THE VARIATIONS IN THE PROFILES OF STRONG FRAUNHOFER LINESnbsp;ALONG A RADIUS OF THE SOLAR DISC

J. HOUTGAST

THE VARIATIONS IN THE PROFILES OF STRONG FRAUNHOFER LINESnbsp;ALONG A RADIUS OF THE SOLAR DISC

THE VARIATIONS IN THE PROFILES OF STRONG FRAUNHOFER LINESnbsp;ALONG A RADIUS OF THE SOLAR DISC

PROEFSCHRIFT

TER VERKRIJGING VAN DE GRAAD VAN DOCTOR IN DE WIS- EN NATUURKUNDE AAN DE RIJKSUNIVERSITEIT TE UTRECHT, OP GEZAG VAN DENnbsp;WAARNEMENDEN RECTOR MAGNIFICUS L. VANnbsp;VUUREN, HOOGLERAAR IN DE FACULTEIT DERnbsp;LETTEREN EN WIJSBEGEERTE, VOLGENS BESLUITnbsp;VAN DE SENAAT DER UNIVERSITEIT TEGEN DEnbsp;BEDENKINGEN VAN DE FACULTEIT DER WIS- ENnbsp;NATUURKUNDE TE VERDEDIGEN OP MAANDAGnbsp;22 JUNI 1942, DES NAMIDDAGS TE 3 UUR

DOOR

JAKOB HOUTGAST

GEBOREN TE ASSEN

1942

DRUKKERIJ Fa. SCHOTANUS 6 JENS UTRECHT

Aan de nagedachtenis van mijn Vader Aan mijn Moedernbsp;Aan mijn Vrouw

Wanneer ik bij de voltooiing van dit proefschrift de voorafgaande jaren overzie, waarbij ook mijn studietijd is inbegrepen, dan word ik mij bewust van een gevoel vannbsp;grote dankbaarheid jegens allen, die het mij mogelijk hebben gemaakt het gesteldenbsp;doel te bereiken.

U, Hoogleraren en Oud^Hoogleraren in de Faculteit der Wis- en Natuurkunde, ben ik zeer erkentelijk voor het hoogstaand wetenschappelijk onderwijs, dat ik vannbsp;U heb ontvangen, en dat mij telkens weer te stade komt.

Mijn wetenschappelijke arbeid onder Uw leiding. Hooggeleerde Minnaert, Hooggeachte Leermeester, begon nu reeds bijna tien jaar geleden. Zeer veel heb ik in die tijd van U geleerd, diepe sporen heeft de samenwerking met U in mij achtergelaten,nbsp;niet alleen door de wetenschappelijke en didactische gaven die Gij bezit, maar evenzeernbsp;door de bezielende wijze, waarop Gij in het werk pleegt vóór te gaan. Om U heennbsp;heeft zich een steeds groeiende School, een ware symbiose tussen physica en astronomienbsp;ontwikkeld, waarvan ook dit proefschrift getuigenis aflegt. Met hoeveel spanning ennbsp;vreugde hebben wij deze dag, die een nieuw tijdperk in onze samenwerking op denbsp;Sterrewacht zou inluiden, verbeid. Nu neemt Gij, bij de plechtigheid, die voor onsnbsp;een feest had kunnen zijn, niet de plaats in, waar ik U in mijn verbeelding zo dikwijlsnbsp;heb gezien — een diepe teleurstelling, die ik steeds zal blijven gevoelen.

Het stemt mij tot grote dankbaarheid, dat Gij, Hooggeleerde Rosenfeld, Hooggeachte Promotor, de zo plotseling leeg gekomen plaats hebt willen innemen. Bij de besprekingen over enkele questies betreffende dit proefschrift waren wij reeds nadernbsp;met elkaar in aanraking gekomen, en, wetende dat Gij de astrophysica een warm hartnbsp;toedraagt, hoop ik ook in de toekomst nog meermalen op Uw hulp te mogen rekenen.

Hooggeleerde Pannekoek, Uw uitgebreide kennis van de astrophysica en Uw systematische en kritische behandeling van' haar problemen, waarvan ik op de gemeenschappelijke colloquia der Amsterdamse en Utrechtse astrophysici zoveel hebnbsp;kunnen leren, is mijn wetenschappelijke vorming in hoge mate ten goede gekomen.

Ein Aufenthalt von über einem Jahr an dem Astrophysikalischen Observatorium zu Potsdam bot mir nicht nur die Gelegenheit das Beobachtungsmaterial für diesenbsp;Dissertation mit wertvollen Ergebnissen zu bereichern, er ist auszerdem von gröszternbsp;Bedeutung geworden für meine Ausbildung. Das danke ich an erster Stelle der unge-zwungenen Zusammenarbeit mit Ihnen, Hochgelehrter ten Bruggencate.nbsp;Mehrere Untersuchungen haben wir zusammen einem guten Ende zuführen können,nbsp;und ich werde immer eine angenehme Erinnerung an eine Zeit behalten, in der esnbsp;unser einziges Ziel war, die Kentnisse hinsichtlich des physikalischen Geschehensnbsp;auf der Sonne zu vermehren. Hochgelehrter von KI über, auch Ihrer vielseitigennbsp;Hilfe in oft schwierigen Umstanden, die sowohl für mich, wie auch für meinenbsp;Familie unentbehrlich war, gedenke ich mit Dankbarkeit.

In elk stadium van de bewerking van dit proefschrift, van de waarnemingen tot de drukproeven, heb ik de hulp gehad van mijn Vrouw; haar belangstelling en medelevennbsp;zijn voor mij een grote steun geweest.

INTRODUCTION AND SURVEY OF THE INVESTIGATION

§ 1. Introduction.

The sun is the only star of which the radiation from the various points of its surface can be studied separately. One part of the detailed studynbsp;of the sun’s disc consists in the investigation of the variation in the solarnbsp;radiation arising from a centre-limb shift of the observed point. As thisnbsp;point approaches the limb, the radiation emerges at continually greaternbsp;angles with the normal and originates on the average in continuallynbsp;higher layers of the sun’s atmosphere, providing us thereby with thenbsp;means to obtain some information concerning the variation with depth ofnbsp;various quantities and processes in that atmosphere. From the darkeningnbsp;of the continuous spectrum towards the limb important conclusionsnbsp;have indeed been already drawn.

In order to investigate the variation with depth of the selective properties, we must refer to the Fraunhofer lines which can for variousnbsp;reasons provide the necessary information. In the first place, becausenbsp;the region where they originate varies from one line to another, and innbsp;the second place, because along the intensity-profile of a strong Fraunhofer line the average depth from which the light reaches us variesnbsp;gradually, while, finally, for every frequency within a Fraunhofer line,nbsp;the depth differs whenever the light arrives from points located atnbsp;different distances from the centre of the sun's disc. Let us hope thatnbsp;from observations combining these possibilities for investigating the depth,nbsp;we may reap such a wealth of information as to enable us to determinenbsp;the run with depth of a few of the most important selective properties.

§ 2. Outline of the investigation.

The testing by means of centre-limb observations, of the various conceptions concerning the constitution of the solar atmosphere and thenbsp;processes acting in the formation of the Fraunhofer lines, will be the

more rigorous, the more widely the observational material varies: the fact that previous investigations in this field have not led to any generalnbsp;results, must be largely ascribed to the invariably too scanty observationalnbsp;data used.

In the first place, it is of importance to trace the variation over the complete extent of the line-profile, but in order to do this properly,nbsp;the profiles must be exempt from deformations due to the spectralnbsp;apparatus. That is why only strong lines were examined, the profilesnbsp;of these being only slightly deformed and then only in the inner parts.nbsp;The observational material was obtained partly at Utrecht and partlynbsp;at Potsdam. The instrumental curve for the latter being known i), thenbsp;profiles obtained from it could be corrected for finite resolving power,nbsp;so that for a number of lines the centre-limb variations of the correctednbsp;central intensities have been determined.

In the second place, a suitable model of the sun’s atmosphere will have to account for the observed centre-limb variations of lines belonging tonbsp;different elements and atomic states, and also to explain the graduallynbsp;changing behaviour from the ultra-violet to the infra-red region of thenbsp;spectrum.

Finally, in order to accurately locate the variations over the sun’s disc, it will be necessary to determine the profiles in a fairly large number ofnbsp;points and as these variations become considerable on approaching thenbsp;limb, it is advisable to take these points, more in particular in its immediate neighbourhoud, near to each other and as close up to the limbnbsp;as possible.

In consideration of the above requirements 23 strong Fraunhofer lines were selected belonging to different elements and with wave lenghtsnbsp;between 3800 and 8700 A. The hydrogen lines were excluded, becausenbsp;with them the Stark-effect would give rise to extra complications. Thenbsp;line profiles were determined for 7 or 8 points of the sun’s disc, fromnbsp;the centre up to 0.005 R from the limb.

§ 3., Comparison of the observations with theory.

The way in which the centre-limb variations can be explained is examined in detail in the theoretical part. To this end the observednbsp;results are investigated with the aid of a schematic model of the solarnbsp;atmosphere, comprising the Schuster-Schwarzschild- and the Milne-

A number like this indicates that the reader is to turn to the references (p. Hi) for further information.

Eddington model as extreme cases¹). We shall see that by means of this model we are able to draw important conclusions as regards thenbsp;thickness of the layers in which the various lines originate.

The centre-limb variations of the central intensities of the observed lines can be explained in conformity with A. Unsold’s 2) and B. Ström-gren’s 3) theoretical investigations concerning their formation.

The question as to what extent selective coherent scattering and true selective absorption contribute separately to the formation of thenbsp;lines has been extensively dealt with. It turns out that these two processesnbsp;do not furnish a satisfactory explanation of the observed behaviour ofnbsp;the wings.

It appears, however, to be possible to explain this behaviour by means of non-coherent scattering by disturbed atoms, which, owing to thenbsp;difference of radiation-density in the inner and outer parts of anbsp;Fraunhofer line, causes an exchance of radiation to take place betweennbsp;the wings and the central parts of the line. A more detailed study isnbsp;then made of this exchange, but whether it can occur to the requirednbsp;extent in the case of damping by collisions without energy transfernbsp;(the process, which plays such a prominent part in the formation ofnbsp;the Fraunhofer lines), remains partly a question for theoretical physicsnbsp;to decide.

The conditions prevailing in the sun’s atmosphere are in some respects favourable for the study of non-coherent scattering. These conditionsnbsp;can, however, not be reproduced artificially, but this does not excludenbsp;the carrying out in the laboratory of certain definite experiments, whichnbsp;Would provide much valuable information concerning the scattering ofnbsp;light by disturbed atoms.

1

With this nomenclature I conform to A, Unsold, Physik der Sternatmospharen. Kapitel XII.

OBSERVATIONAL PART

CHAPTER I

OBSERVATIONS

§ 4. Previous observations.

G. nbsp;nbsp;nbsp;E. Hale and W. S. Adams 4) were the first to photograph andnbsp;visually to compare the spectra of the centre and of the limb of the sun’snbsp;disc. In agreement with Hastings’ results from visual observations, theynbsp;stated that the wings of the strong lines disappear for the greater partnbsp;at the limb, whereas they found, on the other hand, that the central partsnbsp;of some of them are strengthened. The former statement has turned outnbsp;to be indeed one of the characteristic features of lines in the limb-spectrum, the latter does not hold any longer for the lines investigatednbsp;by them and can safely be ascribed to the effect of contrast.

To K. Schwarzschild 5) we owe the first photographic-photometric determinations of intensity-profiles of Fraunhofer lines. He investigatednbsp;the H- and the K line of Ca in the centre and at the limb of the sun’snbsp;disc; from the fact that these lines do not vanish at the limb he inferrednbsp;that in the formation of Fraunhofer lines it is selective scattering andnbsp;not selective absorption that plays the most important part.

In 1927 A. Unsold explained the profiles of strong Fraunhofer lines by means of scattering and damping; applying Schuster’s formula,nbsp;he obtained an agreement between theory and observation, satisfactorynbsp;for the time being, as regards the profiles in the centre- and limb spectranbsp;of the H- and the K line 6),measured by Schwarzschild and the D linesnbsp;of Na'^), measured by himself.

H. nbsp;nbsp;nbsp;H. Plaskett®) investigated in particular the centre-limb variationnbsp;of the Mg b triplet, photographed at three different points of the sun’snbsp;disc. He tried to explain this variation with the aid of various modelsnbsp;of the sun’s atmosphere and found that, in this respect, Eddington’s

model for combined absorption and scattering, though giving rise to some difficulties, was the most successful.

Centre-limb variations of the Mg triplet were also observed by G. Righinis), who investigated the lines Mg 5183.6 and Mg 5172.7 atnbsp;six points of the sun’s disc, and by E. Cherrington lo), including anbsp;careful determination of the central intensities, while Righini comparednbsp;also the equivalent widths in the spectra of the centre and of the limbnbsp;of the sun’s disc^i) of some hundred Fraunhofer lines between A 5288nbsp;and A 5472, T. Royds and A. L. Narayan 12) investigated the H- andnbsp;the K line of Ca , the line Ca 4226.7 and the hydrogen lines Ha to HSnbsp;for seven points on the sun’s disc, while Miss M. G. Adam 14)nbsp;examined the behaviour of numerous weak Fraunhofer lines in the spectranbsp;photographed by H. H. Plaskett.

The wings of a few strong lines (H- and K line of Ca , Fe 4045.8 and Ca 4226.7 at six points of the sun’s disc) are the subject of annbsp;investigation by M. Minnaert and the present writer ts)^ wbo did notnbsp;succeed in explaining with the aid of A. Pannekoek’s 16) model of thenbsp;sun’s atmosphere the observed behaviour on the assumption of selectivenbsp;scattering. The observational results from 20 strong Fraunhofer linesnbsp;photographed at the Heliophysical Institute at Utrecht has already beennbsp;communicated by the writer in abbreviated form i'^). These measurements constitute a considerable part of the material on which the presentnbsp;thesis is based.

C. 'W. Allen 18) measured the D lines of Na in the centre and close to the limb of the disc, paying special attention to the central intensities.nbsp;The latest publication dealing with centre-limb variations, that came tonbsp;my knowledge, is the one by D. S. Evans 19), who determined the profilenbsp;of the line Ha in 5 points of the sun’s disc. ¹)

Centre-limb variations in the spectra of the stars can be observed in the case of eclipsing variables, though we are not in a position to obtain,nbsp;as in the case of the sun, the spectra of separate points of the star’snbsp;surface. The various phases yield, each, the integrated spectrum of thenbsp;non-eclipsed part of the principal star, and it will be clear that thenbsp;centre-limb variation deduced from these spectra cannot be so accuratenbsp;as for the sun. With these stars it is in the most favourable case onlynbsp;of the limb that we can obtain a pure spectrum. Photographs of thisnbsp;kind have been taken by R. O. Redman 20), who observed the eclipsing

1

While reading the proofs I received C. D. Shane’s publication concerning the Na D lines

6

variables U Cephei and U Sagittae; his observations will, no doubt, be valuable, once we have understood the centre-limb variations in the casenbsp;of the sun.

It appears from this survey that much work has already been done in the field of centre-limb observations, but we shall see that what is needednbsp;for a satisfactory checking of theory by experiment is a very extensivenbsp;and, above all, homogeneous material.

§ 5. Introductory remarks on the observations on which the present thesis is based.

The distinguishing feature of the observations discussed in the present thesis is the more extensive scale on which they are planned; in the firstnbsp;place by using a greater number of Fraunhofer lines, and in the secondnbsp;place by increasing, if necessary, the number of points on the sun’s disc.nbsp;This second feature is especially important in connection with the peculiarnbsp;run of the centre-limb variations which is not continually in one andnbsp;the same sense from centre to limb, so that it cannot be determined bynbsp;measurements in only a few points.

The number of Fraunhofer lines to be selected is greatly restricted, if one wants to determine the true profile, as any interfering spectralnbsp;apparatus causes a deformation for which the observed profile cannotnbsp;easily be corrected. As the investigation was started with the gratingnbsp;spectrograph of the Heliophysical Institute at Utrecht, possessing onlynbsp;a moderate resolving power, I had to restrict myself to some twenty ofnbsp;the stronger lines in the solar spectrum. The finite resolving power,nbsp;however, affects the inner part of strong lines always to such an extentnbsp;that, even if it should amount for a spectrograph theoretically to 100,000,nbsp;the measured central intensities may very well deviate rathernbsp;considerably from the true ones. For a judicious use of the Utrechtnbsp;measurements, this must be taken into account. For the exposures atnbsp;Potsdam the large grating spectrograph of the Institut fiir Sonnenphysiknbsp;was used, possessing a much higher resolving power and of which,nbsp;moreover, the instrumental curve was determined, so that the observednbsp;central intensities could be corrected for its influence.

In selecting the strong lines, the hydrogen lines were rejected, because their profiles are determined by the linear Stark effect, and are, therefore,nbsp;likely to give rise to extra complications in interpreting the results. Thenbsp;more obvious thing to do was to examine first the other strong lines,nbsp;of wich the wing profiles are determined by damping by collisions

(M. Minnaert and J. Genard 21), A. Unsold 22)^ P, ten Bruggencate and the writer and of which the shape of the profile for large valuesnbsp;of aA, (c= distance from centre of line) is rendered so beautifully bynbsp;Minnaert’s formula 24)^ according to which the depression i(,—t isnbsp;proportional to i/AA2. The lines remaining in this way belong to differentnbsp;elements and to different atomic states and they lie in different parts ofnbsp;the spectrum (see Table la, p. 21), a fortunate variety of which fullnbsp;advantage has been taken for determining the influence of these factorsnbsp;on the centre^limb variations.

The next point to be considered was for which points of the sun s disc the profiles should be determined. Following Prof, Minnaert’snbsp;suggestion, I started with six points, from the centre of the disc tonbsp;0.98 R; in an image of the sun of about 12 cm diameter, the size of thenbsp;one at Utrecht, the latter point lies at only 1.2 mm from the limb. In ournbsp;opinion, this was the extreme position for obtaining with an ordinarynbsp;technique of exposure a spectrum that could still be ascribed to the actualnbsp;point of adjustment itself. To later series of photographs, however, thenbsp;spectrum of the point at 0.995 R was added. From the beginning I wasnbsp;aware of the fact that the reliability of measurements on photographsnbsp;of this point should not be overestimated, for, quite close to the limb,nbsp;the variations in some parts of the profiles are considerable, while, owingnbsp;to scintillation and to unavoidable minute errors in adjusting the sun’snbsp;image, it is in reality a small region round the point 0.995 R, that formsnbsp;the observed spectrum, which, therefore, cannot be accurately ascribed tonbsp;a definite point of the sun’s disc. When, however, it became clear thatnbsp;measurements referring to this point could lend a strong support to thenbsp;explanation of the origin of Fraunhofer lines, I decided to add to thenbsp;observations at Potsdam the one referring to the point at 0.99 R. In anbsp;series, completed in this way, the profiles were determined for 8 points,nbsp;of which the distances from the centre of the sun’s disc are, in termsnbsp;of its radius; 0.00; 0.60; 0.80; 0.90; 0,95; 0.98; 0.99 and,0.995. From thenbsp;mutual location of these points the extent can be clearly seen to whichnbsp;the increase of the variations on approaching the limb has been taken intonbsp;account.

Apart from a series of the Mg b triplet, which was photographed for me by G. F. W. Mulders at Mount Wilson, all the spectra, discussednbsp;in this thesis, were photographed by me at Utrecht and at Potsdam.nbsp;The technique of exposure is radically different in the two places; thenbsp;fact that, nevertheless, the results agree so satisfactorily speaks well for

the reliability of the measurements. I now proceed to the discussion of the two methods of observation separately.

§ 6. The method of observation at Utrecht.

The sun’s image of the Heliophysical Institute at Utrecht ¹) had a diameter of about 12 cm. By a few simple manipulations, which movenbsp;the second of the two coelostat-mirrors round two axes perpendicularnbsp;to each other, the image can be located arbitrarily in the plane of thenbsp;slit of the spectrograph. At its lower end the vertical spectrograph re.stsnbsp;on a steel point; by moving it as a whole, therefore, the slit can benbsp;adjusted in any direction and in any position, that may be required,nbsp;relatively to the sun’s image. Its focal length is 4 m and the grating isnbsp;ruled over a width of 8 cm with 568 lines to the mm. For further detailsnbsp;the reader is referred to the description by W. H. Julius 25).

In all centre-limb exposures the direction of the slit was at right angles to that of the sun’s radius, along which the various photographsnbsp;were taken, so that from each exposure the spectrum was obtained for anbsp;definite distance from the centre of the sun’s disc. Owing to the curvaturenbsp;of the limb, however, the distance slit—limb is already in the point atnbsp;0.98 R no longer constant; as the slit is about 10 mm long, its middlenbsp;is about 0.2 mm farther from the limb than its ends, or, in other words,nbsp;if the middle of the slit is adjusted on 0.98 R, its ends will be adjustednbsp;on 0.984 R. For that reason the upper and lower strips of the spectrumnbsp;were, as a rule, not used in determining the profiles.

The adjustment on the right points was achieved in the following way. The distances of the points from the limb of the sun’s disc were markednbsp;on a mm scale provided with a sharp straight edge at its one end. Thisnbsp;edge was placed accurately above the slit by making its shadow coincidenbsp;with the latter, whereupon the sun’s limb was adjusted on one of thenbsp;marks. The scale was then shifted so as to leave the slit free, the sun’snbsp;limb now coinciding with some arbitrary division of the scale, where itnbsp;was kept during the exposure, by a compensating adjustment, ifnbsp;necessary. Owing to chromatic aberration of the objective, smallnbsp;adjusting errors may have occurred in some parts of the spectrum, as thenbsp;adjusting was performed visually in the light of the sun’s image.

This image was formed in such a way as to be perfectly sharp in

1

Since 1937 this institute is made a part of the observatory “Sonnenborgh” of the university.

the plane of the slit, this being indeed, for points near the limb, an essential requisite for receiving light in the spectrograph only from thenbsp;right distance from the centre. Visually a region was then selected, thatnbsp;Was not perturbed by spots or faculae. In this selection we were alwaysnbsp;successful, as all photographs were taken during the minimum of solarnbsp;activity, and the exposures were then made along a radius in this region.

The slit-width was always in accordance with P. H. van Cittert’s theory 26)^ prescribing in our case 0,03 mm at 4000 A and 0.06 mmnbsp;at 8000 A. The accurate focus was determined by means of preliminarynbsp;photographs of the solar spectrum in the spectral region concerned.

A platina step-reducer of Zeiss with 5 steps of 2 mm width each was placed on the slit; 1 cm above it the mm scale was applied and 2 cmnbsp;above the slit a general reducer was placed, selected in such a way fornbsp;each exposure from a set of reducers (homogeneously blackened photographic plates with transmissive powers ranging from 40 % to 80 %)nbsp;that, taking the darkening towards the limb into account, one couldnbsp;expect all spectra to show, for the same time of exposure, about the samenbsp;degree of blackening. The spectra from the point at 0.98 R were always,nbsp;and those from the point at 0.95 R often, photographed without anynbsp;auxiliary reducer. For that same time of exposure, the spectrum fromnbsp;the point at 0.995 R would have shown a too slight density; for thatnbsp;reason the exposures on this point were made 1 to 2 times as long. Thenbsp;auxiliary reducers were, all of them, tested as to their homogeneity andnbsp;turned out to satisfy this condition to within 1 %. Finally, a colour filternbsp;Was applied 10 cm above the slit to intercept spectral light of othernbsp;orders and scattered light.

In order to ascertain whether any difference occurred in blackening in the direction of the slit, either from the slit-jaws not being exactlynbsp;parallel or from any other cause, we photographed several times withoutnbsp;step-reducer the spectrum of an unperturbed region in the central partnbsp;of the sun’s disc; without any exception the constancy of the blackeningnbsp;in the direction of the slit left nothing to be desired.

In the beginning we rather feared that, during an exposure on the limb, the scattering in the earth’s atmosphere and in the auxiliary reducersnbsp;might cause an appreciable fraction of the so much larger amount ofnbsp;light from the central parts of the sun’s disc to enter the apparatus. Thisnbsp;Was also why we made these exposures with a tangential slit. In ordernbsp;to judge the amount of scattering, a thermo-element was placednbsp;successively on and immediately next to the image of the sun’s disc and

10

the ratio between the intensities was determined. At a distance of 2 mm this ratio turned out to be already less than 0.001, as well for red as fornbsp;blue light, so that entering of any light from parts of the sun more thannbsp;2 mm distant from the points of adjustment can be completely neglected.nbsp;Moreover, these measurements were carried out expressly, when thenbsp;atmosphere showed strong scattering or intense scintillation, whereas thenbsp;centre-limb exposures were made on days with good visibility andnbsp;preferably slight scintillation. An unfortunate complication in thisnbsp;connection is the fact that transparent air and weak scintillationnbsp;practically never coincide. The degree of scintillation was judged fromnbsp;the amplitude of the wave-motion of the sun’s edge and was expressednbsp;in a scale from 0 to 10; for the photographs, actually used, it variednbsp;from 3 to 7.

The exposures were made in the most luminous of the second order spectra of the grating, of which the dispersion amounts to 0.5 mm/A.nbsp;Only the H- and the K line of Ca were photographed in the first order.nbsp;The plates used for the various wave-length regions are given in Tablenbsp;lb. On a single plate, of which the height is 6 cm, there is room for fournbsp;spectra, so that we had to distribute each series over two plates, whichnbsp;were either cut from one piece or were taken from one and the same box.nbsp;The two plates were developed simultaneously. The plates used werenbsp;always backed; if not originally so, they were backed with black papernbsp;stuck on with glycerine. The plates were developed during 7 minutesnbsp;in metol-hydrochinon borax; after being fixed, they were bathed in a 2 %nbsp;HCl-solution, until the gelatine had become completely transparent. Thenbsp;Ilford infra-red plates were hypersensitized with ammonia, the Agfanbsp;infra-rot plates with methylated alcohol.

Originally, the direction of the radius on which the successive points for the exposures were located, was determined for each series ofnbsp;photographs, because it might be that the centre-limb variations along,nbsp;say, the sun’s equator were different from those from the centre towardsnbsp;the sun’s poles. G. Abetti and I. Castelli 27) found, for example, smallnbsp;differences between the limb-spectra at the equator and at the poles.nbsp;It appeared, however, from a comparison between series referring tonbsp;points located quite differently with respect to the sun’s disc, that thesenbsp;deviations were completely negligible compared with the centre-limbnbsp;variations themselves, so that later on no further attention was paidnbsp;to this question.

11

A survey of the centre-limb photographs, actually discussed, is given in Table 1 (p. 21 and 22).

The characteristic curves for the plates were determined from the spectra of the points at 0.00 R and 0.60 R and then checked by thosenbsp;of the points at 0.80, 0.90 and 0.95 R. The spectrum of the point atnbsp;0.98 R is less suitable for the determination of the characteristic curve,nbsp;because, owing to the darkening towards the limb, the illumination ofnbsp;the slit is not homogeneous. In all series the characteristic curves of thenbsp;two plates were so much alike, that we could work with one curve fornbsp;both plates.

The registering of the spectra was carried out by means of a Moll-®icrophotometer. The maximum widths of the slits corresponded to 0.03 A on the plates for photographs of the second order spectrum. The transmission ratio between registrogram and plate was 5Ö or 7; the latternbsp;ratio only being used when, otherwise, the registered spectrum wouldnbsp;leave insufficient room for the continuous background. This was the casenbsp;with the Ca“’ lines and with the ultra-violet lines of Fe and Mg, with thenbsp;exception of Fe 3859.9.

From four or five steps the intensity-profiles were determined, which always agreed within 5 ;% and as a rule still better. A preliminarynbsp;determination of the run of the continuous background in the gaps madenbsp;by the lines was obtained by drawing a straight line through points ofnbsp;the continuous spectrum lying at a great distance from the lines. Thisnbsp;method fails, however, in the case of the H- and the K line; here anbsp;decided curvature occurs and the continuous background was interpolatednbsp;according to the best fitting curve onwards from 100 A away from thenbsp;centres of the H- and the K line; this was done as well for the intensitynbsp;run itself as for that of log intensity, the latter approximating the linearitynbsp;better, as appears from the run of the continuous background at a greatnbsp;distance. From the agreement between the two determinations, whichnbsp;never differed more than 1 %, it appeared that this interpolation is fairlynbsp;Unambiguous.

The intensity of the ghosts of the grating is in the first order spectrum 1-25 % and in the second order spectrum 5.1 %. As a rule, the ghostsnbsp;lay outside the lines, so that to all intensities the correction according

to the formula i i= (ip — g) ^qq^~—could be applied 28. 29)_ Here I’o

denotes the observed intensity, g the sum of the intensities of the ghosts and i the corrected intensity, all of them in percentages of the intensity

12

of the continuous background. In a few cases as, for example, in that of the D lines of Na, the ghosts lay in the wings and the measurementsnbsp;were then sufficiently accurate for applying the local correction to eachnbsp;measured point.

§ 7» The method of observation at Potsdam.

When I had completed the measurements at Utrecht, I was given the opportunity to go and work temporarily at the Institut fiir Sonnenphysiknbsp;at Potsdam, This meant a very welcome occasion not only for checkingnbsp;the Utrecht results by an exposing-technique differing in so manynbsp;respects from the one at Utrecht, but also for a more accuratenbsp;investigation of the central parts of the Fraunhofer lines than, owingnbsp;to the smaller resolving power, could be performed there. Paying specialnbsp;attention to the central intensities, the profiles of a number of lines,nbsp;already measured at Utrecht, were again determined for the samenbsp;distances from the centre of the sun’s disc, and, besides, for the pointnbsp;at 0.99 R. It being of importance for the problem of central intensitiesnbsp;to know the degree to which these are equal for the components of anbsp;multiplet 2'3)^ the D lines of Na, two of the Mg b lines andnbsp;six lines of the Fe multiplet aSF^—y^Fs® were investigated, so thatnbsp;three more lines were added to the lines of this multiplet, measured atnbsp;Utrecht. The line Fe 3969.3 was omitted, because it lies in the wing ofnbsp;the H line of Ca , and the line Mg 5167.3 because it is strongly disturbednbsp;at its very centre by the line Fe 5167.5. It was in my opinion superfluousnbsp;to determine again the central intensities of the H- and the K line, as,nbsp;owing to the great width of these lines, we may safely assume that, alsonbsp;at Utrecht, the measurements will have been free from the obliteratingnbsp;effect of the spectrograph. This is also evidenced by the agreementnbsp;between the results of different investigators (K., Schwarzschild 5),nbsp;M. Minnaert30)_ A. D. Thackeray ). The central intensity of thenbsp;line Ca 4226.7 was added to those measured at Potsdam, as the accuratenbsp;measurements of this line by R. O. Redman 32) and A. D. Thackeray 3i),nbsp;referring to the centre of the sun’s disc, were available for comparison.nbsp;The ultra-violet and infra-red lines, measured at Utrecht gave rise tonbsp;difficulties at Potsdam, in connection with the special exposing-technique,nbsp;presently to be described; they were, therefore, omitted.

1. Apparatus. In the Institut fiir Sonnenphysik an intense objective of 60 cm diameter forms an image of the sun, of which the diameter is

13

13 cm. For the present investigation this image was thrown on the vertical plane of the slit of the monochromator, mounted by P. ten Bruggencatenbsp;and H. von Kliiber, and serving the purpose of enabling one to admitnbsp;only light from a narrow wave-length region, thereby eliminating straynbsp;light and making accurate intensity-measurements possible. It has alreadynbsp;been described elsewhere in detail !• 33). The image of the sun formednbsp;on the slit of the large spectrograph by the light, let through by thenbsp;monochromator, has about twice the size of the original image, itsnbsp;diameter being 25 cm. The focal length of the horizontal spectrographnbsp;is 12 m; of the grating a width of 12 cm was used, ruled with 600 linesnbsp;per mm. For further details the reader is referred to the description bynbsp;E. Freundlich 34) or to i).

2. Exposures. The centre-limb exposures were, all of them, made in fhe light of the second order spectrum with a dispersion of 1.5 mm/A,nbsp;the monocromator being always inserted in the path of the rays. Thenbsp;preliminaries for the taking of a photograph consisted in the first placenbsp;in selecting an unperturbed region at the distance to be investigated fromnbsp;the centre of the sun’s disc. As the exposures were made only a shortnbsp;time before the maximum of solar activity, it was impossible to select allnbsp;the points from centre to limb on one and the same radius and we werenbsp;obliged to find for each point a new unperturbed region. A rotation ofnbsp;the sun’s image is at Potsdam only possible by changing the azimuthnbsp;of the coelostat-mirror, so that for points at the limb only part of thenbsp;sun’s circumference is available. The image of an unperturbed regionnbsp;was thrown on the first monochromator-slit and kept there steadily bynbsp;careful compensating adjusting. This was achieved by keeping the imagenbsp;of a sharply defined sunspot on the cross-threads of a small auxiliarynbsp;telescope, having in front of its eye-piece a little plate of glass of thenbsp;colour of the wave-length region under investigation, and as the sun’snbsp;image was focussed for that same region, chromatic aberrations of thenbsp;objective were for the greater part eliminated. By forming a sharp imagenbsp;of the first monochromator-slit in the plane of the slit of the spectrograph,nbsp;one is sure that the image of the sun, formed there, is in its turn alsonbsp;sharp.

For the points from 0.00 to 0.90 R, the slit was placed at right angles to a radius of the sun’s disc, for points closer to the limb in the directionnbsp;of a radius. Each of the limb-spectra was photographed twice. First,nbsp;with the slit made so long that both the limb itself and the point at

14

0.95 R fell within its length. On these photographs the points at 0.95 and 0.98 R were measured. The second time, the spectra were photographed, while only slightly more than the part from the limb to 0.98 Rnbsp;fell on the slit, the latter now being illuminated over a length of 3 mm.nbsp;On these photographs the limb-points at 0.98, 0.99 and 0.995 R werenbsp;measured. No systematic difference was found between the line-profilesnbsp;at 0.98 R, obtained from the first and the second procedure.

All centre-limb exposures were made in two ways. First, while the monochromator let through a wave-length region of about 30 A. Fromnbsp;these photographs the intensity of the wings of the strong lines wasnbsp;determined in terms of the intensity of the continuous background; thesenbsp;photographs will henceforth be called quot;continuum-photographs”. Thenbsp;second time, a wave-length region of only 3 to 4 A was let through. Thenbsp;photographs obtained in this way served for measuring the intensity ofnbsp;the lines close to and including their centres; they will henceforth benbsp;called quot;inner-photographs”. In the latter case the monochromator hadnbsp;to be adjusted very carefully, in the first place to locate the Fraunhofernbsp;line, to be measured, exactly in the middle of the spectral region letnbsp;through, and in the second place to cut off this region sharply at bothnbsp;ends. This adjustment was judged visually; a photographic determinationnbsp;of the right positions would have taken a very long time. For that samenbsp;reason the ultra-violet and the infra-red lines were not photographednbsp;at Potsdam.

The photographic material used consisted of Agfa Isopan F or Isopan SS film in a Nettax Kleinbild (small picture) camera, which could benbsp;fastened to the spectrograph; each part, meant for a picture, was usednbsp;for a spectrum, so that it was possible to photograph 36 spectranbsp;successively on one film. Some of these were spectra for standardizing,nbsp;photographed by means of a small grating spectrograph with step-reducer,nbsp;either immediately after the other photographs were taken or in betweennbsp;them. The Fraunhofer lines were obtained with different times ofnbsp;exposure, on the one hand, in order that the spectra should possess aboutnbsp;the same density notwithstanding the darkening towards the limb, sonbsp;that one and the same part of the characteristic curve could be used, and,nbsp;on the other hand, because for the continuum-photographs a shorter timenbsp;of exposure sufficed than for the inner-photographs. For this reason thenbsp;standardizing spectra were photographed in series of different times ofnbsp;exposure, so that the profiles could be deduced from a characteristicnbsp;curve, for which the times of exposure differed by less than a factor

15

2 from those for the solar spectra. We did not notice, for that matter, that the time of exposure ever influenced the shape of the characteristicnbsp;curve in any way.

In order to eliminate too strong contrasts, the films were developed in Rodinal 1 ; 40 at 18° C for 8 minutes, during which the bath wasnbsp;constantly rocked vigorously to and fro. They were then registerednbsp;by

means of a Zeiss photometer, of which the slits were adjusted in such a way that their widths corresponded to 0.02 A on the film, whilenbsp;their lengths corresponded to 8quot; for the points at 0.00 to 0.95 R, downnbsp;to 3quot; for those at 0.99 and 0.995 R (see Fig. 2).

3. Determination o[ the intensity-profiles of the inner part of the lines. The possibility of admitting into the spectrograph a spectral region ofnbsp;only 3 to 4 A offers not only the advantage of eliminating any stray lightnbsp;from other wave lengths, but also that of getting rid of the ghosts. Fornbsp;the lines measured, the first ghost lies at least 2.5 A distant from thenbsp;principal line; when only a region of 4 A is let through, therefore, thenbsp;inner part of a strong Fraunhofer line is entirely free from ghosts andnbsp;the only remaining correction to be applied is the one for the instrumentalnbsp;curve (this §. 5). A region of 4 A, however, is too narrow for locatingnbsp;the continuous background. This requires, therefore, the combining ofnbsp;the spectra photographed with narrow and with wide monochromator-slit,nbsp;which was done in the following way, the same as that used by A. D.nbsp;Thackeray 31). To the intensity-profile obtained from the continuum-

photograph the general correction for ghosts i = (io — g) —

1UÜ — g

(see p. 11) was applied, where for g was taken the sum of the intensities of all disturbing ghosts, as determined from photographs made for thatnbsp;purpose. These photographs were of two kinds. In the first, the linesnbsp;Kr 4320 and Kr 5570 emitted by a Kr discharge tube were photographed;nbsp;on these we could measure the four nearer ghosts on both sides, andnbsp;their aggregate intensities amounted to 3.5 % for 4320 A and to 4 %nbsp;for 5570 A. The second method for determining directly the totalnbsp;intensity of the ghosts consists in measuring the central intensity of anbsp;narrow Fraunhofer line, located in a practically undisturbed part of thenbsp;continuous spectrum, first, on a photograph covering a wave-lengthnbsp;region of 30 A and, again, on one for which this region is restrictednbsp;to a few A only. The surplus of light in the inner parts of the linenbsp;on the first photograph relatively to that on the second photograph

16

is due to the disturbing ghosts, apart from scattered light, which in this connection can be safely neglected. The total intensity of thenbsp;four nearer ghosts, obtained in this way for 5500 A, agreed fairlynbsp;well with the one determined in the first manner. For the wings thenbsp;value of g is less essential and their profile is, therefore, knownnbsp;sufficiently well from the continuum-photographs.

On the continuum- and the inner-photographs a number of points at the same distance AX from the line-centre have been measured. Let r benbsp;the intensity in terms of the continuous spectrum in such a point,nbsp;obtained from the continuum-photograph, and i the intensity in arbitrarynbsp;units obtained from the inner-photograph; the intensity of the continuousnbsp;background in the latter will then amount to 100 t'/r. The line drawnnbsp;fluently through the points determined in this way is then regarded tonbsp;represent the continuous background (Fig. 1), while, finally, the

17

intensities of the inner parts of the line are determined relatively to this continuous background. When, later on, the central intensities arenbsp;corrected for the instrumental curve, vre start, as a matter of course,nbsp;again from the inner-photographs.

The way in which the wave-length region is cut off by the monochromator did not always turn out to be perfectly sharp, and the run of the continuous background belonging to the inner-photograph was not alwaysnbsp;straight. This deviation from straightness can presumably be explainednbsp;by the fact that the image of the first slit was not always centrednbsp;perfectly on the slit of the spectrograph. In principle, however, this doesnbsp;not matter at all; the essential points are, that no light shall have passednbsp;the monochromator from wave lengths farther than about 2 A awaynbsp;from the centre of the line, and that the run of the continuous backgroundnbsp;be correctly determined by the values 100 i/r; both conditions werenbsp;always satisfied.

4. The definition of the sun’s limb in the limb photographs. From the fact that at Potsdam the limb spectra were photographed with a radialnbsp;slit, in such a way, that the sun’s limb is one of the bounding lines ofnbsp;the spectra, it is possible to determine its definition from each of thesenbsp;photographs, on which it is never sharp, owing to scattering, scintillationnbsp;and guiding errors. In the narrow confused region the true position ofnbsp;the limb was estimated visually to within 0.1 mm. If, now, the distancenbsp;of this estimated position from the perfectly sharp lower edge of thenbsp;spectrum, determined by the end of the spectrograph-slit amounts to anbsp;cm, it is fairly easy to register the film by means of an accuratelynbsp;adjustable plate, on which it is clamped during the registering, in strips,nbsp;at distances (a — 0.625) mm, (a— 1.25) mm etc. from the sharp edge ofnbsp;the spectrum, corresponding respectively to the points at 0,995 R, 0.99 Rnbsp;etc. In all series registrograms were made of a few continuum-photographsnbsp;at the limb, in a region free from Fraunhofer lines, in a direction atnbsp;right angles to the dispersion, from which the run of the intensity at thenbsp;sun’s limb was deduced. It was thereby possible a posteriori to locatenbsp;accurately the registered strips in the spectrum and to find the error innbsp;the estimated position of the limb, which was defined in this connectionnbsp;by the equality of the areas S in Fig. 2. This error amounted at the mostnbsp;to 0.2 mm (about 1.quot;5) and did not show any systematic character.nbsp;Accidentaly, therefore, the way of judging the position of the limb on thenbsp;film agrees practically with the definition given above.

18

The intensity-variations at the limb obtained are drawn, for the neighbourhood of A 4100 and A 5900, in Fig. 2, respectively from photographs of the violet Fe lines and of the D lines of Na. In photographsnbsp;made on different days, the deviations at some fixed A are insignificant.nbsp;One can take this as an indication that guiding errors are the principal

cause of the lack of sharpness, as for a few of these photographs the atmospheric conditions were decidedly different. On the inner-photo-graphs, for which the times of exposure were 2 to 3 times as long asnbsp;those for the continuum-photographs the definition is likely to be slightlynbsp;worse. From Fig. 2 the extent can be judged to which the radiation

19

assigned to the measured points is in reality an integrated radiation from the small parts surrounding them. One must bear in mind, however,nbsp;that, as the only consequence of this, the measurements at the extremenbsp;limb must be ascribed to points slightly different from those at 0.995 Rnbsp;etc. In comparing the observations with theory, this will always be takennbsp;into account.

5. Correction o[ the central intensities [or finite resolving power. The instrumental curve of the grating spectrograph has been accuratelynbsp;determined from narrow Kr lines i). An elegant method for correctingnbsp;observed line-profiles for its obliterating effect was developed by H. C.nbsp;Van de Hulst 35)^ while P. Kremer 36) designed an apparatus by meansnbsp;of which the necessary computations of this kind can be quicklynbsp;performed. The two instrumental curves for A 4320 and A 5570,nbsp;determined at Potsdam, were each reduced to A 5000, and their meannbsp;Was used in applying the correction to the observed central intensities,nbsp;taking into account the change of the scale of abscissae proportional tonbsp;Wave length. Curves I and III in Fig. 3 represent this mean instrumentalnbsp;curve for A 5000. It was sufficiently narrowed by operating on it withnbsp;the following peak-function 35) ^ likewise referring to A 5000:

As appears from the above values of the heights of the peaks, the asymmetry of the instrumental curve has been taken duly into account.nbsp;The factor /3, by which the accidental errors are multiplied in thenbsp;corrected profile, amounts in our case to 2.1. Curve II represents thenbsp;instrumental curve, after the peak-function has operated on curve I, sonbsp;that the corrected profile is the true profile obliterated by curve II. Onnbsp;comparing its width with the intensity-variation over a correspondingnbsp;width in the inner part of a — corrected — Fraunhofer line, it appearsnbsp;that in this connection further correction is superflous; the principal effectnbsp;is the suppression of the wings of the original instrumental curve I.

The correction by means of the peak-function could be applied to the spectra photographed with narrow monochromator-slit (see Fig. 1).

20

This has the advantage that the shape of the instrumental curve at distances larger than about 2 A from its centre becomes irrelevant.nbsp;Its shape between 200 mA (that is as far as it was measured) andnbsp;2 A cannot be accurately taken into account. The peak-function,

however, applies partly an automatic correction for this part of the curve, as its total area has been computed on the assumption that its far wingsnbsp;are shaped in conformity to cjx^, where c is determined from the averagenbsp;shape of the wings up to 200 mA (seel)). These imperfections,nbsp;however, have only a slight influence on the final value of the centralnbsp;intensity of a Fraunhofer line.

§ 8. Survey and points in common in the discussion of the complete observational material.

From the photographs, of which a survey is given in Table 1, 1266 profiles were deduced, distributed over the three places of observationnbsp;as follows: Utrecht 857; Potsdam 358 and Mount Wilson 51. It was

21

unfeasible to determine the shape of all these profiles where they were disturbed by blends and, besides, this did not concern us. As it was ournbsp;purpose to determine the variations of the profiles of the strong linesnbsp;themselves, we measured in the first place, if at all possible, points, thatnbsp;could be considered to lie on the undisturbed profile. Only, where thisnbsp;turned out to be impossible, did we measure also, for lack of better.

*) The notations and constants are taken from C. E. Moore ^’).

**) Excitation potential of the lower energy level in electron volts.

***) Ut.; Utrecht; Po.: Potsdam; Mo.: Mount Wilson.

points on the slightly disturbed profile, for, generally speaking, the slight disturbance by a blend will not seriously interfere with the centre-limbnbsp;Variation of a strong line. A point once having been chosen, its intensitynbsp;¦was measured in all profiles of a series at the same distance from thenbsp;centre of the line. This was, in its turn, determined from the mostlynbsp;sharply defined top and from undisturbed points located, as much asnbsp;possible, symmetrically around it.

22

Explanation of the abbreviations: l.s.r.: Ilford special rapid; I.i.r.; Ilford infra red; I.r.p.p,; Ilford rapid process panchromatic; A.I.R. 850; Agfa Infrarot 850 hart; E.K. Ill F; Eastman Kodak 111 F; A.S.G.R.:nbsp;Agfa Spectral Grün Rapid; A.I.F; Agfa Isopan F; A.l.SS: Agfa Isopan SS; cont.; continuum-photograph (see p. 14 and Fig. 1); inn.: inner-photograph (see p. 14 and Fig. 1).

23

It must be emphasized here that the centre-limb variations in a series ate always more reliable than the intensities themselves. This is duenbsp;to using, as far as possible, a homogeneous method in working out thenbsp;data of a series. Yet, the separate series of one and the same line showed,nbsp;not unfrequently, appreciable differences, of which one can form somenbsp;idea by comparing the results, given in Chapter II with those of previousnbsp;publications 15. 17) and by comparing mutually the Utrecht-, Mountnbsp;Wilson- and Potsdam measurements, which are always given separatelynbsp;in the Tables 2—20.

§ 9. Discussion of errors.

1. Accidental errors. The photographic method applied, and conform to which the characteristic curve is obtained from spectra taken via anbsp;standardized step-reducer, has already been frequently applied and itnbsp;has turned out that the accidental errors thereby introduced in thenbsp;relative intensities of the profiles may have values up to 5 A comparison of the measurements of the Utrecht-, Potsdam- and Mountnbsp;Wilson material mutually (Tables 2—20) and with those ofnbsp;other investigators makes it likely that, also in the results communicatednbsp;here, errors of this magnitude occur. The central intensities in the tablesnbsp;Under the heading quot;Potsdam” are, each of them, the average of thenbsp;values obtained from various spectra and films, of which the mutualnbsp;differences amount at most to 3 %. The error, arising from the steepnessnbsp;of the slope of the inner wings of a few Fraunhofer lines, is apt to benbsp;rather considerable, because any small error in AX, the distance from thenbsp;centre of the line, entails a large error in r. This error will, however,nbsp;have no systematic influence on the centre-limb variation, though it willnbsp;give rise to a certain spreading of the observed variation round thenbsp;true one.

2. Systematic errors, a. Stray light. By scattering of light in the spectrograph the measured intensities may be subject to a systematicnbsp;error. There was no fear of this at Utrecht — considering that there thenbsp;step-reducer is applied on the slit of the spectrograph — provided onlynbsp;that the scattered light be spread evenly over the photographed spectrum,nbsp;which, from check photographs, proved to be the case. At Potsdam thenbsp;comparison of the photographs, in the taking of which wide and narrownbsp;spectral regions were let through by the monochromator, showed thatnbsp;stray light is not present to any appreciable amount. From the fact that

24

only light from a region of a few A was admitted, one could hardly expect anything else,

b. nbsp;nbsp;nbsp;Eberhard effect. Another systematic error can arise from the Eber-hard effect, especially in the central intensities and, therefore, also innbsp;their centre-limb variations, as the profiles of the lines at the limb arenbsp;narrower than those at the centre. As in the theoretical interpretationnbsp;of these intensities only the measurements at Posdam are used, we shallnbsp;dwell for a moment on the influence, that this effect has on them. Innbsp;order to reduce it to the utmost, the films were developed in dilutednbsp;Rodinal and were rocked steadily to and fro during the process. Fromnbsp;check measurements on very narrow Kr lines for determining the instrumental curve, the Eberhard effect, although present, appeared to be ofnbsp;little moment 1) and since the profiles of the Fraunhofer lines cover anbsp;larger wave-length region and show a less steep density variation, thenbsp;effect will be in this case still less appreciable and can safely benbsp;neglected. Moreover, in correcting the central intensities, the influencenbsp;of the Eberhard effect on the determination of the instrumental curve isnbsp;opposed to that influence on a Fraunhofer line, a too low central intensitynbsp;being corrected with a too narrow instrumental curve.

This same effect may likewise influence the maxima in an intensity profile, arising from the occurrence of blends. Considering the remarknbsp;made above, one may assume that here, too, the Eberhard effect isnbsp;negligible.

c. nbsp;nbsp;nbsp;Finite resolving power. It is chiefly in those parts of a profile, wherenbsp;the curvature in the run of the intensities is considerable, that the truenbsp;intensities will deviate appreciably from the observed ones. The correctionnbsp;to the central intensities has already been dealt with in detail, and itnbsp;follows from § 7, 5 and the present §, 1 that the corrected central intensities given are still liable to fairly large relative errors. The further pointsnbsp;of the inner part of the lines were not corrected. The effect of the finitenbsp;resolving power on maxima in the intensity-profile, due to blends, willnbsp;likewise be appreciable, when such a maximum is rather sharp, and itnbsp;will decrease its intensity. As regards the centre-limb variation, thisnbsp;influence is in sofar of importance, as the shape of the maximum for thenbsp;centre of the sun’s disc is different from that for the limb, that is, therefore, only in second approximation. That is why no correction wasnbsp;applied for this effect. It is an additional cause by which the equivalentnbsp;widths come out to large (§ 10, 1).

d. nbsp;nbsp;nbsp;Blends. The disturbing effect of blends is in many cases considerable

25

and to take them into account is no simple matter. It may very well be that, owing to their presence, the intensity of points that, to allnbsp;appearances, are only slightly disturbed, is, nevertheless, appreciablynbsp;too low. They do affect the centre-limb variations, because, in the firstnbsp;P^ace, the measured centre-limb variation refers, strictly speaking, tonbsp;points of slightly larger intensities and, in the second place, the blendsnbsp;themselves suffer also a centre-limb variation. Fortunately, however,nbsp;both these factors have only a second order effect. The fact that thisnbsp;disturbance is small, in any case, appears clearly from a comparisonnbsp;between undisturbed points and points of practically the same intensity,nbsp;that are decidedly disturbed by blends; the centre-limb variations are,nbsp;practically speaking, identical, so that we have refrained from applyingnbsp;a correction in this connection.

In the wings, the relative influence of blends is more serious, so that they invalidate more in particular the determination of the c’s (see § 10)nbsp;and consequently that of the equivalent widths, these being partly deduced from the c's. If, owing to their influence, the determination of the c’snbsp;is erroneous, their values will always come out too large, but just as wellnbsp;for the centre of the sun's disc as for the limb. From the c-determinationsnbsp;appeared clearly the by no means unappreciable amount of the errors,nbsp;that may still arise from deducing the continuum from the backgroundnbsp;in the registrograms. These frequently turned out to be locatednbsp;erroneously to an amount of 2 to 3 %, too high as well as too low.

e. nbsp;nbsp;nbsp;Ghosts. The error, remaining after the general correction for ghostsnbsp;(see p. 11), can at the most amount to 1 or 2 %, and can, besides,nbsp;have no influence on the centre-limb variations. Neither can ghostsnbsp;affect appreciably the central intensities, owing to the precautions takennbsp;in making the inner-photographs (§ 7, 3),

f. nbsp;nbsp;nbsp;Correct adjustment on the points of the solar disc. A small differencenbsp;in the adjustment of the tangential slit of the spectrograph may havenbsp;a considerable effect on the limb spectra, because on approaching thenbsp;limb, the profiles vary strongly. As the error may amount to a fewnbsp;0,1 mm, which at Utrecht means about 0.004 R and at Potsdam aboutnbsp;0.002 R, the only thing one can say is that the point at 0.995 R measurednbsp;at Utrecht will lie between 0.991 R and 0.999 R, an a posteriori checknbsp;being in this case impossible. The exposures with a radial slit at Potsdamnbsp;are more favourable in this respect, as, here, a subsequent location onnbsp;the film of the points near the limb is possible (§ 7, 4),

g. nbsp;nbsp;nbsp;Irradiation from neighbouring points of the sun's disc. In con-

26

sideration of what was said in § 7, 4 the measurements referring to the points near the extreme limb cannot be simply ascribed to the apparentnbsp;points of adjustment.

h. nbsp;nbsp;nbsp;Perturbed regions. The attempts to obtain the spectrum of thenbsp;unperturbed photosphere, have certainly not always been successful,nbsp;especially as regards the photographs at Potsdam in 1938 which werenbsp;taken shortly before the time of maximum solar activity. As, however,nbsp;for each point adjusted a new unperturbed region was visually selected,nbsp;any systematic influence on the centre-limb variation is, practicallynbsp;speaking, out of the question.

i. nbsp;nbsp;nbsp;The sun’s altitude. With the longer times of exposure the sun’snbsp;altitude may change materially during the photographing of a completenbsp;centre-limb series. In order to eliminate any sytematic influence of thisnbsp;change, the photographs were made in arbitrary succession.

Summarising we can say that the errors, which do occur, have but a very slight systematic influence on the centre-limb variation, that, however, the location at 0.99 R and 0.995 R, ascribed to the points near thenbsp;extreme limb, must be used with some caution.

CHAPTER II

OBSERVATIONAL RESULTS

§ 10. General remarks.

1. The tables of the intensity^pro[iles. The results of the measurements are collected in the Tables 2 to 20, where, in general, the lines arenbsp;arranged according to increasing wave length. The tables give the relativenbsp;intensity of the selected points of the profiles as a function of sin S' — r/R,nbsp;the distance from the centre of the sun’s disc in terms of its radius. Thenbsp;first column gives the distance, expressed in A-units, of the measurednbsp;point from the centre of the line. Distances towards the violet have thenbsp;suffix V, those towards the red the suffix r. When no v or r is added,nbsp;it means that the average has been taken of the intensities towardsnbsp;the violet and towards the red side. This was only done, when, fornbsp;all points concerned of the sun’s disc, these values did not differ morenbsp;than 2 %.

The intensities are given separately for the various places of observation, Utrecht, Potsdam and (for the Mg b lines) Mount Wilson.

When a measured point was disturbed by blends, its intensities are printed in italics. Slightly disturbed points, of which the centre-limbnbsp;variations will not differ materially from undisturbed ones, have notnbsp;been marked separately. The estimation as to the degree of thenbsp;disturbance is naturally more or less arbitrary; criteria for the absencenbsp;of a disturbance at a point are: equal intensities towards the violet andnbsp;the red; the smooth run of the profile just at that part. If, however,nbsp;a line is strongly disturbed by blends, these criteria fail.

To the intensities of the profiles, deduced from the Potsdam photographs, we have occasionally added the central intensities of blending lines, of which the wave length (after ^8)) of their centres is printed atnbsp;the bottom of the table. They had to be measured in order to be ablenbsp;to correct the profile completely for the effect of the finite resolving

28

power. Afterwards, applying van de Hulst’s correction-method, it turned out that the intensities within these blends need not be known; theirnbsp;central intensities, however, having once been measured, have beennbsp;retained in the tables; they have not been corrected by the instrumentalnbsp;curve. The row indicated by “corrected central intensitities” gives thenbsp;central intensities of the principal lines, from which the effect of thenbsp;instrumental curve of the Potsdam grating spectrograph has beennbsp;eliminated.

The position of the neighbouring continuous spectrum was, where at all possible, checked and, if necessary, corrected by means of thenbsp;straight lines of the Iq — i versus i/AA,2-graph, as explained by M. Min-naert24)^ He showed that the distribution of the light in the wings ofnbsp;a Fraunhofer line is, in many cases, rendered by the expressionnbsp;i/iQ = 1/(1 c's), where s is the ratio between the scattering coefficientnbsp;and the coefficient of continuous absorption, and c' a proportionality-factor. In the wings s varies as l/AX^ (damping), so that therenbsp;i/io=l/(l c/AA,2), from which it follows that Iq — i = cilA\^, thenbsp;formula yielding the value for the constant c, characteristic for eachnbsp;definite profile, this quantity, therefore, being a direct measure for thenbsp;depression at large distances from the centre of a line. Minnaert hasnbsp;not investigated the extent to which this relation is satisfied for profilesnbsp;in the spectrum of points close to the sun’s limb. The following considerations, however, make it clear that his method can always be appliednbsp;with advantage. Starting from the fact that, owing to damping, thenbsp;scattering and absorbing action of an atom varies in the far wings asnbsp;1/AA,2, and that for slight depressions these actions are simply additive,nbsp;one can write: z'o —' = czq/AA^, From this formula c is found graphicallynbsp;by plotting iojAX^ against Iq — i. The tangent in the point i = Zq coincidesnbsp;with the one drawn according to Minnaert’s method, as for z—gt;ro bothnbsp;expressions merge into each other. As it turns out from the observations,nbsp;however, that the formula z'o — z = cz/AA^ remains valid for deepernbsp;depressions than zg — z = czo/AA2, we have used preferably the formernbsp;expression for the determination of the tangent line in z = zo. The valuesnbsp;for c, obtained therefrom, are printed in the last row.

The equivalent widths, given in mA, are partly obtained by plani-metring the smoothed-out profile drawn through the undisturbed points measured. As this method may lead to large errors in the far wings 24),nbsp;their contributions to the equivalent widths have been determined, fromnbsp;a certain definite AA onwards, from the constants c by means of the

29

formula

used in this computation should still lie on the straight part of the graph i versus (/AX'S at about i/i'o = r = 0.90. For a definite centre-limbnbsp;series, the same value for AX was used throughout. The directly measurednbsp;parts of the equivalent widths may have come out systematically toonbsp;large, owing to an insufficient correction for blending and for finitenbsp;resolving power. Likewise, the computation of the contributions from thenbsp;far wings to the equivalent widths by means of the above formula yields,nbsp;mostly, larger values than direct measuring of the areas 24). Owing tonbsp;these factors, the values obtained for these widths will, in general, benbsp;perhaps larger than those of other investigators. This is, however, ofnbsp;only secondary importance for the centre-limb variation, that means fornbsp;the mutual ratios between the equivalent widths at the various pointsnbsp;of the sun’s disc.

For those Fraunhofer lines, that have been measured at different observatories, the equivalent widths as well as the c’s have been determined from their average profiles.

2. nbsp;nbsp;nbsp;The cross-section figures. Though a few profiles for differentnbsp;values of r/R are drawn, belonging to the most characteristic and bestnbsp;determined lines, the centre-limb variations are not represented by meansnbsp;of line-profiles, but by so-called cross-section figures. These are drawnnbsp;for all lines separately: although showing less detail, they give a betternbsp;general idea than the tables. A curve in a cross-section figure representsnbsp;the variation of the relative intensity at some definite distance AX fromnbsp;the centre of a line as a function of cos The use of this quantitynbsp;offers the advantage that the curves are drawn out on approaching thenbsp;sun’s limb, thereby affording a better survey of the variations, which,nbsp;precisely in the narrow part close to the limb, become considerable. Thenbsp;comparison of the observational results with theory will, later on, alwaysnbsp;be carried out with the help of these cross-section curves.

3. nbsp;nbsp;nbsp;The determination of the cs {see also this §, 1). We may sufficenbsp;here with the remark that, by giving figures in detail, referring to thisnbsp;subdivision of the investigation, due attention has been paid to the determination of the c’s and to their centre-limb variation; this was done onnbsp;account of the important conclusions to be drawn from them in thenbsp;theoretical part.

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§11. The lines Fe 3815.9, 3820.4, 3859.9 and Mg 3829.4, 3832.3 and 3838.3 (Tables 2 and 3).

These ultra-violet Fe- and Mg lines are seriously disturbed by blends; only from a few points, in which the profiles are clearly not too stronglynbsp;disturbed, is it possible to determine the centre-limb variation. This

variation is very characteristic of moderate intensities: starting from the centre of the sun’s disc, the intensity of the inner wings increases atnbsp;first, to decrease again closer to the limb; the cross-section curves shownbsp;a depression (Fig. 4 and 5), which is stronger for the Fe- than thenbsp;Mg lines. The three Mg lines show these variations within the obser-

32

vational errors to the same degree, and the same is true for the three Fe lines although, from the point of view of atomic theory, these linesnbsp;are each of a different nature (Table la). The central intensities arenbsp;small; in judging them one should bear in mind that these lines werenbsp;only observed at Utrecht, with a moderate resolving power.

Owing to the strong deformations by blends, the equivalent widths cannot be obtained accurately and a determination of the c’s is entirelynbsp;out of the question.

34

§ 12. The H' and the K line of Ca''' (Tables 4 and 5).

These lines were only measured at Utrecht. They are, however, so wide that the effect of the finite resolving power of the Utrecht spectrograph is presumably of little moment, also as regards the central intensities. In determining the latter, one is confronted with a complication,nbsp;arising from the double reversal in the centre of the lines which, tonbsp;various degrees, is always present at the sun’s limb. In the presentnbsp;connection this reversal was not investigated in further detail and, amongnbsp;the profiles from the limb-points, those with the weaker reversals werenbsp;selected for determining the central intensities, as the stronger reversalsnbsp;are, most likely, due to faculae.

The equivalent widths, as far as the contribution from the wings is concerned, were determined from the violet half of the K line and from

36

the red half of the H line, because in the region between the lines they overlap appreciably.

From the cross-section curves (Fig. 6 and 7) and from the profiles for three different points of the sun’s disc in Fig. 8, one can see clearlynbsp;how and to what extent the lines vanish on approaching the sun's limb.

The run of the continuous background was determined by connecting the continuous spectrum at a few hundreds A on both sides of the linesnbsp;by a fluent line; after that, the exact height was determined still betternbsp;by means of the (to — t) versus t’/AX^-graphs, which are shown completelynbsp;in Fig. 9. For the centre of the sun’s disc the connection remains linearnbsp;down to relative intensities lower than 50 %, for the points near thenbsp;limb the bend in the curves occurs already at higher intensities.

39

It is remarkable that the ratio between the c’s of the two lines is not equal to the doublet-ratio (here, therefore, 1:2) but to 1 : 1.6. Thisnbsp;is the more striking, as for other well-measurable multiplets, such asnbsp;the D lines of Na, the two stronger lines of the Mg b triplet and those

40

of the infra-red lines of Ca , this is much more nearly the case. This deviation is most likely due to the disturbance of the H line by Ht.

The centre-limb variation of c is shown in Fig. 10. As, here, we are concerned only with the variation of c and not with its actual value,

we have plotted for the two lines the fraction nbsp;nbsp;nbsp;the ratio

^ cos 1? = 1

between the c’s and their values for the centre of the sun’s disc) against cos This way affords, moreover, the possibility of a fair comparisonnbsp;between the c-variations of the two lines. These turn out to be slightlynbsp;different, and as, here also, the influence of He may be at work, wenbsp;shall later on, in comparing our observations with theory, only use thenbsp;c-variation of the K line.

¦ Comparison with the observations of other investigators shows that, for the centre of the sun’s disc, the profile and more in particularnbsp;its central intensity, agrees satisfactorily with those obtained bynbsp;K. Schwarzschild 5), M. Minnaert so) and A. D, Thackeray si). Thenbsp;difference between our profiles for centre and limb is of the same naturenbsp;as that found by Schwarzschild (more cannot be said about this, asnbsp;Schwarzschild does not give the exact position of the point for his limbnbsp;exposure). The centre-limb variation agrees fairly well with thatnbsp;determined by T. Royds and A. L. Narayan 12), although they givenbsp;appreciably larger relative intensities. In this connection attention maynbsp;be drawn to a remark of D. S. Evans i^), who found for the hydrogennbsp;lines deviations in the same sense between his own measurements and

41

those by Royds and Narayan. One may, therefore, safely assume the intensities of the lines determined by the latter two to be too small.

§ 13. Six lines of the Fe-multiplef nbsp;nbsp;nbsp;—y®Fg° (Tables~6—11).

The line Fe 3969.3 was omitted, because it lies in the wing of the H line, so that its profile is strongly disturbed. Of the six remainingnbsp;lines, Fe 4045.8, Fe 4063.6 and Fe 4071.8 were measured both atnbsp;Utrecht and at Potsdam, Fe 4005.3, Fe 4132,1 and Fe 4143.9 at Potsdamnbsp;only. The centre-limb variation is, for all these lines, essentially thenbsp;same, as is shown most clearly by the cross-section curves (Fig. 11, 12,nbsp;16, 17 and 18). Ignoring the blends three profiles of the strongest line,nbsp;Fe 4045.8, are drawn in Fig. 14.

In order to avoid a confusion of details, we have drawn the cross-section curves for the central parts of those profiles, that were observed at Potsdam, in the figure of the violet wing, and of those, observed atnbsp;Utrecht, in the figure of the red wing. Of those lines, of which bothnbsp;wings are combined in one figure, only the Potsdam results are given,nbsp;as these will be the least deformed by the finite resolving power. Tonbsp;these we have still added separately in the figures the variation of thenbsp;corrected central intensities: these were deduced for the profilesnbsp;determined at Potsdam in the way described in § 7, 5.

Precision measurements of the central intensities, referring to the centre of the sun’s disc were carried out by R. O. Redman 39) on thenbsp;three stronger of these lines: C. W. Allen ^o), too, corrected hisnbsp;measurements of these lines for the influence of the spectral apparatus.nbsp;Their results in per cent, of the continuous spectrum are here added,nbsp;together with mine for comparison.

The lines Fe 4005.3 and Fe 4132.1 are so seriously disturbed by blends, that their equivalent widths are unreliable, while in their wings thenbsp;blending is such that the c's cannot be determined: the c's of Fe 4143.9nbsp;are for that same reason unreliable. The graph from which they arenbsp;deduced is given in full for the line Fe 4045.8 in Fig. 13. The ratios

42

between the c’s of the best measurable four lines do not agree with the theoretical multiplet ratios, neither do they agree with the ratios followingnbsp;from R. B. and A, S. King’s laboratory experiments after these hadnbsp;been recomputed for 6000° (see also 42)). R is difficult to come to anbsp;decision as to the cause of this difference, although the c-determinationsnbsp;for the lines Fe 4045.8, Fe 4063.6 and Fe 4071.8 would appear to benbsp;too accurate to afford an explanation for such a large discrepancy.

Table 6. nbsp;nbsp;nbsp;Fe 4005.3 4

Besides, we are here concerned only with the line Fe 4045.8, the best determined one, as the observednbsp;ratios between the c’snbsp;(strongest line : other line)nbsp;are larger than the theoretical ones and the blendingnbsp;of Fe 4063.6 and Fe 4071.8nbsp;would affect these values innbsp;exactly the opposite sense.nbsp;Nevertheless, the centre-limb variation of the c-values will presumably benbsp;about the same as for thenbsp;undisturbed wings. This isnbsp;confirmed by Fig. 15, whichnbsp;shows the centre-limb varroos é

^ cos amp;= I the four lines; all of themnbsp;show the remarkable increase of the wings at cos i?nbsp;= 0.3.

44

4 Centre of Zr 4045.601. 4nbsp;nbsp;nbsp;nbsp;„nbsp;nbsp;nbsp;nbsp;4046.083.

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