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The Solar T{otation
in June igii
from Spectrographic
Observations

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B. HUBRECHT

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THE SOLAR ROTATION IN JUNE 191 I
FROM SPECTROGRAPHIC OBSERVATIONS

THE SOLAR ROTATION IN JUNE 1911
FROM SPECTROGRAPHIC OBSERVATIONS

PROEFSCHRIFT TER VERKRIJGING VAN DEN GRAAD VAN DOCTOR IN
DE WIS- EN STERREKUNDE AAN DE RIJKS-UNIVERSITEIT TE UTRECHT
OP GEZAG VAN DEN RECTOR MAGNIFICUS DR. H. SNELLEN HOOG-
LEERAAR IN DE FACULTEIT DER GENEESKUNDE , VOLGENS BESLUIT
VAN DEN SENAAT DER UNIVERSITEIT TEGEN DE BEDENKINGEN VAN
DE FACULTEIT DER WIS- EN NATUURKUNDE TE VERDEDIGEN OP
DINSDAG 6 JULI 1915 DES NAMIDDAGS TE DRIE UUR

DOOR

JAN BASTIAAN HUBRECHT

geboren te utrecht

Cambridge :

Printed at the University Press
1915

ffiambritige:

printed by john clay, m.a.
at the university press

AAN DE NAGEDACHTENIS VAN MIJNEN VADER

Ni

■frv.--),-;\'^

quot;s

a..

■ ■^Ji

.m.

Mijn dank wensch ik te betuigen aan de Faculteit der Wis- en Natuurkunde
welke mij vergunde voor haar te verschijnen met een proefschrift gesteld in de Engelsche
taal. Ik gedenk dan tevens de jaren, nu reeds geruimen tijd in het verleden liggend,
gedurende welke ik het onderwijs van de toenmalige leden der Faculteit genoten
heb. In het hijzonder ben ik veel verschuldigd aan mijnen hooggeachten Promotor,
Professor Nijland. Hoewel mijne latere werkzaamheden op het gebied van het
zonne-onderzoek niet te Utrecht zijn uitgevoerd, was hij het toch die mijne belang-
stellingin de physische astronomie heeft wakker gemaakt, niet het minst door het mij
indertijd mogelijk te maken deel te nemen aan de eclips-expeditie naar Sumatra.

Op die expeditie werd ook op andere wijze de grondslag gelegd voor verdere arbeid,
door mijne kennismaking met Professor Newall. Om onder zijne leiding te werken
vertrok ik in 1906 naar Cambridge. Zijne welwillendheid in het ter mijner be-
schikking stellen van de nieuwste instrumenten aldaar, zijn raad en daad in het oplossen
der practische vraagstukken die zich bij het gebruik daarvan voordeden, en zijne
voortdurende belangstelling en aanmoedigende critiek in de latere ontwikkeling van
het onderzoek hebben het mij mogelijk gemaakt deze bijdrage tot de kennis van de
zon te leveren.

Zonder de bijzonder nauwkeurige metingen voor mij door den heer Tunstall
te Manchester, gedurende mijn verblijf aldaar, uitgevoerd, zouden de verkregen uit-
komsten zeker niet het gewicht hebben dat de lezer hen, op grond van hunne onderlinge
overeenstemming, misschien zal toekennen. Ook zijn deel aan de volgende bladzijden
is dus niet gering en moge hier met waardeering herdacht worden.

TABLE OF CONTENTS

§ i. Introductory

PART I. OBSERVATIONS AND REDUCTIONS

§ 2.nbsp;Instrument and method of observation

§ 3.nbsp;Record of observations

§ 4.nbsp;Measurements

§ 5.nbsp;Reduction to velocities ,

§ 6.nbsp;Additional corrections .

§ 7.nbsp;Complete table of results

PART IL DISCUSSION OF RESULTS DERIVED FROM LINES OF
DIFFERENT WAVE LENGTHS.

§ 8. Comparison of results for individual lines .

• • • •

§ 9. Search for a cause of the variation of velocity-difference with wave

length ........

§ 10. Evidence of a similar effect in earlier investigations
§ ii. Conclusions as to individual lines and elements

PART III. DISCUSSION OF VELOCITY-DIFFERENCES AT
DIFFERENT LATITUDES.

§ 12. Results for pairs of plates.....

§ 13. Probable errors......

§ 14. Symmetry with respect to the solar axis
§ 15. Symmetry with respect to the solar equator

§ 16. Reduction to one quadrant.....

§ 17. Rotation law for the epoch of observation
§ 18. Tentative explanation of plate-to-plate results
§ 19. Comparison with earlier investigations
§ 20. Summary.....

§ i. Introductory

The rotation of the sun as determined by spectroscopic means has been
the subject of several important investigations since the publication of Duner\'s
well-known memoir Recherches sur la rotation du Soleil in 1893. Both in
this work as in his later research^ Duner deals with visual observations only,
as does also Halm in his account of the work done on similar lines at Edinburgh 2.
Since then the subject has been taken up photographically by Adams at Mount
Wilson^, Storey and Wilson at Edinburgh^ J. S. Plaskett and De Lury at Ottawas,
Evershed and Royds at Kodaikanal®, Schlesinger at Allegheny\', H. H. Plaskett
again at Ottawa« and the present author at Cambridge The International
Solar Union has considered the subject of enough importance to institute a special
committee for the solar rotation. This committee met at Mount Wilson in 1910
and again at Bonn in 1913. On the latter occasion the principal subject of dis-
cussion was the discordance of the results obtained by the different observers.
It was unanimously agreed that the main object of each of the investigators at
present occupied with the work should be to clear away this discordance^®. It
is with that object in view that in the present paper the author proposes to deal
more at length than is usual with some of the instrumental and observational
details of the work as well as with the measurements and reductions. Possibly
light may thus be thrown on the causes of these differences which so far seem
to be greater than is compatible with the probable error claimed by each
investigator^ for his results.

In a former paper already alluded to^ the author has published some results
obtained at Cambridge. Two sets of observations were dealt with, one con-
cerning only the solar rotation at the equator and made at epochs extending
over a considerable range of time (Dec. 1910—Oct. 1911), the other made in the
first half of June 1911, giving comparisons of radial velocities at points all round
the sun. The latter set consisted of one series of plates out of four which had
been taken. The other three series have since been measured by Mr N. Tunstall,
a student of the Victoria University of Manchester. It appeared at once that
the consistency of his measures was a good deal greater than that of the author\'s
original measurements of the first series, and accordingly this first series was
remeasured by Mr Tunstall. The results relating to all four series may thus
be regarded as affording homogeneous material for discussion.

1 Nova Acta Reg. Sac. Upsala, 4, i, No. 6, 1906.nbsp;® A.N. 173, 294. 1907-

® Astrophys. J., 26, 203, 1907; 29, no, 1909; Carnegie Institution of Wasliington, Publ. 138, 1911.

« M.N. Lxxi, 674, 1911.nbsp;® Trans. R.S. of Canada, 6, 3, 1912.

® M.N. LXXIII. 554, 1913.nbsp;\' Publ. Allegheny Obs., 3, 13, 1914.

® Journal R. Astr. Soc. of Canada, 8, 307, 1914.nbsp;® M.N. lxxiii, 5. 1912.

Trans. Int. Union for Solar research, iv, 123.

h.nbsp;i

Part I. Observations and Reductions

§ 2. Instrument and method of observation

The observations were made with the instruments which are called the MClean
Solar Instruments. A ccelostat mirror of 16 inches (40 cm.) diameter reflects the
sun\'s rays on to a secondary mirror of similar size which reflects them in a hori-
zontal direction, due North, on to an achromatic 12-inch (30 cm.) lens having a
focal distance of 60 feet (18 m.). These three optical parts are all mounted in a
little building immediately South of the
Newall dome of the Cambridge observatory.
Fig. i gives a diagrammatic presentation of
their arrangement. C is the ccelostat mirror,
with its normal perpendicular to the polar axis
on which it is rotated by clockwork. The axis
is supported in a stout frame which can-be
moved up or down an inclined bed ah worked
parallel to the polar axis on a heavy wedge-
shaped casting. Thus the ccelostat mirror
can on any day of the year be so placed
as to direct the reflected beam on to the
secondary mirror 5 whatever the sun\'s decli-
nation may be. The whole casting supporting
the ccelostat mirror can further be moved
East or West parallel to itself along a couple
of rails cd and ef in order to obtain at every
hour of the day full illumination of the
secondary mirror and therefore also of the image lens 0. The beam of light
travels, unenclosed, right through the Newall dome and the image is formed on
the slit of the spectrograph which is installed in a room adjoining the dome on
its North side. The image, which at the epoch of observation had a mean
diameter of 172 mm., can be moved across the slit by means of cords which
work the slow motions of the secondary mirror. Another cord connection makes
it possible to move the image lens along a sHde ghik in the line of the beam
and so adjust its focus.

The spectrograph is a horizontal instrument of the Littrow form, fitted
with a plane grating of about 60,000 effective rulings. It was designed by
Professor Newall for work on sunspots and solar rotation and described by him
elsewhere as well as in the author\'s paper already referred to. Its description
therefore need not be repeated; reference is only made to the most important
features of both instrument and method of observation in the following remarks.

1 M.iV. LXVIII, 6, 1907.

§ 2]nbsp;Instrument and Method of Observationnbsp;3

The whole spectrograph is capable of rotation round its horizontal axis so
that the slit can be placed tangentially or radially to any required point of the
sun\'s limb. A scale is provided giving the position angle from an arbitrary zero
reading.

The overlapping parts of the spectra of different orders are separated by
means of a small angled prism with dispersion at right angles to the dispersion
of the grating.

The spectra of the two points of the sun\'s limb each time to be compared
were not photographed simultaneously. The exposure at one point was taken
as nearly as possible midway between two half exposures of the other point.
By proceeding in this way no error is introduced provided that any gradual
change in the position of-the lines during the total length of the exposures is of
a linear kind. This condition was amply satisfied as appeared from many tests.
The divided exposure has not in a single case interfered with the definition of
the lines,—a fact which affords sufficient justification of the method.

The region investigated extended from A 4300 to A 4400, this being half the
region allotted to Cambridge in the cooperative scheme decided upon at the meeting
of the Solar Union held at Mount Wilson in 1910. With the great dispersion
used (fourth order, i Â. u. = 1-13 mm.) one plate does not cover the whole region ;
two plates had always to be taken with A 4325 and A 4375 approximately central
on each respectively. Ilford Empress plates were
used throughout, giving comparatively fine grain
without being too slow.

With regard to the position angles, that of the
parallel is always first found by rotating the in-
strument until, when letting the solar image trail

across the slit plate, it remains tangential to a r ---

line drawn upon this plate perpendicularly to thenbsp;^

slit. The spectrograph is then further rotated

through an angle computed from the Ephemerisnbsp;,

given in the Companion to the Observatory until

the slit is tangential to the sun at a point of the

required latitude. Other lines are engraved on thenbsp;. ^

vx 1 , 1 • -u 1nbsp;,nbsp;Fig. 2. Sht plate to show method

silt plate which make it possible to compare, of setting solar image tangential

without again rotating the instrument, the spectra or radial to sht.

not only at the ends of a solar diameter, but also at points separated by 90° from

one another. These are shown diagrammatically in Fig. 2 where SS\' is the

slit, TT the line scribed at right angles to the slit already mentioned, while

Pi\' p2quot;-gt; Pigt; p2quot;-\' ^^^ short lines scribed in such a way that when, as in

the figure, the sun\'s limb is made to coincide with p^ and p-l the centre s of

the slit is at a definite distance h inside the point of the sun\'s limb where the

tangent to the limb is parallel to the sht. Coincidence of the Hmb with p2

and would bring upon the centre of the slit a point just inside the limb at

the other end of the diameter belonging to the latitude in question. But by
bringing the limb in coincidence with p^ and p^ or p^ and p^ we can throw upon
the centre of the slit light from a point just inside the limb at a distance of 90
from the first point. The instrument remains untouched between the two obser-
vations required for each plate; in one observation the slit is tangential, m the

other the slit radial to the sun\'s image.nbsp;, . ..t,

An adjustable diaphragm is placed in front of the slit so that either the

central millimetre s was exposed (single aperture s) or else the two millimetres d

adioining it on either side (double aperture d).

Throughout the series of observations here discussed, plates were taken
comparing pairs of points 90° apart from one another. With the instrument
fixed and the slit therefore in one position angle four
plates were taken, one comparing the spectrum at a
point I (Fig. 3) with that at a point 2, the next that
at 2 with that at 3, the next 3 with 4, and finally
4 with I. This was repeated for the second region of
the spectrum. The slit was then moved to another
position angle by rotating the instrument round its
horizontal axis and a second set of eight plates was
taken with a different starting point. Care was
always taken not to begin the plates of the new set
immediately after the instrument had been moved;
a sufacient interval of time was given to allow
temperature and other conditions to settle down.
A complete quot;seriesquot; of observations consists of six of these sets of eight plates,
starting from 0° e., 15°, 30°, 45°, 60° and 75° s.e. respectively^. Such a series
contains therefore observations taken at intervals of 15° round the suns limb.

§ 3. Record of Observations

Four complete quot;seriesquot; were secured in the first fortnight of June 1911,
as already mentioned on page i. The almost perfect weather conditions
prevailing at the time made it possible to obtain within that short mterval the
192 plates involved. In Table I a complete hst of these plates is given.

Only plates which have been measured and of which the results are
discussed in the present memoir are included in this table. In the fourth
column A denotes the region A 4300—A 4350, B the region A 4350-A 4400. The
exposure times, given in column 5, show considerable variation, especially short
exposures (15 seconds) having been possible after a second pohshmg of the ccelo-
stat mirror on a day when also the atmosphere attained maximum transparency

» The notation o°e., 15° s.e. etc. for points on the sun\'s limb is used throughout the present
publication for the points at the East end of the solar equator, at solar latitude 15 m the solar
S.E. quadrant etc.

Record of Observations
Table I. List of Plates

* Set completed by N 62.
t Set completed by N 63 and N 64.
II To go with plates N9-11. Mirrors polished
To go with N 26 and N 27.

t Set completed by N 60 and N 61.
§ To go with N 24 and N 25.
before taking this plate.

Solar Rotation in Jtme 1911
Table I. List of Plates {continued)

1911
June 4

60° S.E. d
30° s.w. s
60° N.w. d

t To go with N 77 and N 78.
§ To go with N 129 and N 130.

Record of Odserva^ions
Table L List of Plates {continued)

1911
June 7

June 9

75°s.E. d

Solar Rotation in June 1911
Table I. List of Plates {concluded)

10

45° N.W. d
45° N.E. S
45° S.E. d
45° s.w. s

45° N.W. d

45° N.W. 45° N.E. S
quot;N.E. s 45° S.E. d

45

30° S.E. d
60° S.w. s
30° N.W. d
60° N.E. S
30° S.E. d

60° s.w. s
30° N.W. d
60° N.E. s
60° S.E. d
30° s.w. s
60° N.W. d
30° N.E. s
60° S.E. d
30° s.w. s
60° N.W. d
30° N.E. s

75° S.E. dnbsp;15° S.w. s

15° s.w. snbsp;75°N.W. ci

75° N.W.nbsp;15° N.E. s

15° N.E. snbsp;75° S.E. d

75° S.E. dnbsp;15° s.w. s

75° N.W. d
15° N.E. S
75° S.E. d

(Tune 7th). The sixth column gives the latitudes of the two points on the solar
imrcompared The letters d and s denote double or smgle opening in front of
he sS according to the position of the diaphragm mentioned m the preceding
~apr The sht was in the case of the double opening always tangential
Cthe sun\'s limb, in the other case always radial. The second latitude given in
tL colZn was always the one taken in one exposure between two half-exposure
It tte otter. Columns 7 and 8 give the temperatures inside the tube of the
spectoj^aph, half-way between grating and slit, and of the room It is seen

tfa^ trthiik felt cLr which was carefully f ^^quot;quot;lar c\'lTfgivc
succeeded in making the variations inside small andnbsp;^^ 9 f vc

the position angle of the spectrograph This ang e

nosition of the North point of the sun\'s unage on the slit plate (n) the ange
bSweTn wfaris and North point for the date and (iii) the lati ude of the
reqlS To^t. The first alters slightly with the date, and it also alters largely

§ s]nbsp;Record of Observationsnbsp;9

with the figure given in column 10 and referring to the adjustment in horizontal
position of the ccelostat mirror mentioned on page 2. Two positions were found,
96 cm. apart, which had the advantage of giving two positions for the North
point separated by exactly 30°. It was thus sometimes possible after having taken
a series of eight plates for one position angle of the spectrograph, involving four
points all round the sun at 90° apart, to move only the ccelostat mirror and then
at once, without rotating the instrument, to take a similar set of plates involving
four new latitudes differing by 30° from the first four and thus also forming part
of the required series. From footnotes attached to the last column, it can be seen
that sometimes sets of eight plates, belonging together, were taken at different
moments or even on different dates, owing to rejected plates or other causes.

§ 4. Measurements

As has been stated, all the measurements of these plates, discussed in the
present memoir, were made by Mr Tunstall.

The measuring instrument used is the Zeiss comparator B (1909), similar to
the one previously described by Professor Newall^. Two microscopes are fixedly
mounted over a slide which holds the plate underneath the one and, at a fixed
distance corresponding to the distance between the microscopes, a silver scale
100 mm. long and divided into xV mm. underneath the other. The eyepiece of
the scale microscope contains a micrometer arrangement allowing for the setting
of a double wire symmetrically over the nearest scale mark on the proper side.
The micrometer head is divided into 100 parts, while tenths of these divisions
can be estimated. In this way one ten-thousandth of a millimeter can be read
off ; the actual settings of the micrometer wire in the scale microscope were found
by special trial to be accurate within one or two units of this last decimal. The
bisection of spectral lines viewed through the other microscope is achieved by
the movement of the carriage bearing both plate and scale, actuated by direct
pressure of the finger without making use of the slow motion screw. Suitable
trials have shown that no advance in accuracy is obtained by using the slow
motion, while a great loss of time would be incurred. Anticipating a more
complete discussion of the measurements it may be stated that Mr Tunstall\'s
average probable error (due to both plate and scale settings) per displacement of
one line was 0-0004 mni. It is thus seen that the simple push method, advocated
by Professor Newall at the time of his first adoption of the Zeiss instrument, is
thoroughly justified, also for solar work. The excellent workmanship of the
sliding parts has made the method possible. When clean vaseline is apphed,
the smallest pressure of the finger keeps the sHde in motion with a minute velocity,
while as soon as this pressure is relaxed the sUde stops dead at once.

The plate was mounted on the stage parallel to the run of the slide (but see
also page 49). The wires in the plate microscope were then adjusted parallel to

1 M.N. LXV, 648.

H.

the spectrum lines. A diaphragm or mask allows the observer to see either only
the central spectrum or only the two other spectra above and below. The settings
were made in the following succession. Bringing the wire into coincidence with the
first line in the top spectrum, the corresponding scale reading was noted. The mask
was then moved to the other position and the wire brought into coincidence with
the line as it now appeared in its displaced position. All bias is thus eliminated
except that in favour of setting wire and Hne to coincidence in the same manner
in both cases, supposing, for example, that there was anything to choose between
setting the wire on the centre of gravity of the line or midway between the two
edges. But it is clear that a bias of this kind favours consistent measurement.
Without touching the mask the slide is now moved and the wire set on the
next line in the central strip. The mask is then moved and coincidence made
between wire and line as visible in the upper strip. On the third line the first
setting is made in this upper spectrum, the second in the central, and so on alter-
nately. When the last line has been reached a return is made, but now setting
on central and lower spectrum until the first line is reached again. The plate is
taken out and replaced end for end on the stage and the whole process is repeated.
For each single measured displacement of a line we have thus eight settings, four
on the single spectrum and four on the double, consisting of two on the upper
and two on the lower spectrum.

Table II. Selected lines

Plates A

Wave length
4299-149
4302-085

4314-248

4315-138
4320-907

4326-923

4331-811

4337725

4338-084

4339-882

4343-861

4344-670

4346-725

4347-403

4349-107

Wave length

4351-000

4352-908
4358-670
4366-061

4371-442
4373-415
4373-727

4376-107
4379-396
4385-144
4388-571
4390-149

4395-20T

4396-008
4400-555

Element Intensity

Tinbsp;I

Fenbsp;4

Fenbsp;2

Fenbsp;2

Crnbsp;2

Crnbsp;I

Fenbsp;2

Fenbsp;6

vnbsp;4
Crnbsp;2
Fenbsp;3

Vnbsp;2
Tinbsp;3
Tinbsp;I
Scnbsp;3

The whole measuring instrument was set up in a niche of blackened card-
board and covered up in such a way that no light whatever reaches the unused
eye. This considerably reduces the strain; an added advantage can be gained
by using one eye always for the plate microscope and the other for the scale micro-
scope. Artificial hght was employed, providing uniform constant illumination for
both plate and scale. A thick glass plate in front of the illuminating arrange-
ment diminished its heating effect on plate and scale.

Under such conditions of measurement Mr Tunstall was able to make 60
settings in 20 to 25 minutes and to devote as much as four hours a day to measuring

without undue strain on his eyes. It is to be noted that he employed the ordinary
eyepiece throughout. The author\'s method of employing a cylindrical lens, as
in the measures discussed in the earlier paper, and as described in detail at the
time^, was tried by him but rejected in favour of the ordinary method.

Fifteen lines were measured in each of the two spectral regions, i.e. on each
plate. Table II gives the wave lengths, origins and intensities of the lines, while
it also shows which of them belong to the class of enhanced lines. No elements
of atomic weight greater than 59 have lines in this part of the spectrum, while
on the other hand the exposures were such that the hydrogen line B.^ at 4341
was unsuitable for measurement.

§ 5. Reduction to velocities

To obtain the wave length differences from the measured displacements
the dispersion

ds

must be known. This dispersion varies from one end of the plate to the other,
as well as from plate to plate. The general formula for the grating spectroscope
is

mX = h (sin « sin 6) ......................(i),

where m is the order of the spectrum, h the interval between two adjacent lines
on the grating, i the angle of incidence and 6 the angle of emergence. In our
observations we had always w = 4 and h = 16933, when expressed in Angstrom
units. This formula has to be differentiated, keeping i constant, in order to get
the dispersion along the plate. We get

d\\ bnbsp;^nbsp;/ X

.........................(2).

d6 m

Now it is clear that

de^ I
ds~f\'

where ƒ is the focal distance. We thus have

d\\ hnbsp;anbsp;f \\

=nbsp;........................(3)

for the mean dispersion. To find the correcting term wanted giving its variation
with the wave length on one plate we deduce

mf

= ....................

1 M.N. Lxxin, 28, 1912.

and so, putting in ^ from (2)

d\\

=nbsp;......................(5)-

As to the variation of from the centre of one spectral region to the centre

of the other, there we get a different formula. In that case the grating has been
turned on going from one plate to the other so both i and 0 have changed, but
for the centres of the plates respectively i and B are equal and we have

mX= 2h sm 6 ..........................(6)

andnbsp;dk = —cos 0d0........................(7)

For the change in the dispersion in this case we thus get, by putting this into (4),

....................(8)-

In Table III

are given the numerical values for the dispersion for a pair of
plates. The figures for the observed dispersion are directly obtained from the
measured distance in mm. between two lines and their difference in wave length

Table III. Comparison,^ for two plates, of observed and calculated
dispersion {Angstrom units per millimetre)

Meannbsp;Observed Observed Calculated

wave length dispersion mean dispersion dispersion

4307nbsp;o-88i8nbsp;o-88i8

Plate N 208 4320nbsp;0-8799nbsp;0-8792nbsp;0-8797

(region^) 4333nbsp;0-8776nbsp;(for X 4324)nbsp;0-8779

4344nbsp;0-8765nbsp;0-8764,

4355nbsp;0-8781nbsp;0-8788

Plate N 215 4366nbsp;0-8770nbsp;0-8757 0-8773

(regions) 4379nbsp;0-8757nbsp;(for X 4377) 0-8754

4393nbsp;0-8734nbsp;0-8734

according to Rowland\'s table, the mean of these wave lengths being given in the
preceding column. The next column gives the observed mean dispersion for
the whole plate from the two lines at either end. From this mean dispersion the
calculated dispersion in the last column is obtained by applying the variation
found from formula (5), giving to 6 the value which we get from (3). The
agreement between observed and calculated dispersion is seen to be close, while
the difference between the observed mean dispersions for regions A and B has the
value which it should have according to (8).

Accordingly, in the reduction a dispersion factor was employed for each
line calculated in the same way as those in the last column of Table III. For
each plate the observed mean dispersion had to be determined. Its general

mean value for the A plates is 0-8795, for the B plates 0*8758, the range being in
either case not more than 12 units of the last decimal. The values were seen to
group themselves in sets of four, corresponding to sets of plates taken in immediate
succession with the instrument untouched. Some evidence of correlation between
dispersion and temperature appeared, as was to be expected. A double entry
table could now be constructed giving the dispersion factor for each line for each
value of the mean dispersion.

Table IV. Coefficients to convert displacements into velocities

(9),

so that for each wave length difference we get a further factor varying in inverse
ratio with the wave length to convert dX into km. per second, if V, the velocity of

light, is so expressed. The result of the combination is given in Table IV, where
the figures represent the values of

d\\ V R
Ts^ X R-h\'

of which product the third factor, constant for all plates and all lines and Uttle
different from unity, will be explained in the next section.

§ 6. Additional corrections

The correction for not exactly setting on the Umb is applied by the intro-
duction of the factor

R

R-h\'

just alluded to, into the velocity coefficient. R is the sun\'s radius in mm. and
h the distance, radially, inside the hmb. The latter distance is determined by
the manner in which the solar image is set on the sht plate, as is seen from Fig. 2.
The factor is in our case equal to 1-014. Variations in the diameter of the image,
caused by differences in the focus of the image lens, were found to change the
factor in maximo by one in one thousand and could therefore be neglected.

The application of the factor is further only rigorously correct in the case
of a body rotating as a sohd. Only then are we fully justified to take, as was
tacitly done by the method of measurement, the mean of the displacements
between the central spectrum and each of the adjoining spectra as representing
the displacement between the two points exactly central on the sht for the two
latitudes. The error, due to polar retardation, thus introduced amounts, however,
for our observations in maximo to 0-0005 km. per second and has been neglected.

Table V. Additional corrections for setting due to polar retardation

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o°e.nbsp;90 s.