one, for instance,nbsp;would have the visual angle of a telescope to contain 20 degrees, thenbsp;extreme pencils of the field must be bent or refracted in an angle ofnbsp;10 degrees; which, if it be performed by one eye-glass, will causenbsp;an aberration from the figure, in proportion to the cube of that angle;nbsp;but if two glasses are so proportioned and situated, as that the refraction may be equally divided between them, they will each of themnbsp;produce a refraction equal to half the required angle; and thereforenbsp;the aberration being in proportion to the .cube of half the angle takennbsp;twice over, will be but a fourth part of that, which is in proportionnbsp;to the cube of the whole angle; because twice the cube of one is butnbsp;~ of the cube of two; so the aberration from the figure, where twonbsp;eye-glasses are rightly proportioned, is but a fourth of what mustnbsp;unavoidably be, where the whole is performed by a single eye-glass.nbsp;By the same way of reasoning, when the refraction is divided betweennbsp;three glasses, the aberration will be found to be but the ninth part ofnbsp;what would be produced from a single glass; because three times thenbsp;cube of one is but one ninth of the cube of 3. Whence it appears,nbsp;that, by increasing the number of eye-glasses, the indistinctness,nbsp;which is observed near the borders of the field of a telescope, maynbsp;be very much diminished, though not intirely taken away.

The method of correcting the errors arising from the different refrangibility of light is of a different consideration from the former;nbsp;for, whereas the errors from the figure can only be diminished in a

certain proportion to the number of glasses, in this they may be intirely corrected, by the addition �f only one glass; as we find innbsp;the astronomical telescope, that two eye-glasses, rightly proportioned,nbsp;will cause the edges of objects to appear free from colours quite tonbsp;the borders of the field. Also in the day telescope, .where no morenbsp;than two eye-glasses are absolutely necessary for erecting the object,nbsp;we find, by the addition of a third rightly situated, that the colours,nbsp;which would otherwise confuse the image, are intirely removed :�I saynbsp;intirely removed; but this is to be understood with some limitation;nbsp;for though the different colours, which the extreme pencils mustnbsp;necessarily be divided into by the edges of the eye-glasses, may in thisnbsp;manner be brought to the eye in a direction parallel to each other, sonbsp;as, by the humours thereof, to be converged to a point in the retina;nbsp;yet, if the glasses exceed a certain length, the colours may be spreadnbsp;too wide to be capable of being admitted through the pupil or aperturenbsp;of the eye; which is the reason, that, in long telescopes, constructednbsp;in the common manner, with three eye-glasses, the field is alwaysnbsp;very much contracted.

These considerations. Sir, first set me on contriving, how to enlarge the field by increasing the number of eye-glasses, without any hinderance to the distinctness or brightness of the image : and thoughnbsp;others had been about the same woVk before, yet observing, that thenbsp;five-glass telescopes, sold in the shops, would admit of farther improvement, I endeavoured to construct one with the same number ofnbsp;glasses in a better manner; which so far answered my expectations, asnbsp;to be allowed by such persons, as are the best judges, to be a considerable improvement on the former.

Encouraged by this success, I resolved to try, if possibly I might gain some farther enlargement of the field by the addition of anothernbsp;glass: and by placing and proportioning the glasses in such a manner,nbsp;as to correct the aberrations as much as possible, without anynbsp;detriment to the distinctness, I have obtained as large a field, as isnbsp;convenient or necessary, and that even in the longest telescopes,nbsp;which can be made.

These telescopes with six glasses having been well received, and some of them being gone to foreign parts, it seems a proper time tonbsp;settle the account of its origin; which is one of the motives, that hasnbsp;induced me to trouble you with this short sketch of the considerations,nbsp;that gradually led me to its construction; and I am emboldened. Sir,nbsp;to write thus much, from the many favours I have already received atnbsp;your hands, as well as from a sense of your being a proper person tonbsp;iudge in such cases. And though I am sensible, that you are notnbsp;unacquainted with the theory contained in this letter, yet forasmuchnbsp;as the subject has never been fully treated by any author, I shall endeavour, as soon as may be, to draw up a more particular explanationnbsp;of the aberrations of light by refraction; but shall add no more atnbsp;present, only beg leave to take this opportunity of subscribingnbsp;myself

John Dollond.

Letters relating to a Theorem o/ Mr. Euler, the Royal Academy of' Sciences at Berlin, andnbsp;F.R.S. correcting the Aberrations in thenbsp;Ol^ect-Glasses (f Refracting Telescopes.

There is published, in the Memoirs of the Royal Academy at Berlin, for the year 1747, a theorem by Mr. Euler, innbsp;which he shews a method of making object-glasses of telescopes, innbsp;such a manner, as not to be affected by the aberrations arising fromnbsp;the different refrangibility of the rays of light: these object-glassesnbsp;consisting of two meniscus lenses, with water between them.

Mr. John Dollond, who is an excellent analyst and optician, has examined the said theorem, and has discovered a mistake in it, whichnbsp;arises by assuming an hypothesis contrary to the established principlesnbsp;of optics; and, in consequence of this, Mr. Dollond has sent me

the inclosed letter, which contains the discovery of the said mistake, and a demonstration of it.

In order to act in the most candid manner with Mr. Euler, I have proposed to Mr. Dollond to write to him, shewing him the mistake,nbsp;and desiring to know his reasons for that hypothesis; and therefore Inbsp;desire, that this letter of Mr. Dollond�s to me may be kept amongstnbsp;the Society�s papers, till Mr. Euler has had a sufficient time tonbsp;answer Mr. Dollond�s letter to him.

James Short.

A Letter from Mr. John Dollond to James Short, A. M. F.R.S. concerning a Mistale in M. Euler�s Theorem for correcting thenbsp;Aberrations in the Object-Glasses of Refracting Telescopes.

SIR,

The famous experiments of the prism, first tried by Sir Isaac Newton, sufficiently convinced that great man, that thenbsp;perfection of telescopes was impeded by the different refrangibility ofnbsp;the rays of light, and not by the spherical figure of the glasses, asnbsp;the common notion had been till that time; which put the philosopher upon grinding concave metals, in order to come at that hynbsp;reflection, which he despaired of obtaining by refraction. For, thatnbsp;he was satisfied of the impossibility of correcting that aberration by anbsp;multiplicity of refractions, appears by his own words, in his Treatisenbsp;of Light and Colours, Booh I. Part 2. Prop. 3.nbsp;nbsp;nbsp;nbsp;� I found more-

over, that when light goes out of air through several contiguous mediums, as through water and glass, as often as by contrary

refractions it is so corrected, that it emergeth in lines parallel to � those in which it was incident, continues ever -after to be white.nbsp;� But if the emergent rays be inclined to the incident, the w�hitenessnbsp;� of the emerging light will by degrees, in passing on from the placenbsp;� of emergence, become tinged in its edges with colours.�

It is therefore. Sir, somewhat strange, that any body now-a-days should attempt to do that, which so long ago has been demonstratednbsp;impossible. But, as so great a mathematician as Mr. Euler has latelynbsp;published a theorem ¹ for making object-glasses, that should be freenbsp;from the aberration arising from the different refrangibility of light,nbsp;the subject deserves a particular consideration. I have therefore carefully examined every step of his algebraic reasoning, which I havenbsp;found strictly true in every part. But a certain hypothesis in pagenbsp;285, appears to be destitute of support either from reason or experiment, though it be there laid down as the foundation of the wholenbsp;fabriek. This gentleman puts ra: 1 for the ratio of refraction out ofnbsp;air into glass of the mean refrangible rays, and M:1 for that of thenbsp;least refrangible. Also for the ratio of refraction out of air intonbsp;water of the mean refrangible rays he puts n:l, and for the leastnbsp;refrangible A^:l. As to the numbers, he makes 7n=%^,nbsp;and n=-y; which so far answer well enough to experiments. Butnbsp;the difficulty consists in finding the value of A^ in a true proportionnbsp;to the rest.

which is, that m is the same power of M, as n is of N; and therefore puts n=.m^, and N=M�'. Whereas, by all the experiments that havenbsp;hitherto been made, the proportion will come out thus, 7n�l:nbsp;n�i::m�M\n�N.

The letters fixed upon by Mr. Euler tb represent the radii of the four refracting surfaces of his compound object-glass, are � g h and k,nbsp;and the-distance, of the object he expresses by a; then will the focal

it is evident, that the different refrangibility of the rays w'ould make no alteration, either in the place of the image, dr in its magnitude,nbsp;if it were possible to determine the radii of the four surfaces, so as tonbsp;havenbsp;nbsp;nbsp;nbsp;=nbsp;nbsp;nbsp;nbsp;And

this. Sir, I shall readily grant. But when the surfaces are thus proportioned, the sum of the refractions will be=0; that is to say,nbsp;the emergent rays will be parallel to the incident. For, if n (-v�f)

�7 i�i)? then w�A(j-�f)-i-m�Mif�y i'�i-) = 0. Also if n�N�.m-^M: \n � \:m�1, then 1(7�(j�L�f) = 0; or otherwisenbsp; 1�1)�� i=0; which reduces the denominator of the fractionnbsp;expressing the focal distance to f Whence the focal distance will benbsp;= a; or, in other words, the image will be the object itself. And as,nbsp;in this case, there will be no refraction, it will be easy to conceivenbsp;how there should be no aberration.

And now. Sir, I think I have demonstrated, that Mr. Euler�s theorem is intirely founded upon a new law of refraction of his own;nbsp;but that, according to the laws discovered by experiment, the

VOUS m�avez fait un tres sensible plaisir, en ayant dispos� M. Dollond de remettre la proposition de ses objectionsnbsp;contre mes verres objectifs, jusqu��, ce que j�y aurois repondu, etjenbsp;voLis en suis infiniment oblig�. Je prend done la libert� de vousnbsp;addresser ma reponse a lui, en vous priant, apr�s I�avoir daign�e denbsp;votre examen, de la vouloir bien lui remettre: et en cas que vousnbsp;jugiez cette matiere digne de I�attention de la Societ� Royale, je vousnbsp;prierois de lui communiquer les preuves detaill�es de ma theorie, quenbsp;j�ai expos�e dans'cette lettre. Cependant j�espere, que M. Dollond ennbsp;sera satisfait, puisque je tombe d�accord avec lui du peu de succes,nbsp;qu�on sauroit se promettre de mes objectifs, en les travaillant selon lanbsp;maniere ordinaire.

L. Euler.

Etant tres sensible a I�honneur que vous me faites, au sujet des verres objectifs, que j�avois propos�, j�ai celui de vousnbsp;marquer d�abord ingenument, que j�ai rencontre aussi ici le plusnbsp;grands obstacles dans I�execution de ce dessein, vu qu il s�agit denbsp;quatre faces, qui doivent etre travaill�e exactement selon les proportions que j�avois trouv�es; cependant ayant fait les experiences surnbsp;quelquesuns, qui parurent le mieux reussi,- nous avons trouv�, quenbsp;1�intervalle entre les deux foyers des rayons rouges et violets etoitnbsp;beaucoup plus petit, qu�il ne seroit d�un verre simple de la memenbsp;distance focale. Neantmoins je dois avoiier, qu�un tel verre, quandnbsp;m�me il bien seroit parfaitement execut� sur mes principes, auroitnbsp;d�autres defauts, qui le mettroient au dessous m�me des verres ordi-naires; eest qu�un tel verre n�admet qu�un tres petite ouverture ennbsp;consequence des grandes courbures, qu�on doit donner aux faces in-terieures: � desorte que lorsqu�on donne une ouverture ordinaire,nbsp;l�image devient tres confus.

Ainsi puisque vous vous etes donn� la peine, Monsieur, d�executer de tels verres, en en faisant des experiences¹, je vous prie de biennbsp;distinguer les defauts, qui peuvent naitre de la diverse refrangibilit�nbsp;des rayons, de ceux, qui viennent d�une trop grande ouverture: pournbsp;cet effet vous n�aurez qu�a laisser une tres petite ouverture.

Or si ma theorie etoit juste, dont j�aurai bientot I�honneur de parler, il seroit moyen de remedier a ce defaut; il faudroit renoncer �nbsp;la figure spherique qu�on donne ordinairement aux faces des verres, etnbsp;tacher de leur donner une autre figure, et j�ai remarqu� que la figurenbsp;d�urie parabole leur procureroit I�avantage, qu�ils admettroieut unenbsp;ouverture tres considerable. Notre savant M. Lieberkuhn s�est appli-qu� a travailler des verres dont la courbure des faces d�croit depuis lenbsp;milieu vers le bords, et il s�en est aperqu de tres grands avantages.nbsp;Par ces raisons je crois, que ma theorie ne soulfire encore rien de cenbsp;cot�.

Pour la theorie, je conviens avec vous, monsieur, que posaqt la raport de refraction d�un milieu dans un autre quelconque pour lesnbsp;rayons moyens comme m �, 1, et pour les rayons rouges comme Mk \,nbsp;la raison de m�M a m�1 sera toujours si a peu pr�s constant,nbsp;qu�elle satisfera a toutes les experiences, comme la grand Newton anbsp;remarqu�. Cette raison ne differe non plus de ma theorie quenbsp;presque imperceptiblement: car puisque je soutiens que M=m��, etnbsp;que m differe ordinairement fort peu de l�unit�, soit m=l �t et

Mr. Dolloncl, in his letter to Mr. Euler, here referred to, does not say that he had made any trials himself, but only he had understood that such had been made by others,nbsp;without success.

a peu pres, j�aurai nbsp;nbsp;nbsp;(i~^) quot;3nbsp;nbsp;nbsp;nbsp;7�-l = u, clone

sera=l�a, ou fort � peu pres constante, Del� je

m-� 1 conclud, que les experiences d�ou le grand Newton a tire son raport,nbsp;ne sauroient etre contraires k ma theorie.

etoit juste a la rigueur, il n�y auroit plus moyen de remedier au defaut qui resulte de la diverse refrangibilit� des rayons, de quelquenbsp;maniere qu�on disposeroit divers milieux transparens, et qne I�intervallenbsp;entre les divers foyers tiendroit touj ours un raport constant a la distance focale entiere du verre. Mais e�est precisement cette consideration, qui me fournit le plus fort argument: I�oeil me paroit unenbsp;telle machine dioptrique parfaite, qui ne se ressent en aucune manierenbsp;de la diverse refrangibilit� des rayons: quelque petite que soit sanbsp;distance focale, la sensibilit� est si grande, que les divers foyers, s�il ynbsp;,en avoit, ne manqueroient pas de troubler tres considerablement lanbsp;vision. Or il est bien certain, qu�un oeil bien constitue ne sent pointnbsp;I�efFet de la diverse refrangibilit�.

La structure merveilleux de I�oeil, et les diverses.humeurs, dont il est compos�, me confirme infiniment dans ce sentiment. Car s�ilnbsp;s�agissoit seulement de produire une representation sur le fond denbsp;I�oeil, une seule humeur auroit �t� sufEsante; et le Createur n�y auroitnbsp;pas surement employ� plusieurs, Dela je conclud, qu�il est pos�iblenbsp;d� an�antir I�efFet de la diverse refrangibilit� des rayons par une juste

gueur, j�en tire la consequence qu�elle n�est pas parfaiteinent conforme a la nature.

Mais voila une preuve directe de ma these; je conqois diverse milieuz transparens. A, B, C, D, E, qui different entreux �gale-ment par raport � leur densit� optique: desorte que la raison denbsp;refraction de chacun dans le suivant soit le meme. Soit done dans lenbsp;passage du premier dans le second la raison de refraction pour lesnbsp;rayons rouges=7-; 1, et pour les viotets=?;: 1; qui sera la meme dansnbsp;le passage du second dans le troisieme, de celuicy dans le quatrieme,nbsp;du quatrieme dans le cinquieme, et ainsi de suite. Dela il est clair,nbsp;que dans le passage du premier dans le troisieme sera= 7'^: 1 pour lesnbsp;rayons rougeSj et=7;2; i pour les violets: de meme dans le passage dunbsp;premier dans le quatrieme les raisons seront : 1 et t;� : 1.

Done si dans le passage dans un milieu quelconque la raison de refraction des rayons rouges est=r�:l, celle des rayons violets seranbsp;tout cela est parfaitement conforme aux principes du grandnbsp;Newton. Posons r^=R, etvquot;�V, desorte que , et expri-ment les raisons de refraction des rayons rouges et violets dans unnbsp;passage quelconque: et ayant nlr=lR etnlv=l Enous aurons /nbsp;nbsp;nbsp;nbsp;;

IV I V

A Description of a Contrivance Jor measuring small Angles, hy Mr. John Dollond; communicated by Mr. J. Short, F.R S.

Let an object-glass of any convenient focal length (being truly ground and well centred) be divided into two equal parts or segments,nbsp;by cutting it straight through the center; and let a piece of machinerynbsp;be so contrived, as to hold these two segments in the same position tonbsp;each other, as they stood in before they w'ere cut asunder; and to benbsp;capable at the same time of drawing them to different distances fromnbsp;that position, in the manner as is represented in the figure.

Each of these segments will form a distinct image of any object to which they are directed; differing in nothing from that, whichnbsp;might have been made by the whole glass before it was cut, except innbsp;brightness. And while these segments are held in their original position, the images will coincide, and become one single image as atnbsp;first; but, in proportion as they are drawn off from that situation, thenbsp;images will separate more or less, according to the distance they arenbsp;drawn to. By this means the images of two different objects, or ofnbsp;different parts of the same object, not very far from each other, may

34 A Description of a Contrivance for Measuring small Angles', be brought to a contact or coincidence at the focus; and this coincidence may be viewed to a very great nicety with a proper eye-glass.

The measure of the angle subtended by the two objects, whose images are thus brought to a coincidence, depends upon three things;nbsp;first, a careful observation of the coincidence of the images:�nbsp;secondly, an exact measure of the distance, which the glasses are drawnnbsp;out to from that situation, which makes the image single:�and,nbsp;lastly, a true knowledge of the focal distance of the glass. How thenbsp;angle is to be found from these measures, and how it may likewisenbsp;be come at, by viewing two land-objects at a convenient distance,nbsp;will be shewn hereafter in the explanation of the figure. It is easynbsp;to understand, in the meantime,* that the angle will be measured withnbsp;more accuracy, in proportion to the length of the glass, which is usednbsp;for that purpose; but the difficulty of managing long telescopes is nonbsp;less apparent. Therefore the most practicable method of using thisnbsp;micrometer to advantage, is, to apply the divided object-glass to thenbsp;object end of a reflecting telescope: for, as the apertures of thesenbsp;sort of telescopes are large in proportion to their lengths, they willnbsp;admit of very long glasses; nor will the measures be any way affectednbsp;by the metals or glasses, which the reflector is composed of: and thenbsp;angles will be found in the same manner, as though the images werenbsp;viewed with a single eye-glass, in the manner of a common refractingnbsp;astronomical telescope; but with this advantage, that, as the imagesnbsp;will be exhibited larger and distincter by the refleeting telescope;nbsp;and as every part thereof wdll be much more manageable than a longnbsp;refracting telescope; so the contact or coincidence of the images willnbsp;be more accurately observed.

It would be however unnecessary now, as well as improper, to say much about the advantages of this method above those which have hitherto been put in practice;nbsp;because, as a machine is now making for this purpose,nbsp;the experiments, which will shortly be tried, will be morenbsp;convincing, as well as more Intelligible, than any thingnbsp;that might be offered at present.

The two semicircles represent the two segments of the ubject-glass, whose centers C and D are drawn off to thenbsp;distance CD, and the points A and B are two objects, ornbsp;different parts of the same object; therefore the linesnbsp;ACG and B DG represent two rays that pass throughnbsp;the centres or poles of the segments, and are thereforenbsp;not at all refracted, but go straight through to G, where theynbsp;intersect; and G being the respective focus to the distancenbsp;of the objects from the glass, the two images will coincidenbsp;at that point. It appears from the figure, that AB: CD: ;nbsp;GH:GE; and from a common proportion in optics, GH:nbsp;GE:: HE: EF. Therefore, AB: CD:: HE :EF; F beino-the focus of parallel rays; and consequently the anglesnbsp;AEB and CFD are equal. That is, the angle subtendednbsp;by the distance of the centres of the segments from thenbsp;distance of the focus of parallel rays is equal to the anglenbsp;subtended by the distance between the objects A and Bnbsp;from the end of the telescope.

An JEa'planation of an Instrument Jhr measuring small Angles^ the first Account of which teasnbsp;read h^ore the Royal Society, May 10, 1753,nbsp;By Mr. John Dollond. In a Letter to Jamesnbsp;Short, M.A. and F.R.S,

SIR,

The account which I gave you, some time ago, of a new micrometer, was contained in as few words as possible; beingnbsp;rather desirous, that experiments might be made, before I said muchnbsp;concerning it;�but since your many repeated experiments have confirmed what was expected from it, I have endeavoured to draw up anbsp;more full account of this instrument, with demonstrations of thenbsp;principles which it is founded upon, which I here send you enclosed,nbsp;and which you may lay before the Royal Society, if you think proper.

John Dollond.

Before i enter upon particulars relating to this micrometer, it will be proper to make a few preparatory observations on the nature ofnbsp;spherical glasses, so far as may be necessary to render the followingnbsp;explanation more easily understood.

Observation I.�It is a property of all convex spherical glasses to refract the rays of light, which are transmitted through them, in suchnbsp;a manner, as to collect all those that proceed diverging from any onenbsp;point of a luminous object, to some other point; whose distance fromnbsp;the glass depends chiefly on its convexity, and the distance of thenbsp;object from it.

Observation II.�^The point, where the rays are thus collected, may be considered as the image of that point, from which they diverge.nbsp;For if we conceive several radiant points thus emitting rays, which,nbsp;by the refractive quality of the glass, are made to converge to as manynbsp;other points, it will be an easy matter to understand, how every partnbsp;of the object will be truly represented. As this property of sphericalnbsp;glasses is explained and demonstrated by all the writers on optics, itnbsp;being the very foundation of the science, the bare mention of it isnbsp;sufficient for the present purpose.

Observation III.�It will be necessary, however, to observe farther, that the lines connecting every point in the object, with its corresponding ones in the image, do all intersect in a certain point of thenbsp;axis or line passing through the poles of the glass, where its two

38 Explanation of an Instrument for Measuring Small Angles, S^c surfaces are parallel, and may be properly called its centre:- whence itnbsp;appears, that the angles subtended by the object and its image fromnbsp;that point, must be equal: and therefore their diameters will be in thenbsp;same ratio, as their distances from that point.

Observation IV.�As the formation of the image by the glass depends entirely on the property above-mentioned, that is to say, its collectingnbsp;all the light, that is incident on it, from the several points of thenbsp;object into as many other points at its focus; it follows, that any segment of such a glass will also form an image equal, and every waynbsp;similar, to that exhibited by the whole glass; with this difference only,nbsp;that it will be so much darker, as the area of the segment is less thannbsp;that of the whole glass.

Observation V.�The axis of a spherical glass in a line connecting the centres of the spheres, to which the two surfaces are ground; andnbsp;wherever this line passes through the glass, there the surfaces arenbsp;parallel. But if it happens, that this line does not go through thenbsp;substance of the glass, such a glass is said to have no internal centre;nbsp;but it is conceived to be in its plane produced, till it meets the axis:nbsp;and this imaginary point, though external to the glass, is as truly itsnbsp;centre, and is as fixed in its position to it, as if it were actually withinnbsp;its substance.

Observation VI.�If a spherical glass, having its centre or pole near its middle or centre of its circumference, should be divided by anbsp;straight line through the middle; the centre will be in one of the segments only. For how exact soever a person may be supposed to benbsp;in cutting it through the centre; yet �tis hard to conceive, how a mathematical point should be divided in two: therefore the centre will

be internal to one of the segments, and external to the other. But if a small matter be ground away from the straight edge of each segment, both their centres will become external; and so they will morenbsp;easily be brought to a coincidence.

Observation VII.�If these two segments should be held together, so as to make their centres doincide; the images, which they give ofnbsp;any object, will likewise coincide, and become a single one. Thisnbsp;will be the case, when their straight edges are joined to make the glass,nbsp;as it were, whole again; hut let the centres be any-how separated,nbsp;their images will also separate, and each segment give a separate andnbsp;distinct image of any object, to which they may be exposed.

Observation VIW.�^Though the centres of the segments may be drawn from their 'coincidence, by removing the segments in anynbsp;direction whatever; yet the most convenient way for this purpose is,nbsp;to slide their straight edges one along the other, till theynbsp;are removed, as the figure in the margin representsnbsp;them: for thus they may be moved without sufferingnbsp;any false light to come in between them. And by thisnbsp;w'ay of removing them, the distance between their centres may be very conveniently measured; viz. by having a Vernier�snbsp;division, commonly, though falsely, called a Nonnius�s, fixed to thenbsp;brass-work, that holds one segment, so ak to slide along a scale onnbsp;the plate, to which the other part of the glass is fitted.

Observation IX.�As the images of the same object are separated by the motion of the segments, so those of different objects, or different parts of the same object, may be made to coincide. Supposenbsp;the sun, moon, or any planet, to be the object; the two images

thereof may, by this contrivance, be removed, till their opposite edges are in contact; in which case, the distance between the centresnbsp;of the two images will be equal to the diameter of either; and so ofnbsp;any other object whatever.

Observation X.�This divided glass may be used, as a micrometer, three different ways. In the first place, it may be fixed at the end ofnbsp;a tube, of a suitable length to its focal distance, as an object-glass;nbsp;the other end of the tube having an eye-glass fitted as usual in astronomical telescopes. Secondly, it may be applied to the end of a tubenbsp;much shorter than its focal distance, by having another convex glassnbsp;within the tube, to shorten the focal distance of that, which is cutnbsp;in two. Lastly, it may be applied to the open end of a reflectingnbsp;telescope; either of the Newtonian, Gregorian, or Cassegrain construction. And though this last method is much the best, and mostnbsp;convenient, of the three; yet, as the first is the most natural, as wellnbsp;as the easiest to be understood, it will be proper to explain it fully,nbsp;and to demonstrate the principles, on which this micrometer is constructed, by supposing it made use of in the first way:�which beingnbsp;done, the application of it to other methods will be readily understood.

Having thus, by the foregoing observations, given a general idea of the nature and effects of this divided object-glass, I shall proceed tonbsp;demonsti'ate the principles, from whence the measures of the anglesnbsp;are to be obtained by this instrument; which will be done by thenbsp;following propositions.

Suppose a divided object-glass Jixed at the end of a tube, XT according to the first method, and the tube directed tonbsp;the object intended to he measured; and suppose, likewise, the segments removed from their original position,nbsp;in the manner directed under Observation VIII. till thenbsp;opposite edges of the two images are seen in contact atnbsp;the focus of the eye-glass: then, I say, the angle subtended, by the distance between the centres of the segments, from the focus of the eye-glass, where the edgesnbsp;are seen in contact, is equal to the angle subtended bynbsp;the diameter of the object from that same point.

Let the line A B represent the diameter of the object to be measured; and the points CD the centres of thenbsp;two glass segments: also G the focus where the imagesnbsp;of the extremities of the object are coincident. It isnbsp;evident, from Observation III. that ^ G and B G arenbsp;straight lines, that pass through the centres of the segments, and connect the extreme points of the objectnbsp;with their corresponding points in the images; andnbsp;therefore, as the diameter of the object and the distancenbsp;between the centres of the segments are both inscribednbsp;between these two lines, they must needs subtend the

The focal distance C G, or D G, is variable, according to the distance of the object from the glass: so that it decreases as the distance of the object from the glass increases; and when the object is so farnbsp;off, that the focal length of the glass bears no proportion to its distance; then will it be least of all, as C F or D F; and the pointnbsp;F is called the focus of parallel rays. Any other focus, as G, beingnbsp;the focus^of a near object, is called a respective focus; as it respects anbsp;particular distance: but the focus of parallel rays respects all objectsnbsp;that are at a very great distance; such as is that of all the heavenlynbsp;bodies.

The distance H E q/* the object from the glass is m E F, the focal distance of parallel rays, as the distance HG of the object from its image is to EG, the distance of the image from the glass: that is,

The demonstration of this proposition may be gathered from any treatise of dioptrics; it being a general rule for finding the respectivenbsp;focus to any given distance, when the focus of parallel rays is known.

le subtended by the diameter of the object, from the glass, is equal to that subtended, by the opening of the centres of the segments,nbsp;from the focus of parallel rays. That is, the angle A E B equal to

Then, as the two last terms of these two analogies are alike; the two first terms of one will be in the same proportion as the two firstnbsp;terms of the other; which gives the following proportion: AB: CD::nbsp;HE : EF. Whence the truth of the proposition is evident.

From this proposition it appears, that the angle subtended by the diameter of the object from the glass, is found without any regard tonbsp;the distance of the object, or to the distance of the respective focus,nbsp;where the image is seen; as the measure depends intirely upon thenbsp;focus of parallel rays and the opening of the segments. We maynbsp;likewise, from hence, derive a rule for the quantity of the angle,nbsp;without considering the length of the glass. Let an objeet, whosenbsp;diameter is known, be set up at some known distance; the angle itnbsp;will subtend from the glass may then be found by trigonometry; thennbsp;let it be measured by this micrometer, and the distance, between thenbsp;centres of the segments, found on the scale already mentioned, willnbsp;be the constant measure of the same angle, in all other cases: becausenbsp;the distance of the object makes no alteration in the measure of thenbsp;angle, as has been demonstrated: and thus having obtained the distance between the centres of the segments, which answers to any onenbsp;angle, all other distances may be computed by the rule of three.

All that has been hitherto said relates to the first method of using this micrometer; that is, by fitting it to the end of a tube suited tonbsp;its focal length, and by viewing the images with a proper eye-glass, innbsp;the manner of an astronomical telescope. But the length of the

44 Explanation of an Instrument for Measuring Small Angles, S^c, tube, in this way, would be very troublesome; and therefore it will benbsp;proper to consider other methods, for an easier management. I shall,nbsp;therefore, proceed to the second method, mentioned in Observation X.nbsp;which is, by using another object glass to shorten the focus of thatnbsp;which serves for the micrometer. To facilitate the understanding ofnbsp;this method; it will be necessary to premise the following observation.

Observation XI.�Rays of light, which are brought to such con-vergency as to form the image of an object, proceed, after that, diverging, in the manner they did when they issued from the objectnbsp;before they were transmitted through the glass; and therefore theynbsp;may be again collected by another spherical glass, so as to form anbsp;second representation of the same object; which may again be repeatednbsp;by a third glass, ^c. So that the first image may be considered as annbsp;object to the second glass, and the second image will be an object tonbsp;the third, and so on. Though these images may be very different,nbsp;in respect to their magnitudes, yet they will be all similar; being truenbsp;representations of the same object: this will hold good, though thenbsp;second glass should be put so near the first as to receive the rays before the image is formed: for as the rays are tending to meet at anbsp;certain distance, the second will receive them in that degree of con-vergency, and, by an additional refraction, bring them to ^ nearernbsp;focus; but the image will still be similar to that which would have beennbsp;made by the first glass, if the second had not been there.

Upon this principle all refracting telescopes are made; some of which are a combination of four, five, or six glasses. The first glassnbsp;forms an image of the object; the second repeats the image, whichnbsp;it receives from the first; and so on, till the last glass brings a true

representation of the object to the eye. The same may he said of reflecting telescopes: for a spherical mirror acts in the same manner, in that respect, as a spherical glass.

Now let this be applied to the subject in hand. Suppose the focal distance of the divided object-glass to be about forty feet; and supposenbsp;the segments to be opened wide enough to bring the opposite edgesnbsp;of an object in contact: then let another object-glass, uncut, be fixednbsp;within the tube, of a proper degree of convexity, to shorten the focusnbsp;of the other as much as may be required; suppose to twelve feet: bynbsp;what has been just now observed, this glass will represent the twonbsp;images in the same form which would have been exhibited by thenbsp;divided glass, if this other glass had not been there. For though thenbsp;images are not yet formed, when the second glass receives the rays:nbsp;yet, as those rays are converging towards it, the second glass mustnbsp;represent those images in the same position, and form, as the tendency of the rays requires. For while the segments are fixed in theirnbsp;position to each other, their images will also be fixed in their position;nbsp;and let them be repeated ever so. many times, by refraction throughnbsp;spherical glasses, or by reflection from spherical mirrors, they cannbsp;suffer no alteration in their position, to one another. By this means,nbsp;the telescope may be shortened, at pleasure, though the scale for thenbsp;measure of the angles will remain the same. The only inconvenience,nbsp;which the shortness of the telescope introduces, is a want of sufficientnbsp;distinctness; which will so far hinder the exactness of the observation,nbsp;as the contact of the edges cannot be so accurately determined, asnbsp;they might be with longer telescopes.

end of a reflecting telescope: for the reflections and refractions, which the rays must undergo in passing through the telescope, will no waynbsp;alter the position of the images, which the rays, that have passednbsp;through the segments, are tending to: for, as has been already observed, a number of reflections and refractions may repeat the images,nbsp;and alter their magnitudes; but can make no alteration in theirnbsp;proportions.

Therefore this way of fixing the divided glass to a reflecting telescope, which was the third method proposed, is, by far, the best; as such telescopes of moderate and manageable lengths, when well made,nbsp;are capable of magnifying considerably, and shewing objects to greatnbsp;advantage. This micrometer being applicable to the reflecting telescope, with so much certainty, is no inconsiderable advantage; fornbsp;any one will easily understand, that, to measure the diameter of anbsp;planet exactly, it is necessary, that the planet be magnifietl, andnbsp;shown distinctly, which could not be obtained, in the common way,nbsp;without very great lengths; such as rendered it very diffieuU, not tonbsp;say impracticable, to take exact measures. Besides, the common micrometer is limited, in this respect, upon another account; viz. becausenbsp;the diameter of the planet cannot be measured, vvithout having thenbsp;whole planet within the field of the telescope, which confines the magnifying power witliin very narrow bounds; whereas, by this method,nbsp;nothing more is required, than to see the contact of the edges, whichnbsp;allows the magnifying power to be increased at pleasure.

In the common micrometer, the object is to be taken between two wires, so that the contact of its edges with those wires cannot benbsp;observed at one view; and the least motion of the telescope, whilst

the observer is turning his eye from one wire to the other, must oblige him to repeat the observation; whereas, by this method, the contactnbsp;of the edges of the images is not at all affected by the motion of thenbsp;telescope. Whence the comparison of this micrometer with thenbsp;common sort, in this respect, stands thus: the one requires greatnbsp;steadiness in the telescope, but yet it is applicable to none, but suchnbsp;as are very difficult to keep steady; the other does not require suchnbsp;steadiness, though it is applicable to short telescopes, which are easilynbsp;managed.

These advantages not only add to the certainty of the observation, but assist vastly in the expedition; for an observer may make twentynbsp;observations, in this way, where he could scarcely, with much fatigue,nbsp;be sure of one with the�common micrometer. Expedition in makingnbsp;observations, must be allowed a very great advantage, in this climate,nbsp;where the uncertainty of the weather renders astronomical observationsnbsp;so precarious, that nd opportunities, even the most transient, shouldnbsp;be let slip. An instance of this was given to the Royal Society, in annbsp;account of the eclipse of the sun last October.

As the motion of the telescope gives the observer no great inconvenience, iu this method; neither does the motion of the object at all disturb his observation (I mean such a motion, as that of the heavensnbsp;is.) This gives him leave to take the diameter of a planet, in anynbsp;direction; or the distance between two stars or planets, let theirnbsp;situation be how it will; in which respect the common micrometer isnbsp;absolutely defective; as it can give no angles, but such as are perpendicular to the line of their motion; though the diameters of thenbsp;planets, in other directions, are very much wanted; it being highly

probable, from the laws of motion, and what we see in Jupiter, that such planets, as revolve round their axes, have their polar diametersnbsp;shorter than their equatorial ones.

The distances of Jupiter�s satellites from one another, or from Jupiter�s body, cannot be measured, with any certainty, in the common way, as their position is always very far from being at right anglesnbsp;wdth the line of their motion: neither can the moon�s diameter, whichnbsp;must be taken from horn to horn, scarce ever be obtained that way,nbsp;because it very rarely happens, that the diameter, to be measured, liesnbsp;at right angles to the line of her motion. The same may be said ofnbsp;the distance between two stars. But this micrometer gives angles, innbsp;every direction, with equal ease and certainty; the observation beingnbsp;also finished in an instant, without any trouble or fatigue to the observer. For as there are no wires made use of, this way, in the fieldnbsp;of the telescope, so the observer has no concern about any illumination.nbsp;The largeness of the scale deserves also to be taken notice o^ as itnbsp;may, in this micrometer, be increased almost at pleasure, accordingnbsp;as the smallness of the object requires. Another inconveniencenbsp;attending the common micrometer is, the variation of the scale, according to the distance of the object. As the telescope must benbsp;lengthened, or drawn out farther, for short distances ; the scale, whichnbsp;depends upon that length, is thereby increased; which renders thenbsp;measure of the angle very uncertain: whereas, in this micrometer, thenbsp;scale is the same at all distances; so that the angle may be measurednbsp;with the utmost certainty, without any regard to the distance of thenbsp;object.

An Account �� some Experiments concerning tJw different Rffrangibility of Light. Ey Mr. Johnnbsp;Dollond. With a Letter ffrom James Short,nbsp;M.A. F. R. S. Acad. Reg. Suec. Soc.

I HAVE received the enclosed paper from Mr. Dollond, which he desires may be laid before the Royal Society. Itnbsp;contains the theory of correcting the errors arising from the differentnbsp;#efrangibility of the rays of light in the object-glasses of refractingnbsp;telescopes; and I have found, upon examination, that telescopes madenbsp;according to this theory are intirely free from colours, and are as distinct as reflecting telescopes.

James Short.

It is well known, that a ray of light, refracted by passing through mediums of different densities, is at the same time proportionallynbsp;divided or spread into a number of parts, commonly called homogenealnbsp;rays, each of a different colour; and that these, after refraction, proceed diverging; a proof, that they are differently refracted, and thatnbsp;light consists of parts that differ in degrees of refrangihility.

Every ray of light passing from a rarer into a denser medium, is refracted towards the perpendicular; but from a denser into a rarernbsp;one, from the perpendicular; and the sines of the angles of incidencenbsp;and refraction are in a given ratio. But light consisting of parts, whichnbsp;are differently refrangible, each part of an original or compound raynbsp;has a ratio peculiar to itself; and therefore the more a heterogeneousnbsp;ray is refracted, the more will the colours diverge, since the ratios ofnbsp;the sines of the homogeneal rays are constant; and equal refractionsnbsp;produce equal divergencies.

That this is the case when light is refracted by one given medium only, as suppose any particular sort of glass, is out of all dispute, beingnbsp;indeed self-evident; but that the divergency of the colours will be thenbsp;same under equal refractions, whatsoever mediums the light may benbsp;refracted by, though generally supposed, does not appear quite sonbsp;clearly.

However, as no medium is known, which will refract light without diverging the colours, and as difference of refrangihility seems thence

to be a property inherent in light itself, opticians have, upon that consideration, concluded, that equal refractions must produce equalnbsp;divergencies in every sort of medium: whence it should also follow,nbsp;that equal and contrary refractions must not only destroy each other,nbsp;but that the divergency of the colours from one refraction wouldnbsp;likewise be corrected by the other; and there could be no possibilitynbsp;of producing any such thing as refraction, which would not be affectednbsp;by the different refrangihility of light; or, in other words, that however a ray of light might be refracted backwards and forwards bynbsp;different mediums, as water, glass, S^c. provided it was so done, thatnbsp;the emergent ray should be parallel to the incident one, it would evernbsp;after be white; and conversely, if it should come out inclined to thenbsp;incident, it would diverge, and ever after be coloured. From whencenbsp;it was natural to infer, that all spherical object-glasses of telescopesnbsp;must be equally affected by the different refrangihility of light, innbsp;proportion to their apertures, whatever material they may be formednbsp;of.

But it seems w�orthy of consideration, that notwithstanding this notion has been generally adopted as an incontestable truth, yet itnbsp;does not seem to have been hitherto so confirmed by evident experiments, as the nature of so important a matter justly demands; andnbsp;this it was that determined me to attempt putting the thing to issuenbsp;by the following experiment.

I cemented together two plates of parallel glass at their edges, e� as to form a prismatic or wedge-like vessel, when stopped at the endsnbsp;or bases; and its edge being turned downwards, I placed therein anbsp;glass prism with one of its edges upwards, and filled up the vacancy

.with clear water: thus the refraction of the prism was contrived to be contrary to that of the water, so that a ray of light transmittednbsp;through both these refracting mediums would be refracted by thenbsp;difference only between the two refractions. Wherefore, as I foundnbsp;the water to refract more or less than the glass prism, I diminishednbsp;or increased the angle between the glass plates, till I found the twonbsp;contrary refractions to be equal; which I discovered by viewing annbsp;object through this double prism; which, when it appeared neithernbsp;raised nor depressed, I was satisfied, that the refractions were equal,nbsp;and that the emergent rays were parallel to the incident.

Now, according to the prevailing opinion, the object should have appeared through this double prism quite of its natural colour; for ifnbsp;the difference of refrangibility had been equal in the two equal refractions, they would have rectified each other: but the experimentnbsp;fully proved the fallacy of this received opinion, by showing the divergency of the light by the prism to be almost double of that by thenbsp;water; for the object, though not at all refracted, w^as yet as muchnbsp;infected with prismatic colours, as if it had been seen through a glassnbsp;wedge only, whose refracting angle was near 30 degrees.

iV.-fi. This experiment will be readily perceived to be the same as that which Sir Isaac Newton mentions¹; but how it comes tonbsp;differ so very remarkably in the result, I shall not take upon menbsp;to account for; but will only add, that I used all possible pre-

caution and care in the process, and that I keep the apparatus by me to evince the truth of what I write, whenever I may be properly required so to do.

I plainly saw then, that if the refracting angle of the water-vessel could have admitted of a sufficient increase, the divergency of thenbsp;coloured rays would have been greatly diminished, or entirely rectified ; and there would have been a very great refraction without colour,nbsp;as now I had a great discolouring without refraction: but the incon-veniency of so large an angle, as that of the vessel must have been,nbsp;to bring the light to an equal divergency with that of the glass prism,nbsp;w'hose angle was about 6o degrees, made it necessary to try some experiments of the same kind, by smaller angles.

I ground a wedge of common plate glass to an angle of somewhat less than g degrees, which refracted the mean rays about 5 degrees.nbsp;I then made a wedge-like vessel, as in the former experiment, andnbsp;filling it with water, managed it so, that it refracted equally with thenbsp;glass wedge; or, in other words, the difference of their refractionsnbsp;was nothing, and objects viewed through them appeared neithernbsp;raised nor depressed. This was done with an intent to observe thenbsp;same thing over again in these small angles, which I had seen in thenbsp;prism : and it appeared indeed the same in proportion, or as near asnbsp;I could judge; for notwithstanding the refractions were here alsonbsp;equal, yet the divergency of the colours by the glass was vastlynbsp;greater than that by the water; for objects seen by these two refractions were very much discoloured. Now this was a demonstration,nbsp;that the divergency of the light, by the different refrangibility, was

far from being equal in these two refractions. I also saw, from the position of the colours, that the excess of divergency was in thenbsp;glass; so that I increased the angle of the water-wedge, by differentnbsp;trials, till the divergency of the light by the water was equal to thatnbsp;by the glass; that is, till the object, though considerably refracted,nbsp;by the excess of the refraction of the water, appeared neverthelessnbsp;quite free from any colours proceeding from the different refrangibilitynbsp;of light; and, as near as I could then measure, the refraction by thenbsp;water was about 4 of that by the glass. Indeed I was not very exactnbsp;in taking the measures, because my business was not at that time aboutnbsp;the proportions, so much as to show, that the divergency of thenbsp;colours, by different substances, was by no means in proportion to thenbsp;refractions; and that there was a possibility of refraction without anynbsp;divergency of the light at all.

Having, about the beginning of the year 1757, tried these experiments, I soon after set about grinding telescopic object-glasses upon the new principles of refractions, which I had gathered from them;nbsp;which object-glasses were compounded of tw'O spherical glasses withnbsp;water between them. These glasses I had the satisfaction to find, asnbsp;I had expected, free from the errors arising from the different refrangibility of light; for the refractions, by which the rays were broughtnbsp;to a focus, were everywhere the differences between two contrary refractions, in the same manner, and in the same proportions, as in thenbsp;experiment with the wedges.

However, the images formed at the foci of these object-glasses were still very far from being so distinct as might have been expected fromnbsp;the removal of so great a disturbance; and yet it was not very diffi-

cult to guess at the reason, when I considered, that the radii of the spherical surfaces of those glasses were required to be so short, innbsp;order to make the refractions in the required proportions, that theynbsp;must produce aberrations, or errors, in the image, as great, ornbsp;greater, than those from the different refrangihility of light. Andnbsp;therefore, seeing no method of getting over that difficulty, I gavenbsp;up all hopes of succeeding in that way.

And yet, as these experiments clearly proved, that different substances diverged the light very differently, in proportion to the refraction ; I began to suspect, that such a variety might possibly be found in different sorts of glass, especially as experience had already shown,nbsp;that some made much better object-glasses, in the usual way, thannbsp;others: and as no satisfactory cause had as yet been assigned for suchnbsp;difference, there was great reason to presume, that it might be owing,nbsp;to the different divergency of the light by their refractions.

Wherefore, the next business to be undertaken, was to grind wedges of different kinds of glass, and apply them together, so thatnbsp;the refractions might be made in contrary directions, in order to discover, as in the foregoing experiments, whether the refraction and divergency of the colours would vanish together. But a considerablenbsp;time elapsed before I could set about that work; for though I was determined to try it at my leisure, for satisfying my own curiosity, yet Inbsp;did not expect to meet with a difference sufficient to give room fornbsp;any great improvement of telescopes; so that it was not till the latternbsp;end of the year that I undertook it, when my first trials convincednbsp;me, that this business really deserved my utmost attention and application.

I discovered a difference, far beyond my hopes, in the refractive qualities of different kinds of glass, with respect to their divergencynbsp;of colours. The yellow or straw-coloured foreign sort, commonlynbsp;called Venice glass, and the English crown glass, are very nearly alikenbsp;in that respect, though in general the crown glass seems to divergenbsp;the light rather the least of the two. The common plate glass madenbsp;in England diverges more; and the white crystal or flint English glass,nbsp;as it is called, most of all.

It was not now my business to examine into the particular qualities of every kind of glass that I could come at, much less to amuse myself with conjectures about the cause, but to fix upon such two sortsnbsp;whose difference was the greatest; which I soon found to be thenbsp;crown, and the white flint or crystal. I therefore ground a wedge ofnbsp;white flint of about 25 degrees, and another of crown of about 29 degrees, which refracted nearly alike; but their divergency of the colours was very different. I then ground several others of crown tonbsp;different angles, till I got one, which was equal, with respect to thenbsp;divergency of the light, to that in the white flint: for when theynbsp;were put together, so as to refract in contrary directions, the refracted light was intirely free from colour. Then measuring the refractions of each wedge, I found that of the white glass to be to thatnbsp;of the crown nearly as 2 to 3; and this proportion would hold verynbsp;nearly in all small angles. Wherefore any two wedges made in thisnbsp;proportion, and applied together, so as to refract in a contrary direction, would refract the light without any difference of refrangi-bility.

To make therefore two spherical glasses, that shall refract the light in contrary directions, it is easy to understand, that one mustnbsp;be concave, and the other convex; and as the rays are to convergenbsp;to a real focus, the excess of refraction must evidently be in the convex ; and as the convex is to refract most, it appears from the experiment, that it must be made with crown glass, and the concave withnbsp;white flint glass.

And further, as the refractions of spherical glasses are in an inverse ratio of their focal distanc�s; it follows, that the focal distances of the two glasses should be inversely as the ratios of thenbsp;refractions of the wedges : for being thus proportioned, every ray ofnbsp;light that passes through this combined glass, at whatever distancenbsp;it may pass from its axis, will constantly be refracted, by the difference between two contrary refractions, in the proportion required ;nbsp;and therefore the different refrangihility of the light will be intirelynbsp;removed.

Having thus got rid of the principal cause of the imperfection of refracting telescopes, there seemed to be nothing more to do,nbsp;but to go to work upon this principle: but I had not made manynbsp;attempts, before I found, that the removal of one impediment hadnbsp;introduced another equally detrimental (the same as I had beforenbsp;found in two glasses with water'between them) : for the two glasses,nbsp;that were to be combined together, were the segments of verynbsp;deep spheres; and therefore the aberrations from the spherical surfaces became very considerable, and greatly disturbed the distinctnessnbsp;of the image. Though this appeared at first a very great difficulty,nbsp;yet I was not long without hopes of a remedy: for considering

the surfaces of spherical glasses admit of great variations, though the focal distance be limited, and that by these variations theirnbsp;aberrations may be made more or less, almost at pleasure, I plainlynbsp;saw the possibility of making the aberrations of any two glassesnbsp;equal; and as in this case the refractions of the two glasses werenbsp;contrary to each other, their aberrations, being equal, would intirelynbsp;vanish.

And thus, at last, I obtained a perfect theory for making object-glasses, to the apertures of which I could scarcely conceive any limits: for if the practice could come up to the theory, they must certainlynbsp;admit of very extensive ones, and of course bear very great magni-fying powers.

But the difficulties attending the practice are very considerable. In the first place, the focal distances, as well as the particular surfaces,nbsp;must be very nicely proportioned to the densities or refracting powersnbsp;of the glasses ; which are very apt to vary in the same sort of glassnbsp;made at different times. Secondly, the centres of the two glassesnbsp;must be placed truly on the common axis of the telescope, otherwise the desired effect will be in a great measure destroyed. Add tonbsp;these, that there are four surfaces to be wrought perfectly spherical;nbsp;and any person, but moderately practised in optical operations,nbsp;will allow, that there must be the greatest accuracy throughout thenbsp;whole work.

Notwithstanding so many difficulties, as I have enumerated, I have, after numerous; trials, and a resolute perseverance, brought the matternbsp;at last to such an issue, that I can construct refracting telescopes, with

such apertures and magnifying powers, under limited lengths, as, in the opinion of the best and undeniable judges, who have experienced them, far exceed any thing that has been hitherto produced,nbsp;as representing objects with great distinctness, and in their truenbsp;colours.

�John Dollond.

Some Account of the Discovay, made hy the late Mr. John Dollond, F.R S. which led to thenbsp;grand Improvement wf llefracting� Telescopes,nbsp;in Order to correct some 3Iisrepresentations, innbsp;Foreign Publications, of that Discovery: withnbsp;an Attempt to account for the Mistake in annbsp;Experiment made hy Sir Isaac Newton; onnbsp;which Experiment, the Improvement qf� the Refracting Telescope intirely depended. By Peternbsp;Dollond, Member of the American Philosophical Society at Philadelphia.

My intention in writing the following paper was, to correct several false representations, relating to the invention of the achromaticnbsp;refracting telescope, and to secure to my late father, Mr. Johnnbsp;Dollond^ as well as to this country, the honour of so valuable a discovery.

With this view, the paper was presented to the Royal Society, by the Rev. Dr. Maskelyne, Astronomer Royal, in expectation of itsnbsp;being published in the Philosophical Transactions. It was read at anbsp;meeting of the Society on the 21st of May, 1789; but afterwards,nbsp;contrary to my expectation, it was resolved, in a council of the Society, that the paper should not be printed in their Transactions; Inbsp;therefore take this method of submitting it to the public; as I humbly conceive, it relates to a subject of a sufficient degree of importancenbsp;to claim their attention.

Peter Dollond.

The correction of any inaccuracies or false representations in the history of science is certainly of some consequence to the public, andnbsp;deserves the attention of the Royal Society; particularly so, whennbsp;such false representation tends to deprive any one of that praise, tonbsp;which he may be justly entitled, by having contributed towards thenbsp;advancement of science; even though it may be in things of littlenbsp;moment. Then certainly it must be much more so, when it relatesnbsp;to matters of great importance; such as was the discovery whichnbsp;brought forward the grand improvement of the refracting telescope.

^ I was led to these reflections, by having seen some accounts of that discovery in different publications, which were related in a mannernbsp;that lessened the merit of my late father John Dollond, and gave itnbsp;to others, who never thought themselves in any manner entitled tonbsp;claim with him, or ever appeared to be inclined so to do. Their ownnbsp;characters were too exalted in science to need any additional merit ofnbsp;any discovery, to which they had not an undoubted right.

The celebrated M. Euler, of Berlin, and M. Klinginstierna, professor of mathematics at Upsal, in Sweden, are the persons alluded to. These gentlemen have been mentioned by different foreignnbsp;authors, who have had occasion to give accounts of the improvement of the refracting telescope, as being the discoverers of thenbsp;principle on which that improvement was founded; and nothingnbsp;has been left to Dollond, but the credit of being the first who put the

�4 Some Account of the Discovery made by Mr. John Dollond, same into practice; whereby he has been deprived of the honournbsp;which is justly due to his memory, for having made so useful a discovery.

In order to set this matter in a proper light, I shall mention so much from Sir Isaac Newton�s Optics, as is necessary for the purpose;nbsp;and then endeavour to prove, that what was attempted by Euler andnbsp;Klinginstierna was not done from any knowledge of the principle onnbsp;which the improvement was founded; but that Dollond was actuallynbsp;the discoverer of that principle, as well as the person who first put thenbsp;same in practice.

When Newton had made his great discovery of the different re-frangibility of light, he fully explained that to be the cause of the imperfection of refracting telescopes, and that it was not occasionednbsp;by the spherical figures of the glasses, as has been the generallynbsp;received opinion. But as mathematicians had made many attempts tonbsp;correct the errors arising from spherical figures, by giving the glassesnbsp;figures from the conic sections, he took that opportunity of mentioning an ingenious thought of his own, of composing the object-glassesnbsp;of two glasses with water between them; by which means he says,nbsp;that the spherical: figures of the glasses might have been corrected,nbsp;and telescopes brought to a sufficient perfection, had it not been fornbsp;the different refrangibility of the several sorts of rays.�Netvtons Optics, 3d. Edition, p. QO.

Newton having completed the principal experiments relating to the different refrangibility of light, and having determined the proportions

experiment of the second part of the first book of his Optics, to discover their proportions in different refracting mediums. This experiment he tried, by placing a prism of glass in a prismatic vessel of water. Refracting the light through these different mediums, henbsp;found that light, as often as by contrary refractions it is so correctednbsp;that it emergeth in lines parallel to those in which it was incident,nbsp;continues ever after to be white; but if the emergent rays be inclinednbsp;to the incident, the light will become coloured.�Neiutons Optics,nbsp;p. 112.

The conclusion drawn from this experiment was, that the divergency of the different coloured rays was constantly in a given proportion to the mean refraction in all sorts of refracting mediums.nbsp;This was the principle established by the Newtonian experiment, andnbsp;was doubted by no one, until the beginning of the year 1757; whennbsp;Dollond tried the same experiment as above related, and found thenbsp;result to be very different; for the light after being refracted in contrary directions through the glass and water prisms, if the emergentnbsp;rays were parallel to the incident rays, they were found to be considerably coloured; from whence it followed, that the dissipation ofnbsp;the different coloured rays was not in the same proportion to the meannbsp;refraction in water as in glass. And further experiments proved, thatnbsp;there was also a very considerable difference of the same nature to benbsp;found in different kinds of glass.�See this Appendix, p. 50.

This was the new principle, which brought forward the improvement of refracting telescopes; a principle so contrary to the generally received opinion, that Euler had much difficulty to prevailnbsp;on himself to believe what was told him by his friends on that subject;

66 Some Account of the Discovery made by Mr. Jofin Dollond, as appears by his own papers published in the Memoirs of the Royalnbsp;Academy at Berlin. For he first supposes the goodness of Dollond�snbsp;telescopes to be owing to the greenish colour of the crown-glass,nbsp;which did not transmit all the red rays; he afterwards endeavours tonbsp;account for it from the construction of the eye-glasses; and at lastnbsp;declares it to be very extraordinary, that the English optician shouldnbsp;have made such an improvement, by reasoning, as it were, in a manner quite contrary to the nature of things; for so indeed the newnbsp;discovered principle appeared to him. Notwithstanding these declarations of Euler, which were published in the year 1762, M. De lanbsp;Lande, in the second volume of his Astronomy, p. 837) publishednbsp;in the year 1704, says, that Euler, in 1747, endeavoured to correctnbsp;the different refrangibility of light, by a method which Newtonnbsp;pointed out for correcting the errors of the spherical figures of thenbsp;glasses; which was, by two lenses with water between them, as recited above: and he says, that Dollond tried to confute Euler, whonbsp;had demonstrated an error in Newton�s theory of colours; but thenbsp;dispute having given occasion to Dollond to examine the thing morenbsp;narrowly, he afterwards acknowledged the error of Newton, and innbsp;the year 1759 he found out a method of making achromatic telescopesnbsp;that succeeded very well.

Now this account of De la Lande�s is by no means the true state of the facts, as appears by the Letters which passed between Eulernbsp;and Dollond, see the former part of this Appendix, pp. 21�32; fornbsp;though Euler argues from his hypothesis, that the result of Newton�snbsp;experiment could not be exactly as he relates it, yet he does not pretend to controvert any of Newton�s laws of refraction, as being con-

trary to experiment, but believed, that the divergency of the ditFerent coloured rays differed scarce sensibly from bearing a given proportionnbsp;to the mean refraction, in all sorts of refracting mediums; by which,nbsp;it appears, that the error afterwards discovered by Dollond was notnbsp;even suspected by Euler; therefore that part of DelaLande�s accountnbsp;cannot be true; for Dollond could not be said to acknowledge an error,nbsp;supposed to be discovered by Euler in Newton�s theory of colours,nbsp;by having actually discovered one himself of a different nature. Thenbsp;true state of the fact is, that in 1747 Euler endeavoured to correctnbsp;the errors arising from the different refrangibility of light in object-glasses, by a method which was not founded on any experiment,nbsp;but on an hypothesis, which did not appear to be on a true principle,nbsp;so that the attempts which were made to put this method in practicenbsp;did not succeed: this was certainly the case; for after M. Clairautnbsp;had examined the controversy between Euler and Dollond, he pronounced, that what Euler had done appeared to be more ingeniousnbsp;than useful.

Euler indeed says, that the structure of the eye gave him the greatest reason to suppose, that the different refrangibility mightnbsp;be corrected by several refractions through different kinds of mediums;nbsp;for which purpose he thought the eye to be so constructed. Butnbsp;this reasoning had no weight with Dollond, as he perceived andnbsp;mentioned to his friends, that the refractions of the eye, at the severalnbsp;surfaces and humours, are all made the same w'ay, and consequently,nbsp;for want of contrary refractions, the colours produced by the firstnbsp;refractions could not be taken away. How this can subsist with thenbsp;perfection of our vision, has been ingeniously explained by the

Astronomer Royal, in an account which he proposes to lay before the Society�See p. 78 of this Appendix.

Klinginstierna has likewise been considered as a party concerned in the improvement of the refracting telescope; though De la Landenbsp;does not mention his name, yet some others do. This has been oonbsp;casioned by his having, in the year 1755, considered the controversynbsp;between Euler and Dollond, and having formed a theorem of his own,nbsp;by which he was also induced to believe, that the result of Newton�snbsp;experiment could not be as he had related it; except when the anglesnbsp;of the refracting mediums were small. This he communicated tonbsp;Dollond, in a letter to his friend Mr. Mallet, who was then innbsp;England. As this theorem has never been published in English, I shallnbsp;give a copy of it here, as taken by my father from Klinginstierna�snbsp;letter to Mallet, that mathematicians may judge of the truth of thenbsp;deductions.

� Remarks on the Law of Refraction of Rays of Light of different Kinds, through different Mediums. See Newton's Optics, Book I. Partnbsp;ii. Prop. 3. Exper. viii.

� Upon any right line, as TH, let there be drawn two arches TIH, TGH, and let a right line TIG be drawn intersecting the archesnbsp;in I and G, Join IH and GH; let F E K be a transparent wedge,nbsp;having its acute angle FEK equal to the angle IHG; let the twonbsp;faces of this wedge be contiguous to two different transparent mediums ; and let the ratio of refraction out of the medium, thatnbsp;joins the surface EF into the wedge, be as the ratio of TH to TI,nbsp;and the ratio of refraction out of the wedge into the medium joining the surface EK as the ratio of TG to TH.

� Now if AB represents a ray of light entering into the wedge, and the angle AB a is made equal to HIG, then will the angle CBnbsp;a be equal to the angle THE Ang. BC h�ang. THG and DC h�nbsp;HGL; so that the incident ray AB will be parallel to the emergentnbsp;ray CD, which has been twice refracted.

� Now if tbe incident ray is compounded of divers simple rays, each of which, after two refractions, should emerge parallel to thenbsp;common incident ray, the refractions of each will be represented bynbsp;so many right lines T i g joining H i, H g, the same as before.

� According to Newton�s law of refraction quoted above TH�TI should be in a constant ratio to TH�TG; that is, if an arch of anbsp;circle is described on the centre T with the interval TH, meetingnbsp;the lines TIG, Tig in L and I; then by that supposition LI shouldnbsp;be to LG as H to Ig. But these proportions will not hold, unless Lnbsp;and / were in an arch described on the chord TH, but they are in annbsp;arch whose centre is T.

70 Some Account of the Discovery made by Mr. John Dollond, clearly from his 8th experiment, which our wedge with two contiguous mediums refers to.

� If we should suppose such a law of refraction as we find necessary to bring out every simple ray parallel to the incident, after two refractions through this wedge FEK, it can be demonstrated, that thenbsp;same law will not have the same effect in another wedge of a differentnbsp;angle, but for every different angle there will be a different law required.

� Whence it seems to follow, that there must be some mistake in this experiment of Newton�s, which he himself gives as an universalnbsp;one, for it does not seem likely that the law which really obtains innbsp;nature should depend upon a greater or less angle of a wedge.

� Nevertheless it must be observed, that the less the refractions are, the nigher will the Newtonian law be to that which is required fornbsp;producing a perfect parallellism of the emergent rays to the commonnbsp;incident ray ; for in this case LI to LG will be very nearly in a givennbsp;ratio. It does not seem that the aberration of the rays in object-glasses, proceeding from the different refrangibility, can be correctednbsp;by any refractions, which is what Mr.^ Newton plainly insists upon.nbsp;However, this whole affair deserves to be more accurately examinednbsp;by experiments.�

I shall here only remark, that it appears by this copy of a letter from Klinginstierna, that the supposed error in the result of Newton�snbsp;experiment, which he thus labours to demonstrate, is the same asnbsp;before attempted to be ascertained by Euler, and not the errornbsp;which was afterwards discovered by Dollond.

The account given by De la Lande, of the improvement of the refracting telescope, was copied by most foreign writers on the subject, with little variation, except in giving sometimes a little more of thenbsp;honour to Euler, and also making mention of Klinginstierna.

But in the Eulogy on Euler, written and published by M. N. Fuss, professor of mathematics at St. Petersburg, in the year 1783, p. 41nbsp;and 42, he gives the whole of the discovery to Euler, except � thatnbsp;Dollond is allowed to have found out two sorts of glass, whichnbsp;crowned at last, in 1757, the happy conjecture of Euler, by the invention of achromatic telescopes, which formed a new epoch innbsp;astronomy and dioptrics.� As this account is the most curious of anynbsp;I have found, I shall here give it at length, and contrast it with whatnbsp;Euler says himself on the subject, in a paper read before the Royalnbsp;Academy of Sciences at Berlin, ip 1704, and published in thenbsp;volume of their Memoirs for 1766, p. II9.

Mr. Fuss says, �� The examination of the Newtonian theory, had given Euler an opportunity of investigating the different refrangibilitynbsp;of light, and the bad effects which the dispersion of the colours produced in refracting telescopes, which had been almost intirely abandoned upon account of this defect. The consideration of thenbsp;wonderful structure of the eye made him suppose, that a. certainnbsp;combination of different transparent bodies could remedy this inconvenience. He proposed for this purpose, in the year 1747, object-glasses composed of two glasses, the cavity between which could benbsp;filled with water.

� His opinion was attacked by the famous English artist, Dollond, who opposed to him the authority of Newton; M. Euler soon shewed

72 Some Account of the Discovery made by Mr. John Dollond, him the error of his principles. Some experiments made upon me-niscuseSj the cavities of which were filled with different liquids, confirmed him in his opinion: and Mr. Dollond, who had in the meannbsp;time discovered two sorts of glass, which were proper for examiningnbsp;it further, crowned at last, in 1757, the happy conjecture of M.nbsp;Euler, by the invention of achromatic telescopes, which formed annbsp;epoch in astronomy and dioptrics.

� The success of Mr. Dollond, who availed himself, with so much advantage, of a discovery, which he had at first attacked as contrarynbsp;to experiment, induced M. Euler to extend his researches furthernbsp;upon the subject of dioptric instruments, amp;:c7�

I shall now subjoin a translation of M. Euler�s paper, read at the Academy of Sciences at Berlin in the year 1764.

� Although I have already frequently discussed this subject, I see myself again obliged to resume it, in consequence of the astonishingnbsp;discoveries which have been lately made upon the nature of glass, andnbsp;its different kinds. I am not ashamed frankly to avow, that the firstnbsp;accounts, which were published of it, appeared so suspicious, andnbsp;even so contrary to the best established principles, that I could notnbsp;prevail upon myself to give credit to them. That there should be twonbsp;kinds of glass, in which the refraction of the mean rays is nearlynbsp;equal, whilst that of the extremes differs most enormously, appearednbsp;to me to shock good sense; and perhaps I should never have submittednbsp;to the proofs, which Mr. Dollond produced to support this strangenbsp;phenomenon, if Mr. Clairaut, who must at first have been equallynbsp;surprized at it, had not most positively assured me, that Dollond�snbsp;experiments were but too well founded. But at length the experi-

Tnents made at Petersburg by M. Zeiher have effectually succeeded in removing my prejudice; that ingenious philosopher having incontestably proved that it is the lead, which is used in some compositions ofnbsp;glass, that produces in it that strange quality of augmenting the dispersion of the extreme rays, without changing sensibly the refractionnbsp;of the mean; and by increasing the quantity of lead in the composition of glass, he has been enabled to make glass, which produces anbsp;much greater dispersion of the rays than the flint-glass of Dollond.

Now I must intirely renounce this principle, which until now has appeared so well-founded, that the dispersion of the extreme raysnbsp;depends solely upon the refraction of the mean rays; and I am obliged to acknowledge, that the dispersion depends principally upon thenbsp;quality of the glass, without the mean refraction thereof being sensibly affected thereby.�

As it appears by the above paper, that Euler was at last so convinced of the truth of the discovery made by Dollond, as to renounce his favourite hypothesis, it must be inferred, that the account givennbsp;of this matter by Fuss is very far from being the true state of thenbsp;facts, and indeed so much so, as to be very inexcusable, even in annbsp;eulogy.

There is another publication of a later date, which I shall take the liberty of mentioning, � Extracts of the Observations made at thenbsp;Royal Observatory at Paris, in the year ]787j by Count Cassini.quot; Innbsp;page 106 he gives an account of the improvement of the refractingnbsp;telescope, by way of prelude to his describing a method proposed bynbsp;M. 1�Abb� Rochon, of putting fluids, and also a kind of mastic, between the glasses of achromatic object-glasses, as a good method of

74 So7?ie Account of the Discovery made hy Mr. John Dollond, mending bad glasses, or, as he calls it, a method to correctnbsp;the non-sphericity of the glasses; which he mentions as being similarnbsp;to that ingenious idea proposed by Newton, for correcting the errorsnbsp;of the spherical figures of object-glasses. The account he gives ofnbsp;the improvement of the refracting telescope is as follows. He says.nbsp;� It was the celebrated Euler who first proposed to correct the errorsnbsp;arising from the different refrangibility, by using different refractingnbsp;mediums, such as water and glass. The late Mr. Dollond havingnbsp;availed himself of and realized this ingenious idea, has a just right tonbsp;partake of the glory.��By these publications it seems, that Dollond,nbsp;who explained the fallacy of Euler�s hypothesis, who afterwards discovered the true principle, on which the different refrangibility ofnbsp;light could be corrected, and he, who put the same in practice, sonbsp;much to the benefit of science, is only to be allowed to partake ofnbsp;the glory, and that with Euler, who never himself thought he hadnbsp;the least right to claim any part of the discovery w'ith Dollond, asnbsp;most fully appears by the paper above recited from the Berlinnbsp;Memoirs.

I can account for these false representations no other way than by supposing; that those who wrote them have not taken sufficient painsnbsp;to inform themselves of the true history of the discovery; for Inbsp;would not wish to attribute what they have said to any partiality; andnbsp;I am induced to hope, that when the state of facts which I have herenbsp;adduced shall be candidly considered, that they will retract their declarations, and acknowledge, that Dollond was the sole discoverer ofnbsp;the principle which led to the improvement of refracting telescopes,

I now come to a more agreeable part of this paper, which is, to endeavour to reconcile the different results of the 8th experiment of

the second part of the 1st Book of Newton�s Optics, as related by himself, and as it w^as found by Dollond, when he tried the samenbsp;experiment, in'the year 1757. Newton says, that light, as often asnbsp;by contrary refractions it is so corrected, that jt emergeth in linesnbsp;parallel to the incident, continues ever after to be white. Now Dollondnbsp;says when he tried the same experiment, and made the mean refraction of the water equal to that of the glass prism, so that the lightnbsp;emerged in lines parallel to the incident, he foi..id the divergency ofnbsp;the light by the glass prism to be nearly double to what it was by thenbsp;water prism. The light appeared to be so evidently coloured, that itnbsp;was directly said by some persons, that if Newton had actually triednbsp;the experiment, he must have perceived it to have been so. Yet whonbsp;could for a moment doubt the veracity of such a character ?�thereforenbsp;different conjectures were made by different persons. Mr. Murdochnbsp;in particular gave a paper to the Royal Society in defence of Newton;nbsp;but it was such as very little tended to clear up the matter. Philosophical Transactions, vol. liii. p. I92.�Some have supposed thatnbsp;Newton made use of water strongly impregnated with Saccharumnbsp;Saturni, because he mentions sometimes using such water, to increasenbsp;the I'efraction, when he used w'ater prisms instead of glass prisms.nbsp;Newtons Optics, p. 62.�And others have supposed,,that he tried thenbsp;experiment with so strong a persuasion in his own mind, that the divergency of the colours was always in the same proportion to the meannbsp;refraction, in all sorts of refracting mediums, that he did riot attendnbsp;so much to that experiment as he ought to have done, or as he usuallynbsp;did. None of these suppositions having appeared at all satisfactory, Inbsp;have therefore endeavoured to find out the true cause of the difference,

76 Some Account the Discovery made by Mr. John Dollond, and thereby shew, how the experiment may be made to agree withnbsp;Newton�s description of it, and to get rid of those doubts, whichnbsp;have hitherto remained to be cleared up.

It is well known, that in Newton�s time the English were not the most famous for making optical instruments:�telescopes, opera-glasses,nbsp;amp;c. were imported from Italy in great numbers, and particularly fromnbsp;Venice; where was manufactured a kind of glass which was much morenbsp;proper for optical purposes than any made in England at that time. Thenbsp;glass made at Venice was nearly of the same refractive quality as ournbsp;crown glass, but of a much better colour, being sufficiently clear andnbsp;transparent for the purpose of prisms. It is probable that Newton�snbsp;prisms were made with this kind of glass; and it appears to be the morenbsp;so, because he mentions the specific gravity of common glass to benbsp;to water as 2.58 to 1. Newtons Opt. p. 247, which nearly answersnbsp;to the specific gravity w'e find the Venetian glass generally to have�nbsp;Having a very thick plate of this kind of glass, which was presentednbsp;to me about twenty-five years ago by the late professor Allemand, ofnbsp;Leyden, and which he then informed me had been made many years,nbsp;I cut a piece from this plate of glass to form a prism, which I conceivednbsp;would be similar to those made use of by Newton himself. Inbsp;have tried the Newtonian experiment with this prism, and find itnbsp;answers so nearly to what Newton relates, that the difference whichnbsp;remains may very easily be supposed to arise from any little difference, which may and does often happen in the same kind of glassnbsp;made at the same place at different times. Now the glass prismnbsp;made use of by Dollond to try the same experiment was made ofnbsp;Englisft flint glass, the specific gravity of which I have never known

to be less than 3, 22. This difference in the densities of the prisms used by Newton and Dollond was sufficient to cause all the difference which appeared to the two experimenters in trying the samenbsp;experiment.

From this it appears, that Newton was accurate in this experiment as in all others, and that his not having discovered that, which wasnbsp;discovered by Dollond so many years afterwards, was owing intirely tonbsp;accident; for if his prism had been made of glass of a greater or lessnbsp;density, he would certainly have then made the discovery, and refracting telescopes would not have remained so long in their original, imperfect state.

An Attempt to explain a Difficulty in the Theory ff' Vision, depending on the different Rff'rangi-bility of Light. By the Rev. Nevil Maskelyne,nbsp;D.D. F.R S. and Astronomer Royal.

T. HE ideas of sight are so striking and beautiful, that vve are apt to consider them as perfectly distinct. The celebrated Euler, taking thisnbsp;for granted, has supposed, in the Memoirs of the Royal Academy ofnbsp;Sciences at Berlin for 1747, that the several humours of the humannbsp;eye were contrived in such a manner as to prevent the latitude ofnbsp;focus arising from the different refrangibility of light, and considersnbsp;this as a new reason for admiring the structure of the eye; for thatnbsp;a single transparent medium, of a proper figure, would have beennbsp;sufficient to represent images of outward objects in an imperfect manner; but to make the organ of sight absolutely complete, it wasnbsp;necessary it should be composed of several transparent mediums.

An Attempt to explain a Igt;iffim]ty in the 'l^eory of Vision, ^c. 79 properly figured, and fitted together agreeable to the rules of thenbsp;sublimest geometry, in order to obviate the effect of the different re-frangibility of light in disturbing the distinctness of the image;, andnbsp;hence he concludes, that it is possible to dispose four refracting surfaces, in such a manner as to bring all sorts of rays to one focus, atnbsp;whatever distance the object be placed. He then assumes a certainnbsp;hypothesis of refraction of the differently refrangible rays, and buildsnbsp;thereon an ingenious theory of an achromatic object-glass, composednbsp;of two meniscus glasses with water between them, with the help of annbsp;analytical calculation, simple and elegant, as his usually are.

He has not, however, demonstrated the necessary existence of his hypothesis, his arguments for which are more metaphysical thannbsp;geometrical; and, as it was founded on no experiments, so those madenbsp;since have shewn its fallacy, and that it does not obtain in nature.nbsp;Moreover, which is rather extraordinary, it does not account, according to his own ideas, for the very phenomenon which first suggestednbsp;it to him, namely, the great distinctness of the human vision, as wasnbsp;observed to me, many years ago, by the late Mr. John Dollond, F.R.S.nbsp;to whom we are so much obliged for the invention of the achromaticnbsp;telescope;¹ for the refractions at the several humours of the eye

As a misstatement of this fact has been made by both Paley and Priestley, we shall quote their own words for the satisfaction of the reader.�� At last it came into thenbsp;mind of a sagacious optician, to, inquire how this matter was managed in the eye; innbsp;which there was exactly the same difficulty to contend with, as in the telescope. Hisnbsp;observation taught him, that, in the eye, the evil was cured by combining togethernbsp;lenses composed of different substances, i. e, of substances which possessed different

being all made one way, the colours produced by the first refraction will be increased at the two subsequent ones instead of being corrected,nbsp;whether we make use of Newton�s or Euler�s law of refraction of thenbsp;differently refrangible rays.

Thus Euler produced an hypothetical principle, neither fit for rendering a telescope achromatic, nor to account for the distinctness of the human vision; and the difficulty of reconciling that distinctnessnbsp;with the principle of the different refrangibility of light discovered bynbsp;Sir Isaac Newton remains in full force.

In order to go to the bottom of this difficulty, as the best probable means of obviating it, I have calculated the refractions of the mean,nbsp;most, and least refrangible rays at the several humours of the eye, andnbsp;thence inferred the diffusion of the rays, proceeding from a point innbsp;an object, at their falling upon the retina, and the external anglenbsp;which such coloured image of a point upon the retina corresponds to.

refracting powers. Our artist borrowed from thence his hint j and produced a correction of the defect, by imitating, in glasses made from different materials, the effects of thenbsp;different humours through which the rays of light pass before they reach the bottom ofnbsp;the eye.��See Paley, p. 23.nbsp;nbsp;nbsp;nbsp;quot; M. Euler did not pretend to controvert the experiments

of Newton; but he said that they were not contrary to his hypothesis, but in so small a degree as might be neglected, and asserted that, if they were admitted in all theirnbsp;extent, it would be impossible to correct the difference of refrangibility occasioned by thenbsp;transmission of the rays from one medium into another of different density; a correctionnbsp;which, he thought, was very possible, since he supposed it to be actually effected in thenbsp;structure of the eye, which he thought was made to consist of different mediums fornbsp;that very purpose. To this kind of reasoning Mr. Dollond made no reply; but bynbsp;appealing to tlie experiments of Newton, and the great circumspection with which itnbsp;was known that he conducted all his inquiries.��See Priestley, p. 453.,

I took the dimensions of the eye from M. Petit, as related by Dr. Jurin; and, the specific gravities of the aqueous and vitreous humoursnbsp;having been found to be nearly the same with that of water, and thenbsp;refraction of the vitreous humour of an ox�s eye having been found by-Mr. Hawksbee to be the same as that of wateiy and the ratio of refraction out of air into the crystalline humour of an ox�s eye havingnbsp;been found by the same accurate experimenter to be as 1 to ,68327, Inbsp;took the refraction of the mean refrangible rays out of air into thenbsp;aqueous or vitreous humour, the same as into water, as 1 to ,74853,nbsp;or 1,33595 to Ij and out of air into the crystalline humour as 1 tonbsp;,68327, or 1,46355 to 1, Hence I find, according to Sir Isaac Newton�s two theorems, related at Part II. of Book I. of Optics, p. 113,nbsp;that the ratio of refraction of the most, mean, and least refrangiblenbsp;rays at the cornea should be as 1 to ,74512, ,74853 and ,75197 ; atnbsp;the fore-surface of the crystalline as 1 to ,91173, ,91282, and ,91392;nbsp;and at the hinder-surface of the crystalline as 1 to 1,09681, 1,09550,nbsp;and 1,09420.

Now, taking with Dr. Jurin 15 inches for the distance at which the generality of eyes in their mean state see with most distinctness,nbsp;I find the rays from a point of an object so situate will be collectednbsp;into three several foci, viz. the most, mean, and least refrangiblenbsp;rays at the respective distances behind the crystalline, ,5930, ,0034,nbsp;and ,6141 of an inch, the focus of the most refrangible rays beingnbsp;,0211 inch short of the focus of the least refrangible ones.

Moreover, assuming the diameter of the pencil of rays at the cornea, proceeding from the object at 15 inches distance, to be a-th of an inch in a strong light, which is a large allowance for it,' the semi-

angle of the pencil of mean refrangible rays at their concourse upon the retina will be 7� 12', whose tangent to the radius unity, or ,1204nbsp;multiplied into ,0211 inch, the interval of the foci of the extreme refrangible rays, gives ,002667 inch for the diffusion of the differentnbsp;coloured rays, or the diameter of the indistinct circle upon the retina.nbsp;Now, I find, that the diameter of the image of an object upon thenbsp;retina is to the object as ,6055 inch to the distance of the object fromnbsp;the centre of curvature of the cornea; or the size of the image is thenbsp;same as would be formed by a very thin convex lens, whose focal distance is, 6055 inch, and consequently a line in an object which subtendsnbsp;an angle of l' at the centre of the cornea will be represented on thenbsp;retina by aline of �j./^thinch. Hence the diameter of the indistinctnbsp;circle on the retina before found, ,002667 will answer to an externalnbsp;angle of ,002667 X 5678'= 15'8'', or every point in an object shouldnbsp;appear to subtend an angle of about 15', on account of the differentnbsp;refrangibility of the rays of light.

I shall now endeavour to shew that this angle of ocular aberration is compatible with the distinctness of our vision. This aberration isnbsp;of the same kind as that which we experience in the common refracting telescope. Now, by computation from the tabular aperturesnbsp;and magnifying powers of such telescopes, it is certain that they admitnbsp;of an angular indistinctness at the eye or no less than 57'; thereforenbsp;the ocular aberration is near four times less than in a common refractingnbsp;telescope, and consequently the real indistinctness, being as the squarenbsp;of the angular aberration, will be 14 or 15 times less in the eye thannbsp;in a common refracting telescope, which may be easily allowed to benbsp;imperceptible.

Moreover, Sir Isaac Newton has observed, with respect to the like difficulty of accounting for the distinctness with which refracting�nbsp;telescopes represent objects, that the erring rays are not scatterednbsp;uniformly over the circle of dissipation in the focus of the object-glass, but collected infinitely more densely in the centre than in anynbsp;other part of the circle, and in the way from the centre to the circumference grow continually rarer and rarer, so as at the circumference to become infinitely rare; and by reason of their rarity arenbsp;not strong enough to be visible, unless in the centre and very near it.

He farther observes, that the most luminous of the prismatic colours are the yellow and orange, which affect the sense morenbsp;strongly than all the rest together; and next to these in strength arenbsp;the red and green; and that the blue, indigo, and violet, comparednbsp;with these, are much darker and fainter, and compared withnbsp;the other stronger colours, little to be regarded; and that thereforenbsp;the images of the objects are to be placed not in the focus of thenbsp;mean refrangible rays, which are in the confine of green and blue,nbsp;but in the middle of the orange and yellow, there where the colour isnbsp;most luminous, that which is in the brightest yellow, that yellow whichnbsp;inclines more to orange than to green.

From all these considerations, and by an elaborate calculation, he infers, that though the whole breadth of the image of a lucid pointnbsp;be of the diameter of the aperture of the object-glass, yet thenbsp;sensible image of the same is scarce broader than a circle whose diameter is -rro-fti of the diameter of the aperture of the object-glass of a good telescope; and hence he accounts for the apparentnbsp;diameters of the fixed stars as observed with telescopes by astronomers, although in reality they are but points.

The like reasoning is applicable to the circle of dissipation on the retina of the human eye; and therefore we may lessen the angularnbsp;aberration, before computed at 13', in the ratio of 250 to 55, whichnbsp;will reduce it to 3' 18quot;.

This reduced angle of aberration may perhaps be double the apparent diameter of the brightest fixed stars to an eye disposed for seeing most distinctly by parallel rays; or, if short-sighted, assisted by a proper concave lens; which may be thought a sufficient approximation innbsp;an explication grounded on a dissipation of rays, to which a precisenbsp;limit cannot be assigned, on account of the continual increase ofnbsp;density from the circumference to the centre. Certainly some suchnbsp;angle of aberration is necessary to account for the stars appearingnbsp;under any sensible angle to such an eye; and if we were, without rea-son,\ to suppose the images on the retina to be perfect, we should benbsp;put to a much greater difficulty to account for the fixed stars appearingnbsp;otherwise than as points, than we have now been to account for thenbsp;actual distinctness of our sight.

The less apparent diameter of the smaller fixed stars agrees also with this theory; for the less luminous the circle of dissipation is, thenbsp;nearer we must look towards its centre to find rays sufficiently densenbsp;to move the sense. From Sir Isaac Newton�s geometrical account ofnbsp;the relative deiisity of the rays in the circle of dissipation, given in hisnbsp;system of the world, it may be inferred, that the apparent diametersnbsp;of the fixed stars, as depending on this cause, are nearly as theirnbsp;whole quantity of light.

In farther elucidation of this subject let me add my own experiment. When I look at the brighter fixed stars, at considerable

elevations, through a concave glass fitted, as I am short-sighted, to shew them with most distinctness, they appear to me without scintillation, and as a small round circle of fire of a sensible magnitude. Ifnbsp;I look at them without the concave glass, or with one not suited tonbsp;my eye, they appear to cast out rays of a determinate figure, not exactly the sanae in both eyes, somewhat like branches of trees (whichnbsp;doubtless arise from something in the construction of the eye) and tonbsp;scintillate a little, if the air be not very clear. To see day objectsnbsp;with most distinctness, I require a less concave lens by one degreenbsp;than for seeing the stars best by night, the cause of which seems tonbsp;be, that the bottom of the eye being illuminated by the day objects,nbsp;and thereby rendered a light ground, obscures the fainter colours bluenbsp;indigo and violet in the circle of dissipation, and therefore the bestnbsp;image of the object will be found in the focus of the bright yellownbsp;rays, and not in that of the mean refrangible ones, or the dark green,nbsp;agreeable to Newton�s remark, and consequently nearer the retina ofnbsp;a short-sighted person; but the parts of the retina surrounding thenbsp;circle of dissipation of a star being in the dark, the fainter colours,nbsp;blue, indigo, and violet, will have some share in forming the image,nbsp;and consequently the focus will be shorter.

The apparent diameter of the stars here accounted for is' different from that �xplained by Dr. Jurin, in his Essay on Distinct and Indistinct Vision, arising from the natural constitution of the generalitynbsp;of eyes to see objects most distinct at moderate distances, and fewnbsp;being capable of altering their conformation enough to see distantnbsp;objects, and among them the celestial ones, with equal distinctness.

But the cause of error, which I have pointed out, will affect all eyes, even those which are adapted to distant objects.

our religious and oratorical philosopher Derham, � all the. glories of the heavens and earth are brought and exquisitely pictured.�

Nor does it appear, that any material advantage would have been obtained, if the image of objects on the retina had been made absolutely perfect, unless the acuteness of the optic nerve should hav�nbsp;been increased at the same time; as the minimum visihile depends nonbsp;less on that circumstance than the other. But that the sensibility ofnbsp;the optic nerve could not have been much increased beyond what it is,nbsp;without great inconvenience to us, may be easily conceived, if we onlynbsp;consider the forcible impression made on our eye by a bright sky, ornbsp;even the day objects illuminated by a strong sun. Hence we maynbsp;conclude, that such an alteration would have rendered our sight painful instead of pleasant, and noxious instead of useful. We mightnbsp;indeed have been enabled to see more in the starry heavens with thenbsp;naked eye, but it must have been at the expence of our daily laboursnbsp;and occupations, the immediate and necessary employment of man.

fusion of the rays upon the retina by the different refrangibility of light. It may be said, that the ocular aberration, being a separatenbsp;cause from any effect of the telescojje, should subsist equally when wenbsp;observe a star through a telescope as when we look at it with thenbsp;naked eye; and that therefore the fixed stars could not appear sonbsp;small as they have been found to do through the best telescopes, andnbsp;particularly by Dr. Herschel with his excellent ones. To this I answer,nbsp;that the ocular aberration, which is proportional to the diameter ofnbsp;the pupil when we use the naked eye, is proportional to the diameternbsp;of the pencil of rays at the eye when we look through a telescope,nbsp;which being many times less than that of the pupil itself, the ocularnbsp;aberration will be diminished in proportion, and become insensible.

An Account (yf an Improvement made by Mr. Peter Dollond in his New Telescopes. In a Letternbsp;to James Short, M.A. F. R. S. with a Letter oj'nbsp;Mr. Short�s to the Rev. Thomas Birch, B.D.nbsp;Secret. R. S.

I HAVE sent you inclosed, a letter which I received this morning from Mr. Dollond, eoncerning an improvement whichnbsp;he has made in his new telescopes. He, some months ago, sent menbsp;a telescope, in this new way, of 3� feet focal length, with an aperturenbsp;of inches; I examined it, and I approved of it; I have tried itnbsp;I with a magnifying power of 150 times, and I found the image distinct,nbsp;bright, and free from colours.

James Short.

SIR,

I TAKE the liberty of sending you the following short account of an improvement I have lately made in the compoundnbsp;object glasses of refracting telescopes.

The dissipation of the rays of light may be perfectly corrected in object glasses, by combining mediums of different refractive qualities;nbsp;and the errors or aberrations of the spherical surfaces may be correctednbsp;by the contrary refractions of two lenses, made of the different mediums; yet as the excess of refraction is in the convex lens, andnbsp;though the surfaces of the concave lens may be so proportioned as tonbsp;aberrate exactly equal to the convex lens, near the axis; yet as thenbsp;refractions of the two lenses are not equal, the equality of the aberrations cannot be continued to any great distance from the axis.

In the year 1758, when my father had constructed some object glasses for telescopes in this rtianner, viz. with one convex lens ofnbsp;crown glass, and one concave lens of white flint glass; he attempted

yo Account of an Improvement made by Mr. Peter Dollond, to make short object glasses to be used with concave eye glasses, innbsp;the same manner; but as the field of view, in using a concave eyenbsp;glass depends on the aperture of the object glass, the limits of thenbsp;aperture were found to be too small: this led my father to considernbsp;that if the refraction of the crown glass (in which the excess was)nbsp;should be divided by means of having two lenses made of crownnbsp;glass instead of one, the aberration would thereby be decreased, andnbsp;the apertures might then be larger: this was tried with success innbsp;those object glasses, when concave eye glasses were used, and thesenbsp;have been ever since made in this manner: some trials were likewisenbsp;made, at the same time, to enlarge the apertures of longer objectnbsp;glasses, where convex eye glasses were used, by the same method;nbsp;but these not succeeding, in the same manner, the method of makingnbsp;them with one lens of crown glass, and one of white flint glass, wasnbsp;continued.

As I could not see any good reason why the method, which was practised with so much success, when concave eye glasses were used,nbsp;should not do with convex ones; I determined to try some furthernbsp;experiments in that way. After a few trials, I found it might benbsp;done; and in a short time I finished an object glass of 5 feet focalnbsp;length, with an aperture of inches, composed of two convex lensesnbsp;of crown glass, and one concave of white flint glass.

Thinking that the apertures might be yet admitted larger; I attempted to make one of 3^ feet focal length, with the same aperture of 3|: inches, which I have now completed, and am ready to shownbsp;the same to the Royal Society, if desired.

A Letter from Mr. Peter DoUond, to Nevil Mas-kelyne, F.R.S. ^ Astronomer Royal; describing some Additions and Alterations made to Hadley�snbsp;Quadrant, to render it more serviceable at Sea.

The particular attention which you have always shown to any improvement tending to the advantage of astronomynbsp;or navigation, makes me take the liberty to trouble you with an account of some additions and alterations which I have lately madenbsp;to the Hadley�s quadrant.

The general use of this instrument at sea is so well known, that no mention need be made of the importance of any improvements innbsp;the construction, that may render the observations more exact, andnbsp;occasion more frequent opportunities of making them.

The glasses of the Hadley�s quadrant should have their two surfaces perfect planes, and perfectly parallel to each other. From severalnbsp;years practice in grinding these glasses, I have found out methods ofnbsp;making them to great exactness; but the advantage, that should arisenbsp;from the goodness of the glasses, has often times been defeated bynbsp;the index glass being bent by the brass frame that contains it: tonbsp;prevent this, I have contrived the frame, so that the glass lies onnbsp;three points, and the part that presses against the front of the glassnbsp;has also three points exactly opposite to the former. These pointsnbsp;are made to confine the glass by three screws at the back, that actnbsp;exactly opposite to the points between which the glass is placed.nbsp;This little contrivance may be of some use; but the principal improvements are in the methods of adjusting the glasses, particularlynbsp;for the back observation.

The method hitherto practised for adjusting that part of the instrument, by means of the opposite horizons at sea, has been attended with so many difficulties that it has scarcely ever been used; for so little dependance could be placed on the observations taken this way,nbsp;that the best Hadley�s sextants made for the purposes of observingnbsp;the distances of the moon from the sun or fixed stars, have beennbsp;always made without the horizon glass for the back observation; fornbsp;want of which, many valuable observations of the sun and moon havenbsp;been lost, when their distance has exceeded 120 degrees.

To make the adjustment of the back observation easy and exact, I have applied an index to the back horizon glass, by which it may benbsp;moved into a parallel position to the index glass, in order to give itnbsp;the two adjustments, in the same manner as the fore horizon glass is

adjusted. Then^ by moving the index to which the back horizon glass is fixed, exactly 90 degrees (which is known by the divisionsnbsp;made for that purpose) the glass will be thereby set at right anglesnbsp;to the inc^ex glass, and consequently will be properly adjusted for use,nbsp;and the observations may be made with the same accuracy by this,nbsp;as by the fore observation.

To adjust the horizon glasses in the perpendicular position to the plane of the instrument, I have contrived to move each of them bynbsp;a single screw, that goes through the frame of the quadrant, and isnbsp;turned by means of a milled head at the back, which may be donenbsp;by the observer while he is looking at the object.

To these improvements. Sir, I have added your method of placing darkening glasses behind the horizon glasses, which you have beennbsp;so kind as to give me liberty to apply to my instruments. Thesenbsp;glasses, which serve for darkening the object seen by direct vision,nbsp;in adjusting the instrument by the sun or moon, I have placed innbsp;such a manner as to be turned behind the fore horizon glass, or behind the back horizon glass, that they may be used with either; therenbsp;are three of these glasses of different degrees of darkness; thenbsp;lightest or palest I do imagine will be of use in taking the sun�s altitude when the horizon appears glaring, which I believe often happensnbsp;by the reflection of the sea.

If these additions and alterations should be thought to be real improvements, which I cannot doubt. Sir, if they are honoured with your approbation, I hope they may serve in conjunction with thosenbsp;improvements you have made yourself in respect to the obviating anynbsp;possible errors in the parallelism of the planes of the index glass, and

in regard to the adjustment of the telescope parallel to the plane of the quadrant, to extend the use of this most valuable nautical instrument, and to add to the exactness of the celestial observations takennbsp;with it to determine the longitude at sea. But of these particulars Inbsp;need say no more, since you are, without doubt, in every respect,nbsp;the properest person to give an account of them.

peter Dollond.

Remarhs on the Hadley's Quadrant, tending prin~ cipallij to 7'emove the Difficulties which havenbsp;hitherto attended the Use of the Dack-observation,nbsp;and to obviate the Errors that might arise ffromnbsp;a Want of Parallelism in the two Surfaces ofnbsp;the Index-Glass. By Nevil Maskelyne, P.R.S.nbsp;Astronomer Royal.

Th� back-observation with Hadley�s quadrant being founded on the same principles, and in theory, equally perfect with the fore observation, and being at the same time necessary to extend the use of thenbsp;instrument up to 180 degrees (it being impracticable to measurenbsp;angles, with any convenience beyond 120 degrees with the foreobservation) it may seem surprizing that it hath not been broughtnbsp;equally into general use, more especially since the method of findingnbsp;the longitude by observations of the moon, has been practised at seanbsp;for some years past; since this method would receive considerable

advantage from the use of the back-observation In taking distances of the sun and moon between the first and last quarter, could suchnbsp;observations be as much depended upon as the fore-observation. Thenbsp;causes of this seem to have been principally these two, the difficultynbsp;of adjusting the back-horizon-glass, and the want of a method ofnbsp;directing the sight parallel to the plane of the quadrant. The back-horizon-glass, like the fore-one, requires two adjustments:�the first,nbsp;or common one, disposes it at right angles to the index glass, whennbsp;the index stands at (O) upon the arch; which is usually performed bynbsp;setting (o) of the index of the arch of the quadrant by double thenbsp;dip of the horizon of the sea, and then holding the quadrant verticalnbsp;with the arch downwards, and turning the back-horizon-glass about,nbsp;by means of its lever or perpetual screw, till the reflected back-horizonnbsp;appears to coincide with the fore-horizon seen directly. But thisnbsp;operation is so difficult in practice with the back-horizon-glass whollynbsp;silvered, except a small transparent slit in the middle, as it has beennbsp;usually made, that few (if any) persons have ever received proper satisfaction from it. If the back-horizon-glass was silvered in everynbsp;respect like the fore-horizon-glass (which it ought to be) the uppernbsp;part being left unsilvered, and a telescope was applied to it, perhapsnbsp;this adjustment might be rendered somewhat easier and more exact;nbsp;but it could not even thus be made so exact as the adjustment of thenbsp;fore-horizon-glass may, by making use of the sun�s limbs.

The second adjustment of the back-horizon-glass, in the common construction of the quadrant, is still more troublesome, since it cannotnbsp;be executed without setting the index 00 degrees off the arch, in order to place the index-glass parallel to the back-horizon-glass; when

this adjustment may be performed in the same manner as the corresponding adjustment of the fore-horizon-glass. But the bending of the index, that follows the setting it off the arch, is a very disagreeable circumstance, having a tendency, especially on board of ship, tonbsp;expose both the index and centre work to damage; and may even,nbsp;without extraordinary precautions taken by the instrument maker innbsp;placing the plane of the index-glass exactly according to the lengthnbsp;of the index, disturb its perpendicularity to the plane of the quadrant:nbsp;on thes� accounts it would be much better if this adjustment of thenbsp;back-horizon-glass could be performed, like those of the fore-horizon-gldss, with the index remaining upon the arch of the quadrant.nbsp;Fortunately, this desideratum has been lately etFected by an ingeniousnbsp;contrivance invented by Mr. Dollond, which he has given an accountnbsp;of in a letter addressed to me¹, which I have presented to this Society, by means of an additional index applied to the back-horizon-glass; whereby both the adjustments may be made by thenbsp;same observations and with nearly the same exactness as those of thenbsp;fore-horizon-glass-for a further knowledge of which see the accountnbsp;itself.

Besides the difficulty of adjusting the back-horizon-glass, the want of a method of directing the line of sight parallel to the planenbsp;of the quadrant has proved also a considerable obstacle to the use ofnbsp;the back-observation: this will easily appear from the following proposition, that the error of the angle measured arising from any smallnbsp;deviation of the visual ray from a parallelism to the plane of the quad-

yzi

rant, is to twice an arch equal to the verse-sine of the deviation, as the tangent of half the angle measured by the quadrant is to radius,nbsp;very nearly. Thus a deviation of 1� in the line of sight, will produce an error of about l' in measuring an angle of 90�, whether bynbsp;the fore or back-observation ; but the same deviation will produce annbsp;error of 4' in measuring an angle of 130�, of 6' in taking an anglenbsp;of 160�, and 12' in taking an angle of 170�. Hence a prettynbsp;exact adjustment of the line of sight, or axis of the telescope,nbsp;is requisite in measuring large angles, such as those are taken by thenbsp;back-observation: and therefore a director of the sight ought by nonbsp;means to be omitted in the construction of the instrument (as itnbsp;commonly has been since Mr. Hadley�s time, though recommendednbsp;by him), except a telescope be made use of, which, if rightly placed,nbsp;answers the same purpose better, especially in observing the distancenbsp;of the moon from the sun between the first and last quarter. Thenbsp;director of the sight may be placed exact enough by construction ;nbsp;but the telescope cannot, and Mr. Hadley, not having been awarenbsp;of the importance of an exact position of it, has accordingly givennbsp;no directions for the placing of it. I shall therefore endeavour tonbsp;supply this defect in the following remarks.

In the first place, I would by all means recommend an adjusting piece to be applied to the telescope, whereby its axis may be broughtnbsp;parallel to the plane of the quadrant; in the next place, the back-horizon-glass ought to be silvered in the same manner as the forehorizon-glass ; and thirdly, two thick silver wires should be placednbsp;within the eye-tube in the focus of the eye-glass parallel to onenbsp;another, and to the plane of the quadrant. If they were put at such

a distance as to divide the diameter of the field of view into three equal parts, it might be as convenient as any other interval. In thisnbsp;manner wires were placed in the telescope by Mr. Hadley, as appearsnbsp;by his accountof the instrument in Philosophical Transactions, No. 420.nbsp;These wires are to be adj usted parallel to the plane of the quadrant, bynbsp;turning the eye-tube round about which contains the wires, till theynbsp;appear parallel to the plane of the quadrant. The axis of the telescope, by which is meant the line joining the centre of the object-glassnbsp;and the middle point between the two wires, is to be adjusted parallelnbsp;to the plane of-the quadrant by either of the two following methods.

Method I.�When the distance of the moon from the sun is greater than 90 degrees, by giving a sweep with the quadrant andnbsp;moving the index, bring the nearest limbs to touch one another atnbsp;the wire nearest the plane of the quadrant. Then, the index remaining unmoved, make the like observation at the wire farthest fromnbsp;the plane of the quadrant; and note whether the nearest limbs are innbsp;contact as they were at the other wire: if they are, the axis of thenbsp;telescope is parallel to the plane of the quadrant: but if they are not,nbsp;it is inclined to the same, and must be corrected as follows. If thenbsp;nearest limbs of the sun and moon seem to lap over one another atnbsp;the wire farthest from the plane of the quadrant, the object end ofnbsp;the telescope is inclined from the plane of the quadrant, and must benbsp;altered by the adjustment made for that purpose: but, if the nearestnbsp;limbs of the sun and moon do not come to touch one another at thenbsp;wire farthest from the plane of the quadrant, the object end of thenbsp;.telescope is inclined towards the plane of the quadrant, and must benbsp;altered by the adjustment accordingly. Let these operations be re-

peated until the observation is the same at both the parallel wires, and the axis of the telescope will be adjusted parallel to the planenbsp;of the quadrant. In like manner, the axis of the telescope may benbsp;also adjusted parallel to the plane of the quadrant for the fore-observation.

Method II.�Set the index to (o) and hold the plane of the quadrant parallel to the horizon of the sea, with the divided arch upwards, thenbsp;two wires being parallel to, and including both the direct fore-horizon,nbsp;and the reflected back-horizon, between them. Raise or lower thenbsp;plane of the quadrant until the direct and reflected horizons coincidenbsp;together: if the coincidence happens in the middle between the twonbsp;wires, or rather, to be more exact, above the middle by such a part ofnbsp;the field of view as answers to the number of minutes in the depression of the horizon (which may be easily estimated if the angularnbsp;interval of the wires be first found by experiment, in manner hereafter mentioned) the axis of the telescope is parallel to the plane ofnbsp;the quadrant; but if it does not, the line of sight is inclined to thenbsp;plane of the quadrant, and must be corrected as follows. If the directnbsp;and reflected horizons, when they coincide, appear higher above thenbsp;middle between the wires, than what the quantity of the depressionnbsp;of the horizon amounts to, the object end of the telescope is inclinednbsp;from the plane of the quadrant, and must be altered by the adjustment made for that purpose; but if the two horizons appear tonbsp;coincide in a lower part of the field of the telescope, the object endnbsp;of the telescope is inclined towards the plane of the quadrant, andnbsp;must be altered by the adjustment accordingly. Repeat these operations till the two horizons appear to coincide above the middle between

the two wires, by the quantity of the depression of the horizon, and the axis of the telescope will be adjusted parallel to the plane of the quadrant. In order to find the angular interval between the wires, hold thenbsp;quadrant perpendicular to the horizon, as in observing altitudes ; andnbsp;turn about the eye-tube with the wires until they are parallel to, and in-'elude the direct fore-horizon and reflected back-horizon between them.nbsp;Move the index from (O) along the divided arch, at the same timenbsp;raising or lowering the telescope by the motion of the quadrant untilnbsp;the direct horizon appears to coincide with the upper wire, and thenbsp;reflected back-horizon with the lower wire; the number of degreesnbsp;and minutes shown upon the arch, increased by double the depressionnbsp;of the horizon, will be the angular interval of the wires ; its proportion to the depression of the horizbn will be therefore known; andnbsp;hence the space in the field of the telescope answering to the depression of the horizon, may be easily estimated near enough fornbsp;adjusfing the axis of the telescope in the manner before mentioned.nbsp;The first of the two methods here given for adjusting the position ofnbsp;the telescope will probably be found most convenient; and the greaternbsp;the distance of the sun and moon is, the more nearly may the adjustment be made, because the same deviation of the axis of thenbsp;telescope will cause a greater error.

The telescope should be fixed by the instrument-maker so as to command a full field of view when the instrument is placed at 90�nbsp;if the instrument be an octant, or 120� if it be a sextant; becausenbsp;the index-glass then stands more oblique with respect to the incidentnbsp;and reflected rays, and* consequently the field of view of the telescopCjnbsp;as far as it depends upon the index-glass, will be more contracted

than in any other position of the index; but if there is a fair field of view in this case, there necessarily must be so in every other positionnbsp;of the index.

The two parallel wires will be very useful on many occasions, as well in the fore as the back-observation. In taking the altitude ofnbsp;the sun, moon, or star, direct the sight towards the part of thenbsp;horizon underneath, or opposite to the object, according as younbsp;intend to observe by the fore or back-observation, and hold thenbsp;quadrant that the wires may constantly appear perpendicular to thenbsp;horizon, and move the index till you see the object come downnbsp;towards the horizon in the fore-observation, or up to it in thenbsp;back-observation, .and turn the instrument in order to bring thenbsp;object between the wires; then move the index- till the sunnbsp;or moon�s limb, or the star touch the horizon. The nearernbsp;the object is brought to an imaginary line in the middle betweennbsp;the wires (it is indifferent what part of the line it is broughtnbsp;to) and the truer the wires are kept perpendicular to the horizon,nbsp;the more exact will the observation be. In the fore-observation, thenbsp;object appears in its real position; but in the back-observation, thenbsp;object being brought through the zenith to the horizon, the realnbsp;upper-limb will appear the lowest; and the contrary. Either limbnbsp;of the sun may be used in either observation; but it will be mostnbsp;convenient in general to make the sun appear against the sky, and notnbsp;against the sea; and then the objects appearing inverted through thenbsp;telescope, the sun will appear lowest, and the horizon highest. Thenbsp;observed altitude is to be corrected for dip, refraction, and sun�snbsp;semi-diameter, as usual.

In taking the distance of the nearest limbs of the sun and moon, whether by the fore or back-observation, having first set the indexnbsp;to the distance nearly, by the help of the Nautical Almanac, andnbsp;brought the moon to appear anywhere on or near the diameter of thenbsp;field of view of the telescope, which bisects the interval between thenbsp;wires, give a sweep to the quadrant, and the sun and moon will passnbsp;by one another; if in this motion the nearest limbs, at their nearestnbsp;approach, just come to touch one another, without lapping over, onnbsp;or near any part of the diameter of the field of the telescope whichnbsp;bisects the interval between the wires, the index is rightly set; but ifnbsp;the nearest limbs either do not come to meet, or lap over one another,nbsp;alter the index, and repeat the observation till the nearest limbs comenbsp;to touch one another properly. This method of observing will benbsp;found much more easy and expeditious than without the wires, sincenbsp;in that case it would be necessary to make the limbs touch very nearnbsp;the centre of the telescope, but here it is only necessary to makenbsp;them do so anywhere on or near the diameter of the field of thenbsp;telescope which bisects the interval between the two wires.

;It may not be amiss here to make some remarks on the rules that have been usually given for observing the sun�s altitude, both with thenbsp;fore and back-observation, which have all been defective, and to pointnbsp;out the proper directions to be followed, when a telescope is not usednbsp;-with two parallel wires to direct the quadrant-perpendicular to thenbsp;horizon, and to shew the principles on which these directions arenbsp;founded.

Observers are commonly told, that in making the fore-observation they should move the index to bring the sun down to the part of thenbsp;horizon directly beneath them, and turn the quadrant about upon thenbsp;axis of vision; and when the sun touches the horizon at the lowestnbsp;part of the arch described by them, the quadrant will shew thenbsp;altitude above the visible horizon. I allow that this rule would benbsp;true, if a person could by sight certainly know the part of the horizon exactly beneath the sun; but, as this is impossible, the preceptnbsp;is incomplete. Moreover, in taking the sun�s altitude in or near thenbsp;zenith, this rule intirely fails, and the best observers advise to holdnbsp;the quadrant vertical, and turn one�s self about upon the heel, stopping when the sun glides along the horizon without cutting it: and itnbsp;is certain that this is a good rule in this case, and capable with care ofnbsp;answering the intended purpose. We have thus two rules for thenbsp;same thing, which is a proof that neither of them is an universal one,nbsp;or sufficient in all cases alone.

In taking the back-observation, observers have been advised either to turn the quadrant about upon the axis of vision, or, holding thenbsp;quadrant upright, to turn themselves about upon the heel, indifferently.nbsp;The true state of the case is this; that, in taking the sun�s altitude,nbsp;whether by the fore or back-observation, these tw'o methods must benbsp;combined together; that is to say, the observer must turn the quadrant about upon the axis of vision, and at the same time turn himselfnbsp;about upon his heel, so as to keep the sun always in that part of thenbsp;horizon-glass which is at the same distance as the eye from the planenbsp;of the quadrant: for, unl^ess the caution of observing the objects innbsp;the proper part of the horizon-glass be attended to, it is evident the

angles measured cannot be true ones. In this way the,reflected sun will: describe an arch of a parallel circle round the true sun, whose convexnbsp;side will be downwards in the fore-observation, and upwards in thenbsp;back-observation, and consequently, when, by moving the index, thenbsp;lowest point of the arch in the fore-observation, or the uppermostnbsp;point of the arch in the back-observation, is made to touch the horizon, the quadrant will stand in a vertical plane, and the altitude abovenbsp;the visible horizon will be properly observed.

The reason of these operations may be thus explained:�the image of the sun being always kept in the axis of vision, the index will always show on the quadrant the distance between the sun and anynbsp;object seen directly which its image appears to touch; therefore, asnbsp;long as the index remains unmoved, the image of the sun will describe an arch everywhere equidistant from the sun in the heavens,,nbsp;and consequently a parallel circle about the sun, as a pole; such anbsp;translation of the sun�s image can only be produced by the quadrantnbsp;being turned about upon a line drawn from the eye to the sun, as annbsp;axis; a motion of rotation upon this line may be resolved into two,nbsp;one upon the axis of vision, and the other upon a line on the quadrant perpendicular to the axis of vision; and consequently a propernbsp;combination of these two motions will keep the image of the sunnbsp;constantly in the axis of vision, and cause both jointly to run over anbsp;parallel circle about the sun in the heavens ; but when the quadrant isnbsp;vertical, a line thereon perpendicular to the axis of vision becomes anbsp;vertical axis; and, as a small motion of the quadrant is all that isnbsp;wanted, it will never differ much in practice from a vertical axis;nbsp;therefore the observer, by properly combining and proportioning two

tnotions, one of the quadrant upon the axis of vision, and the other of himself upon his heel, keeping himself upright (which gives thenbsp;quadrant a motion upon a vertical axis) will cause the image of thenbsp;sun to describe a small arch of a parallel eircle about the sun in thenbsp;heavens, without departing considerably from the axis of vision.

If it should be asked, why the observer should be direeted to perform two motions rather than the single one equivalent to them on a linenbsp;drawn from the eye to the sun as an axis, I answer, that we are not capable, while looking towards the horizon, of judging how to turn thenbsp;quadrant about upon the elevated line going to the sun as an axis, bynbsp;any other means than by combining the two motions above-mentioned,nbsp;so as to keep the sun�s image always in the proper part of the horizon-glass. When the sun is near the horizon, the line going from thenbsp;eye to the sun will not be far removed from the axis of vision; andnbsp;consequently the principal motion of the quadrant will be performednbsp;on the axis of vision, and the part of the motion made on the verticalnbsp;axis will be but small. On the contrary, when the sun is near thenbsp;zenith, the line going to the sun is not far removed from a verticalnbsp;line, and consequently the principal motion of the quadrant will benbsp;performed on a vertical axis, by the observer�s turning himself about,nbsp;and the part of the motion made on � the axis of vision will be butnbsp;small. In intermediate altitudes of the sun, the motions of the quadrant on the axis of vision and on a vertical axis will be more equallynbsp;divided. Hence appears the reason of the method used by the bestnbsp;observers in taking the sun�s altitude when near the zenith by holding the quadrant vertical and turning about upon the heel, and the

As it may conduce to the setting this matter in a still clearer light, I shall here describe in order the several rrlotions that will be given tonbsp;the reflected image, by turning the quadrant about upon the axis ofnbsp;vision, a vertical axis, or the line drawn from the eye to the sun,nbsp;successively.

I. nbsp;nbsp;nbsp;If the quadrant is turned about upon the axis of vision, thenbsp;same being directed to the point of the horizon exactly beneathnbsp;or opposite the sun, the image of the sun will move from rightnbsp;to left, or from left to right, across the horizon-glass, the samenbsp;way as the arch of the quadrant is carried, both in the fore andnbsp;back-observations, with a velocity which is to the angular velocitynbsp;of the quadrant as the sine of the sun�s altitude to the radius,nbsp;describing an arch convex downwards in both cases; and whennbsp;the motion of the sun in this arch is parallel to the horizon, thenbsp;quadrant is held truly perpendicular to the horizon, and consequently in a proper position for taking the sun�s altitude. But,nbsp;if the axis of vision be directed to, and turned round a point innbsp;the horizon beside the vertical circle passing through the sun, thenbsp;sun�s image, when its motion is parallel to the horizon, will benbsp;neither in the axis of vision nor the sun�s vertical, but betweennbsp;both; at the same time, the plane of the quadrant will not benbsp;vertical, and the altitude found by bringing the sun�s image tonbsp;touch the horizon will not be the true altitude.

II. nbsp;nbsp;nbsp;If the quadrant be held perpendicular to the horizon, and turned

about upon a vertical axis, or one nearly so, the sun will describe an arch convex downwards in the fore-observation, and upwardsnbsp;in the back-observation, the motion of the sun being the samenbsp;way as the axis of vision is carried in both cases, and being tonbsp;the angular motion of the quadrant, as the verse-sine of the sun�snbsp;altitude to the radius in the fore-observation, but as the verse-sine of the supplement of the sun�s altitude to 180� to the radiusnbsp;in the back-observation. The sun therefore will move slowernbsp;than the axis of vision in the fore-observation, and consequentlynbsp;will be left behind, with respect to the axis of vision, or seem tonbsp;move backwards; and the sun will move quicker than the axis ofnbsp;vision in the back-observation, or will seem to get before it.nbsp;When the motion of the sun in this arch is parallel to the horizon,nbsp;th� plane of the quadrant coincides with the vertical circle passingnbsp;through the sun, and consequently the quadrant is in a propernbsp;position for taking the sun�s altitude. But if the quadrant benbsp;held a little deviating from the perpendicular position to the horizon, and turned about upon an axis, either vertical or onlynbsp;nearly so, the arch described by the sun apparently will cut thenbsp;horizon, but will never move parallel to it, and consequently thenbsp;quadrant will not be brought into a proper position for observingnbsp;the sun�s altitude.

III. If the quadrant be turned on the line going to the sun as an axis, the reflected sun will be kept constantly in the axis of vision,nbsp;and will describe an arch of a parallel circle about the real sun,nbsp;with a velocity which is to the angular motion of the quadrant,nbsp;as the sine of the sun�s altitude is to the radius; and when the

motion of the reflected sun is parallel to the horizon, the quadrant is vertical.

Hence naturally arise the three methods of taking an altitude, which have been mentioned before. In the first, the axis of vision isnbsp;supposed always directed to one and the same part of the horizon,nbsp;namely, that which is in the sun�s vertical. In the second, the observer is required to hold the quadrant truly vertical, and to turnnbsp;himself upon a vertical axis; but it is evident neither of these motionsnbsp;can be accurately performed. In the third method, the observer isnbsp;only required to move both himself and the quadrant, so as to keepnbsp;the sun always in or near the axis of vision, which may be performednbsp;very well, because the axis of vision is a visible and certain directionnbsp;for it. One exception, however, should be made to this general rule,nbsp;namely, in taking the sun�s - altitude when very lov/, by the back-observation : in which case it will be best to use the second method,nbsp;or else to hold the quadrant perpendicular by judgment; which willnbsp;be much facilitated by using a telescope containing wires in its focusnbsp;parallel to the plane of the quadrant, as described in p. 103 of thisnbsp;Appendix: for, in this case, the perpendicular position of the quadrant cannot be attained so near by the method of turning thenbsp;quadrant on a line going to the sun as an axis, as it can by any othernbsp;method.

It remains to treat of the errors which may arise from a defect of parallelism in the two surfaces of the index-glass, and to point out thenbsp;means of obviating them in the celestial observations. It is wellnbsp;known, that if a pencil of parallel rays falls upon a glass whose two

surfaces are inclined to one another, and some of the rays are reflected at the fore-surface, and others passing into the glass and suffering anbsp;reflection at the back-surface and two refractions at the fore-surfacenbsp;emerge again from the glass, these latter rays will not be parallel tonbsp;those reflected at the fore-surface, as they would have been if thenbsp;surfaces of the glass had been parallel, but will be inclined to thenbsp;same. I find that the angle of their mutual inclination, which maynbsp;be called the deviation of the rays reflected from the back-surface,nbsp;will be to double the inclination of the surfaces of the glass (which isnbsp;here supposed to be but small), as the tangent of the angle of incidence out of air into glass, is to the tangent of the angle of refraction.nbsp;Hence, in rays falling near the perpendicular, the deviation will benbsp;about three times the inclination of the surfaces; and if the anglesnbsp;of incidence be 50�, 6o�, 70�, 80� or 85�, the deviations of the reflected rays will be about 4, 5, 7j 13, or 20 times the inclination ofnbsp;the surfaces, respectively. Had the deviation been the same at allnbsp;incidences of the rays on the index-glass, no error would have beennbsp;produced in the observation; because the course of the ray wouldnbsp;have been equally affected in the adjustment of the instrument, as innbsp;the observation. But, from what has been just laid down, this is farnbsp;from being the case, the deviation increasing according to the obliquity with which the rays fall upon the index-glass; so that in verynbsp;oblique incidences of the rays, such as happen in measuring a largenbsp;angle by the fore -observation or a small angle by the back-observation,nbsp;the least defect in the parallelism of the planes of the two surfaces ofnbsp;the index glass may produce a sensible error in the observation.

thickest or thinnest edge of the index-glass, or, to express the same thing in other words, the common section of tlie planes of thenbsp;surfaces of the index-glass stands perpendicular to the plane of thenbsp;quadrant; but, if the common section of the planes is inclined tonbsp;the plane of the quadrant, the error arising from the defect of thenbsp;parallelism of the surfaces will be lessened in the proportion of thenbsp;sine of the inclination to the radius; so that at last, when thenbsp;common section becomes parallel to the plane of the quadrant, thenbsp;error entirely vanishes. For this reason : Mr. Hadley very properlynbsp;directed the thickest and thinnest edges of the index-glass to be placednbsp;parallel to the plane of the quadrant. But as it may well be questioned whether this care is always taken by the instrument-maker, andnbsp;it cannot be supposed that the glasses can be ground perfect parallelnbsp;planes, it would certainly be an advantage acquired to the instrument,nbsp;could the error arising from a want of parallelism of the planes benbsp;removed in whatever position the common section of the planesnbsp;should be placed with respect to the plane of the quadrant. This willnbsp;be effected for celestial observations, if the upper part of the index-glass be left unsilvered on the back, and made rough and blacked, thenbsp;lower part of the glass being silvered as usual, which must be coverednbsp;whenever any celestial observations are made. Then, if the telescope be sufficiently raised above the plane of the quadrant, it isnbsp;evident that the observations will be made by the rays reflected fromnbsp;the fore-surface of the upper part of the index-glass, and consequently,nbsp;if the quadrant be adjusted by making use of the same part of thenbsp;index-glass, the observations will be true, w'hether the two surfaces ofnbsp;the index-glass be parallel planes or not. The sun or moon may

be thus observed by reflection from the unsilvered parts of the index-glass and horizon-glasSj so that a paler darkening glass will suffice, and they will appear much distincter than from an index-glass whollynbsp;silvered with a deep darkening glass; for although the surfaces of anbsp;glass may be parallel, yet there always arises some little confusion fromnbsp;the double reflection. Neither will the moon appear too weak by twonbsp;unsilvered reflections, even when her crescent is very small, exceptnbsp;she should be hazy or clouded; and then the light may be increasednbsp;by lowering the telescope so as to take in part of the silvered reflectionnbsp;of the index-glass, which in this case must be uncovered: the same isnbsp;also to be understood with respect to the sun, should his light be toonbsp;much weakened by haziness or thin clouds. The horizon-glassesnbsp;should be adjusted, or the error of adjustment found by the sun ornbsp;moon; the first will be in general the best object for the purpose;nbsp;and, as the sun or moon seen directly through the unsilvered part ofnbsp;the horizon-glass will be much brighter than the image of the samenbsp;seen by two unsilvered reflections, it must be weakened by a darkening glass placed beyond the horizon-glass, the reflected image beingnbsp;farther weakened, if necessary, by a paler darkening glass placed innbsp;the usual manner between the index-glass and the horizon-glass.

If a quadrant was designed principally for taking the distance of the moon from the sun and fixed stars, and was not wanted for observing terrestrial angles, it would be the best way to have none ofnbsp;the glasses silvered, but to leave the horizon-glasses intirely transparent, and to put a red glass for an index-glass of the same matternbsp;with the darkening glasses, which would reflect light from the foresurface only.

The sun�s altitude might also be obsen^ed with this instrument, either by the fore or back-observation; and the altitude of the moonnbsp;might be taken with it in the night. But the altitudes of stars couldnbsp;not be observed with it, nor the moon�s altitude in the day time, whichnbsp;would however be no great inconvenience, as these observations mightnbsp;be well enough supplied by common quadrants.

The following rules for the size of the glasses and the silvering them, and the height of the telescope may be of use. The indexnbsp;glass and two horizon-glasses should be all of equal height, and evennbsp;with one another in height both at top and bottom. The telescopenbsp;should be moveable parallel to itself nearer to or farther from thenbsp;plane of the quadrant, and the range of its motion should be suchnbsp;that its axis when at the lowest station should point about -Po-th of annbsp;inch low'er than the top of the silvering of the horizon-glasses, andnbsp;when at the highest station should point to the height of the middlenbsp;of the unsilvered part of the index-glass. The height of the glasses,nbsp;and the quantity of parts silvered and parts unsilvered, should varynbsp;according to the aperture of the object-glass, as in the following table ; where the first column of figures shews the dimensions in partsnbsp;of an inch answering to an aperture of the object-glass of -^ths ofnbsp;an inch in diameter; the second column what answer to an aperturenbsp;of the object-glass ofnbsp;nbsp;nbsp;nbsp;of an inch in diameter; and the third,

what are suitable to ah aperture of the object-glass of T^ths of an inch in diameter.

Diameter of aperture of object-glasss .....

Height of glasses ...........................

Height of silvered part of index glass.....

Height of unsilvered part of ditto ........

Height of silvered part of horizon-glasses Height of unsilvered part of ditto ........

1,37

0,77

0,60

0,42

0,95

If the telescope has a common object-glass, the first aperture of -fVths of an inch will be most convenient; but if it has an achromaticnbsp;object-glass, one of the other apertures of ornbsp;nbsp;nbsp;nbsp;of an inch,

will be most proper. The field of view of the telescope should be 5 or 6 degrees, and the objects should be rendered as distinct as possiblenbsp;throughout the whole field, by applying two eye-glasses to the telescope. The breadth of the glasses should be determined as usual,nbsp;according to the obliquity with which the rays fall on them and thenbsp;aperture of the object-glass.

I shall conclude this paper with some easy rules for finding the apparent angular distance between any two near land objects by thenbsp;Hadley�s quadrant.

To find the angular distance between two near objects by the foreobservation. Adjust the fore-horizon-glass by the object intended to be taken as the direct-object; and the angle measured by the fore-observation on the arch of the quadrant between this object and anynbsp;other object seen by reflection will be the true angle between themnbsp;as seen from the centre of the index-glass. But, if the quadrant benbsp;already well adjusted by a distant object, and you do not chuse to alternbsp;it by adjusting it by a near one, move the index, and bring the image

of the near direct object to coincide with the same seen directly, and the number of minutes by which (O) of the index stands to thenbsp;right hand of (O) of the quadrant upon the arch of the excess is thenbsp;correction, which added to the angle measured by the arch of thenbsp;quadrant between this direct object and any other object seen by reflection will give the true angular distance between them reduced tonbsp;the centre of the index.

It is supposed that the horizon-glass is truly adjusted; if it is not, let it be so. Observe the distance of the objects by the back-observation, and take the supplement of the degrees and minutes standingnbsp;upon the arch to 180 degrees, which call the instrumental angularnbsp;distance of the objects; this is to be corrected as follows. Keep thenbsp;centre of the quadrant or index-glass in the same place as it had innbsp;the foregoing observation, and observe the distance between the nearnbsp;object, which has been just taken as the direct object, and some distant object, twice; by making both objects to be the direct andnbsp;reflected ones alternately, holding the divided arch upwards in onenbsp;case and downwards in the other, still preserving the place of the centre of the quadrant. The difference of these two observations willnbsp;be the correction, which added to the instrumental angular distance,nbsp;found as above in the first observation between the first object andnbsp;any other object seen by reflection, will give the true angular distancenbsp;between them reduced to the centre of the index glass.

But if you should happen to be in a place where you cannot command a convenient distant object, the following method may be used.

The back-horizon-glass being adjusted, find the instrumental angular distance between the objects; this is to be corrected by means of the following operations. Set up a mark at any convenient distance opposite or nearly so to the object which has been taken as thenbsp;direct object; and looking at the direct object move the index of thenbsp;quadrant, and bring the image of the mark to coincide with the direct object, and read off the degrees and minutes standing on thenbsp;arch of the quadrant, which substract from 180 degrees, if (O) ofnbsp;the index falls upon the quadrantal arch; but add to 180 degrees, ifnbsp;it falls upon the arch of excess; and you will have the instrumentalnbsp;angular distance of the object and mark. Invert the plane of thenbsp;quadrant, taking care at the same time not to change the place of itsnbsp;centre, and looking at the same direct object as before, move the index of the quadrant, and bring the image of the mark to coincidenbsp;again with the direct object, and read off the degrees and minutesnbsp;standing on the arch, and thence also find the instrumental angularnbsp;distance of the object and mark. Take the sum of this and the former instrumental angular distance; half of its difference from 300�nbsp;will be the correction, which added to the instrumental angular distance first found between the same direct object and the other objectnbsp;seen by reflection will give the true angular distance between themnbsp;reduced to the centre of the index-glass.

It is to be observed, that if the mark be set up at the same distance from the quadrant as the direct object is, there will be no occasion tonbsp;invert the plane of the quadrant, but the observer need only make

the image of the mark coincide with the direct object, then turn himself half round, and now taking the mark for the direct object cause, the image of the former direct object to coincide with the mark, thenbsp;divided arch of the quadrant being kept upwards, and the place ofnbsp;the centre of the quadrant remaining also the same in both cases:nbsp;half the difference of the sum of the two instrumental angles fromnbsp;360� will be the correction of the adjustment as before.

Should only one of the objects be near, and the other remote (that is to say, half a rnile distant or more) let the distant object be takennbsp;for the direct one, and the near object for the reflected one; and thenbsp;true distance of the objects as seen from the centre of the index-glassnbsp;will be obtained without requiring any correction, whether it be thenbsp;back or fore-observation that is made use of; only observing, as usual,nbsp;to take the supplement of what is shown upon the arch to 180� innbsp;the back-observation.

An Account ^ an Apparatus applied to the Equatorial Instrument Jhr correcting the Errorsnbsp;arising Jrom the R^raction in Altitude- Bynbsp;Mr. Peter Dollond, Optician; communicated tonbsp;the Royal Society hy the Astronomer Royal.

The refraction of the atmosphere occasions the stars or planets to appear higher above the horizon than they really are; therefore, anbsp;correction for this refraction should be made in a vertical direction tonbsp;the horizon.

The equatorial instrument is so constructed, that the correction cannot be made by the arches or circles which compose it, when thenbsp;star, amp;c. is in any other vertical arch except that of the meridian;nbsp;because the declination arch is never in a vertical position but whennbsp;the telescope is in the plane of the meridian.

To correct this error, a method of moving the eye-tube which contains the wires of the telescope in a vertical direction to the horizon has been practised; but as the eye-tube is obliged to be turnednbsp;round in order to move it in that direction, in the different obliquenbsp;positions of the instrument, the wires are thereby put out of theirnbsp;proper situation in every other position of the instrument, exceptnbsp;when it is in the plane of the meridian; for the equatorial wirenbsp;should always be parallel to the equator, that the star in passing overnbsp;the field of the telescope may move along with it, otherwise one cannot judge whether the telescope be set to the proper declination,nbsp;except at the instant the star is brought to the intersection of thenbsp;wires, which is only a momentary observation.

The method I have now put in practice for correcting the refraction of the atmosphere is, by applying two lenses before the object-glass ofnbsp;the telescope; one of them convex, and the other concave; bothnbsp;ground on spheres of the same radius, which in those I havenbsp;made is thirty feet. The convex lens is round, of the same diameternbsp;as the object-glass of the telescope, and fixed into a brass frame ornbsp;apparatus, which fits on to the end of the telescope. The concavenbsp;lens is of the same width, but nearly two inches longer than it isnbsp;wide, and is fixed in an oblong frame, which is made to slide on thenbsp;frame that the other lens is fixed into, and close to it. These two lensesnbsp;being wrought on spheres of the same radius, the refraction of thenbsp;one will be exactly destroyed by that of the other, and the focalnbsp;length of the object-glass will not he altered by their being appliednbsp;before it: and if the centres of these two lenses coincide with each

other, and also with that of the object-glass, the image of any object formed in the tefescope will not Be moved or suffer any change in itsnbsp;position. But if one of the lenses be moved on the other, in the direction of a vertical arch, so as to separate its centre from that ofnbsp;the other lens, it will occasion a refraction, and the'image will changenbsp;its altitude in the telescope. ' The quantity of the refraction will benbsp;always in proportion to the motion of the lens, so that by a scale ofnbsp;equal parts applied to the brass frame, the lens maybe set to occasionnbsp;a refraction equal to the refraction of the atmosphere in any altitude.nbsp;If the concave lens be moved downwards, that is, towards the horizon,nbsp;its refraction will then be in a cqntrary direction to that of the atmosphere, and the star will appear in the telescope as if no refractionnbsp;had taken place.

There is a small circular spirit level fixed on one side of the apparatus,, which serves to set it in such a position, that the centres of the twonbsp;lenses may be in the plane of a vertical arch. This level is also usednbsp;for adjusting a small quadrant, which is fixed to it,, and divided intonbsp;degrees, to shew the elevation of the telescope when directed to thenbsp;star; then the quantity of refraction answering to that altitude maynbsp;be found by the common tables, and the concave lens set accordingly,nbsp;by means of the scale at the side, which is divided into half minutes,nbsp;and, if required, by using a nonius, may be divided into seconds.

It must be observedj that when a star or planet is but a few degrees above the horizon, the refraction of the atmosphere occasions it to benbsp;considerably coloured. The refraction of the lens acting in a contrarynbsp;direction would exactly correct that colour, if the dissipation of the

rays of light were the same in glass as in air; but as it is greater in glass than in air, the colours occasi�ned by the refraction of the atmosphere will be rather more than corrected by those occasioned bynbsp;the refraction of the lens.

The following is a drawing of the refraction apparatus, which may serve to give a more clear idea of it

.�U

AA. The circular brass tube, which fits on to the end of the telescope. BB. The oblong concave lens in its frame, which slides over the fixednbsp;convex lens.

c. The circular spirit level, which shews when the oblong lens is in a vertical arch.

D. nbsp;nbsp;nbsp;ThcAjuadrant to which the spirit level is fixed, for shewing the

E. nbsp;nbsp;nbsp;The milled head fixed to a pinion, by which the whole apparatus is

turned round on the end of the telescope, in order to set the oblong lens in a vertical arch.

p. Another pinion for setting the quadrant to the angular elevation of the telescope. By means of these two pinions the air bubble must be brought to the middle of the level.nbsp;aa. Is the scale, with divisions answering to minutes and half minutesnbsp;of the refraction occasioned by the concave lens.

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LIFE OF JOHN DOLLOND, F.R.S.

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iK.

4: '

.•

LIFE

JOHN DOLLOND, F.R.S.

With a copious Appendix of alJ the Papers referred to.

1808.

Ij nbsp;nbsp;nbsp;■*■ ' •

1^

LIFE

JOHN DOLLOND, F.R.S.

APPENDIX.

A Letter J^rom Mr. John Dollond to Mr. James Short, F.R S. concerning an Improvement ofnbsp;Refracting Telescopes.

SIR,

John Dollond.

James Short.

SIR,

L. Euler.

IV I V

A Description of a Contrivance Jor measuring small Angles, hy Mr. John Dollond; communicated by Mr. J. Short, F.R S.

SIR,

John Dollond.

37

i.

James Short.

�John Dollond.

Peter Dollond.

63

James Short.

89

SIR,

peter Dollond.

96

1,37

0,95

L,

.�U

A,

FI

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