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PHOTOGRAPHIC MEASURES
OF CLOSE DOUBLE STARS.

D. REUIJL.

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PHOTOGRAPHIC MEASURES
OF CLOSE DOUBLE STARS.

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PHOTOGRAPHIC MEASURES
OF CLOSE DOUBLE STARS.

PROEFSCHRIFT

ter verkrijging van den graad van doctor
in de wis- en natuurkunde aan de rijks-
universiteit te utrecht. op gezag van den
rector magnificus dR. l. s. ornstein. hoog-
leeraar in de faculteit der wis- en natuur-
kunde, volgens besluit van den senaat der
universiteit tegen de bedenkingen van de
faculteit der wis- en natuurkunde te ver-
dedigen op

maandag 5 october 1931
des namiddags te 4 uur
DOOR

DIRK REUIJL,

geboren te kampen.

P. DEN BOER

SENATUS VETERANORUM TYPOGRAPHUS ET LIBRORUM EDITOR

UTRECHTnbsp;MCMXXXI.

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Het verschijnen van dit proefschrift biedt mij de gelegenheid,
mijn hartelijken dank te betuigen aan allen, die tot mijn weten-
schappelijke vorming hebben bijgedragen.

In de eerste plaats denk ik dan aan U, Utrechtsche Hoog-
leeraren.

In het bijzonder dank ik U. Hooggeleerde NIJLAND. Hoog-
geachte Promotor, voor Uw bereidwilligheid, de leiding van dit
proefschrift op U te nemen. Voor Uw belangstelling en steun
en voot de wijze waarop Gij Uw tijd tot mijn beschikking
hebt gesteld, betuig ik U mijn groote erkentelijkheid.

U, Hooggeleerde ORNSTEIN, dank ik voor Uw welwillend-
heid, mij in staat te stellen, van de voortreffelijke inrichting
van Uw Laboratorium gebruik te maken.

U, Zeergeleerde VAN DER BILT, dank ik zeer hartelijk
voor het vele, waarmee Gij mij tot steun zijt geweest.

Aan U, Zeergeleerde MINNAERT, betuig ik mijn grooten
dank voor Uw raad en steun, zoowel tijdens mijn academische
studie, als bij het werk voor dit proefschrift,

Iwish to express my feelings of gratitude to Dr. MITCHELL
for giving me the opportunity to work with the excellent in-
struments of his Observatory.

I wish to express my sincere thanks to Dr. VAN DE KAMP
for his interest in my work and for giving me many helpful
suggestions and much valuable advice.

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aan mijn vader en moeder
aan mijn vrouw

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CONTENTS.

page

§ 1. Introduction...............

§ 2. Program...............7,

§ 3. Observational Material........12.

§ 4. Measures..................

§ 5. Errors................23.

§ 6. Discussion of the Measures.......26.

a)nbsp;Relation between p and Di........26.

b)nbsp;.................3L

c)nbsp;Adopted standard system...........

d)nbsp;Photographic effects.............

e)nbsp;Systematic errors.............

§ 7. Researches by others.........44.

§ 8. Artificial Double Stars.........50.

§ 9. Catalogue..............58.

Literature..............77,

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INTRODUCTION.

In the past 35 years photography has become one of the
most powerful aids to the study of astronomy. It has been
developed to such an extent ithat at the present time its
application covers almost all fields of astronomical research.

One of its last conquests is double star astronomy.

The earliest photographic observaition of a double star was
made by Bond in 1858 with a 15 Inch equatorial telescope
at the Harvard College Observatory. From a number of plates
the distance and position angle of Mizar were derived.

Since then ithere has been relatively little progress. At the
present time the number of photographic measures is still
small as compared with visual observations at the micrometer.
This may partly be ascribed to the fact that with the same
telescope the limiting separation is greater for the photographic
plate than for the micrometer.

In the observation of photographically close doubles
peculiar difficulties arise as is also the case in the visual
observation of micrometrically close pairs.

The great advantage of photographic measures over visual
ones has clearly been shown by the results of Hertz-
sprung (1920) and others. The accuracy of the distance
obtained from one image only is about the same as the
mean of micrometer observations on 3 to 4 nights.

Micrometer observations very often are seriously affected
by systematic or personal errors. In photographic work
errors of this kind — at least for the wide pairs — are
practically negligible.

However this absence of systematic errors holds only
for pairs of separation larger than about \'quot;quot;,15 on the
photographic plate. Below this limit the measures are

affected by errors due to the action of repulsive and attract-
ing forces.

The maitter has been studied or mentioned in a number of
publication 2) Ko stink sky states the presence of systematic
publication K o s t i n s k y states the presence of systematic
errors occurring in measures of satellites. Quoting from
page 150:

_____pour deux images très voisines et très différentes

en dimension, une sorte d\'influence d\'une image sur l\'autre
,,,, doit affecter spécialement la distance mutuelle ap-
parente entre le satellite et la planète,quot;

In a second publication (1909) Kostinsky states that
measures of close doubles taken with different exposure
times show an increase in distance with growing exposure
time. For images overlapping °quot;°,014 the repulsion amounts
to -f °quot;°.020, Expressed as a function of Di, the distance
between the inner borders, the repulsion is given by:

80-Pi

7.9 (1 — e 100 ) , the unit being one micron,

Kostinsky puts forward three hypotheses, finally combin-
ing two of them as the most probable explanation of the
phenomenon;

______dass die Centra infolge einer reellen Deformation

der Bilder von unserem Auge imwillkürlich in entgegen-
gesetzten Richtungen verrückt werden,,----quot; (p, 27, 28).

According io Ross (1924) three effects are likely to
occur:

1.nbsp;turbidity effect,

2.nbsp;gelatine effect,

3.nbsp;„Kostinskyquot; effect.

The first two will make the distance too small, the third
one causes a repulsion.

1. The turbidity effect is due to the interaction of the
light of the two images. This causes an elongation of the
images at their adjacent sides. The distance of the centers
will thus ^be measured too small when bisections on the
pear shaped areas are made.

The amount of the attraction is dependent upon

aj) tihe distance Di of the iimer borders, the attraction
increasing with decreasing Di,

b) a factor A, this being the growth A (in microns) of
the diameter of the image with doubling of the exposure
time.

Assuming that Scheiner\'s equation holds for all
exposure ranges in question, A is defined by

A = r log 2

the term astrogamma F being proposed by Ross to denote
the coefficient of log E in

diameter = a F log E.

Ross has shown that the equation of Scheiner can be
readily deduced from B o u g u e r\'s law of intensity variation

— ZX

I = Ioe

, .nbsp;2 log 2 1

=nbsp;A-

Thus A is a measure of the seeing or definition. Its
influence on the turbidity attraction is such as to have an
increase in attraction with growing A, i. e. with declining
seeing.

The attraction reaches a maximum value amounting to
V2 A in the case of contact. Under average conditions A
amounts to 30 microns. The corresponding maximum
attraction in the case of contact is —^quot;quot;.OlS.

2,nbsp;The attraction caused by the gelatine effect is due
to the contraction during the process of drying, the adjacent
images behaving as one single image. Excluding pyro metol,
Ross finds the amount of contraction to be independent of
the class of developer. Moreover the contraction proves to
be independent of the separation within the limits of the
experiment. For doubles of separation or less the effect
amounts to —quot;quot;quot;.0016 in the average,

3,nbsp;The repulsive action of the Kostinsky effect must be
ascribed to a peculiar reaction of the developer. The
reaction products spreading outwards from the centers of

the images will evidently be twice as concentrated, roughly
speaking, in between the two images as in the neighbour-

hood of the outer borders.

Hence the inner borders will suffer from this deficiency
of the developer in the intermediate space and the images
will get flattened at the adjacent sides. This flattening is
very often apparent to the eye. It causes an increase m
distance when bisections on both images are made.

It is reasonable to assume that the Kostinsky repulsion
increases with increasing size and density of the image and
with decreasing distance Di. Thus for one and the same star
the repulsion will grow with increasing exposure time The
assumption proves to be justified in view of the results of

Ross and others,nbsp;. , „ ^nbsp;u

It will be readily seen that the Kostinsky effect may be

considered a consequence of the Eberhard effect. According
to Eberhard (1926) the developer affects the density of
an image. Of two images of equal surface intensity but of
unequal size the larger will be of smaller density. Assuming
the same chemical or physical process to occur in the
development of the double star image, the distortion of the
inner borders can thus be readily accounted for.

As the small gelatine effect is practically constant and
the turbidity action depends on the distance of the inner
borders and the definition only, Ross is able to apply
corrections for both. The corrected distances will then only be
affected by the Kostinsky repulsion, assuming Ross\' results

and theory to be correct,nbsp;t^ ,

In some of his experiments Ross finds the Kostinsky

repulsion to be quot;quot;quot;.015.

For further information concerning the above mentioned
effects the reader is referred to the quoted publications
and to § 6 of the present publication.

In connection herewith attention is called to possible
further effects of physiological nature.

a) There is little doubt that the bisection of the com-
ponent of a double image will be influenced by the pre-
sence of the neighbouring image. It is a difficult matter to

decide to which extent the bisections will be affected, the
sign of the error being even uncertain.

b) Moreover the question is put forward whether bisect-
ion errors of a pear shaped object occur in the sense as
mentioned imder (1).

Evidently we must discriminate between two effects in
this case. The first is the already mentioned turbidity effect,
the addition of blackened grains in the intermediate space,
causing the images to extend towards each other. The
second one is the physiological error, varying from one
observer to the other. For a certain observer it may be
such as to have bisections made outside of the centers,
the boimdary lines being a family of lemniscates as indicated
by Ross, In view of various results it seems that generally the
turbidity attraction overshadows this particular type of
physiological error.

For the sake of completeness and convenience some oither
researches concerning the problem will shortly be mentioned,
Lau (1912) has measured the artificially produced double
stars of a region which was exposed twice with a shift of
11quot; — i, e. quot;quot;quot;,177 on the plate. He finds an apparent repuls-
ion for greater intensity, the quantitative agreement with
Kostinsky\'s measures being very close also,

Bellamy \'\'] (1917) has investigated 436 doubles of the
Oxford Astrographic Catalogue by comparing the distances
with the visually determined values in the Bumham General
Catalogue, He finds the distances too small, the errors
growing with decreasing distance,

Mitchell and Olivier ») (1920) have measured the
distance of Krueger 60 on 27 plates, extending over a
period of 3 years, the distance decreasing from 2quot;,4 to 1quot;.8.
Comparison with Barnard\'s micrometer measures shows
neither attraction nor repulsion,

Hertzsprung (1920) finds that for close pairs both
attraction and repulsion may occur. The first in the case
of faint fuzzy images, the latter for sharp well exposed
images.

Van den Bos (1923) finds negative differences photo-

graphie minus visual below 4quot;.5 - i.e. quot;-.114 on his
plates — increasing with diminishing distance of the

components,nbsp;,111nbsp;j

From laboratory experiments Przybyllok and
Labitzke (1929) find neither attracting nor repulsmg

effects,nbsp;,nbsp;,

The results of Shajn (1927) aire in close agreement

with the laboratory data obtained by Ross. All images
being overexposed, the effect cf the Kostinsky action on
the distance measurements is very pronounced.

It may be mentioned in connection with this particular
problem concerning the distance between double star com-
ponents that similar results were obtained for close
spectral lines. In some cases the distances turn oùt too.
large, in others attracting forces must have acted upon
the images.

Measuring réseau lines intersecting at small angles
Turner (1917) finds attraction near the pomt of
intersection.

An attempt is made (§ 7) to interpret the results
mentioned above by closer examination of the methods
applied to obtain the data and discussion thereof.

§ 2.
PROGRAM.

The double star program in progress at the Leander
McCormick Observatory consists mainly in photographing
double stars with the purpose to determine absolute posit-
ions, i, e. the positions with respect to sets of comparison
stars. In this program the number of close pairs was
relatively small owing mainly to the observational difficult-
ies, e, g. the dependence on the seeing and the streneous
guiding. Moreover in view of the knowledge of possible
systematic errors the closer pairs were avoided for this
reason also.

The extension of the program towards the closer pairs,
suggesited to me by Dr, van de Kamp, seemed a suitable
subject for a dissertation. The work involves additional
labour as has been mentioned and requires much patience
from the observer.

Thus the plan originated to photograph and measure
these close pairs and to investigate the measures for
systematic errors.

During the summer of 1929 a number of plates was taken
under such exposure times as to secure a suitable set of
comparison stars on the plate. By means of a rotating
sector the brightness of the double was cut down, to the
mean magnitude of the comparison stars.

The intercomparison of the measures of this first series
showed discordances in the distance measures, the latter
evidently being affected by the Kostinsky effect. Com-
parison with micrometer measures revealed an other kind
of errors, the photographic distances being smaller for the
closer pairs. An analogous treatment of Hertzsprung\'s
measures yielded similar results, in good quantitative
agreement with my own measures. The preliminary results

were presented at the forty-third meeting of the American
Astronomical Society in a paper, the abstract of which
appeared in Popular Astronomy 38, 406; 1930.
The following results were derived:

Table 1, McCormick material.

Jmrn — 20quot;.8

N is the number of stars. The total number of images
amounts to 116.

Table 2. Potsdam material.

imm 15//4

The McCormick material was devided into underexposed,
normal and overexposed images. Thus the following values
of Ppi^ — Pmcr were derived:

Table 3. McCormick material.

Group (1) shows the influence of the attracting effects
only, as the Kostinsky effect is expected to be small for
weak images.

The increase of ppj^ — pj^ with increasing exposure
time (Kostinsky effect) — particularly in the case of the
closer pairs — is very pronounced.

In view of these results it was decided to secujre a set
of plates on close pairs exposed in the same manner as
performed by Hertzsprung (1920), In connection with this
work extensive measurements in the laboratory should be
performed in order to derive the absolute amount of
possible photographic effects, either repulsing or attracting,
A description of the method and some preliminary results
thereof may be found in paragraph 8, Due toi a course of
circumstances this work had to be stopped for the time
being. Hence the material obtained at the telescope had to
be treated in a somewhat different manner than was intended.
Instead of correcting the double star distances by means
of the corrections derived from experiments on artificial
pairs the corrections had to be found from the telescopic
material itself, comparing the latter with micrometric
determinations.

It will be readily seen that this method has a fundamental
drawback compared with the laboratory method. In the
latter the „truequot; distance between the components can be
determined and used. From double star photographs in
most cases no such true value can be found as all images,

whether under- or overexposed, may be affected by
systematic errors. Therefore the value adopted as the true
distance is the one determined from micrometer observ-
ations. It is known that the latter are affected by accident-
al errors of considerable size and often by systematic or
personal errors of the same order of magnitude. The
probable error of the mean of distance observations made
on 3 to 4 nights is of the order of quot;.1. This error may be
decreased by increasing the number of nights, but exhibits
only the internal agreement of the measures as was e.g.
pointed out by van den Bos (1925).

The accidental plate error, i.e. the error of the distance
of a single image, is about quot;.1 on McCormick plates.
Therefore the accuracy of the mean distance derived from
a large number of images will be very high as compared
v^th the accuracy of a micrometric distance as determined
by one and the same observer.

Up to the present time our knowledge of the systematic
errors of micrometer observations, particularly of the recent
ones, is relatively small. It was therefore decided to treat
all observations as if affected by accidental errors only and
use a large number of determinations by different observers.
It proved to be advisable to plot both recent and
earlier observations as most pairs, even those marked
„fixedquot; by Bvu-nham, show some change in distance in the
course of time. Extrapolating to the epoch of the photo-
graphic observation gives a value for the distance which may
bc used as the „standardquot; value for comparison with the
photographic distances, (see p, 32),

These standard distances are free from errors of the kind
which may affect the positions of close photographic
images.

The number of comparisons must be sufficiently large.
In that case it is assumed that the standard values will be
free from systematic errors.

In the selection of stars for the observing program I have
limited myself to doubles whose components are of about
the same brightness. For nearly all stars the difference in

brightness between the components is less than To exceed
this limit would tend to introduce a magnitude error, which on
account of its often very troublesome influence should be
avoided by any means.

In connection with the exposure times stars of about the
seventh magnitude (photovisual) are the most suitable.
Hence stars of magnitude 9quot; requiring exposure times
about ten times as large were taken in exceptional cases
only. For a few stars brighter than 7quot; photographs were
obtained with the aid of the rotating sector.

Thus the program was made up applying the above
mentioned criteria in the first place. Secondly preference
was given to stars on which photographic measures had
been made by others and to those for which a large number
of recent micrometer observations was available.

As no special attention was paid to such properties as
orbital motion, common proper motion, etc, not all stars
on the program are interesting ones from this point of view.
For reasons which will be mentioned in the next
paragraph the selection favors stars of high declination.

§ 3.

OBSERVATIONAL MATERIAL,
a) The 1930 material.

The plates were taken with the 26 inch visual refractor of
the Leander McCormick Observatory of the University of
Virginia, A description of the instrument may be found in
„Parallaxes of 260 Starsquot;, by S, A, Mitchell (Columbia Univer-
sity Press, 1920), A colour filter Wratten No, 12, minus blue,
in front of the plate admits light of wave lengths between
5300 A and 5900 A to the plate, the maximum sensitivity being
at about 5550 A, when Cramer Isochromatic plates are used.
All plates were taken as near to the meridian as possible,
the greatest hour angle being smaller than one hour East or
West, As the mounting of the telescope on the pier is fairly
light the former is rather sensitive to wind. Therefore
preference was given to stars of high declination. This selection
furthermore offers the advantage of making the necessary
guiding on account of irregularities of the driving clockwork
less troublesome.

Table 4 gives the number of stars for different declinations.

Table 4,

The geographic latitude of the observatory is 38° 2\' 1quot;,
The table shows that 56 % of the doubles, exposed on 51 %
of the total number of plates, were taken within about 20
degrees of the Zenith, The telescope is in constant use during
all clear nights for various classes of research. The time
available for the present work was limited to hours during
the middle part of the night and had to be made as profitable
as possible. Therefore a card system was made, arranged so
as to give the necessary information at the telescope. After
having pointed the latter approximately the field in the finder
was compared with the field as copied from the Bonner Durch-
musterung charts and the direction accordingly adjusted.

Next the double star was set near the centre of the field of
the large telescope and a suitable guiding star selected.

Most of the exposures were made on Cramer Iso Presto
plates as shown by Table 5,

Table 5,

The exposures were made by giving the telescope small
shifts in declination and after completion of a row of 10 to 12
images shifting in right ascension, and so forlth. The equipment
of the telescope does not include a shutter. Therefore the
beginning and the end of each exposure were performed
respectively by quickly putting the guiding star on the cross
of wires in the guiding eyepiece and moving it off.

The time required for either manipulation is less than half
a second and therefore small compared even with the shortest
exposure time (12 sec.). In fact most images do not show any
guiding error at all. Images having tails whether due to this

cause or to poor guiding were rejected before measurement.
Or, if measurable yet, the measures were given smaller weight.
Although the instrumental part of the work was performed
with the utmost care, this does not prevent however certain
images from being affected by atmospheric influences, errors
of telescope and plates or anomalous action of the developer.
Yet one should remember that the measurable images among
all exposures were selected after development.

Finding as a rule that the images did not suffer from the
above mentioned way of exposing I applied this method
without hesitation for all exposures.

Having made the last exposure the clock work of the
telescope was stopped and a bright star allowed to trail over
the plate.

For exposure times the geometric series 12—15—19—24—
30—38—48—60—.,. sec, (Hertzsprung 1920) was used. The
initial expostue time is dependent upon the star\'s apparent
magnitude, the transparency of the atmosphere and the seeing,
whereas the total range was chosen according to distance and
seeing. The numbers of doubles, plates and images for different
distances and qualities are grouped in Table 6,

The qualities of the plates indicate to which extent the
plates answer the purpose to which they were taken. In a few
cases for instance plates were purposely taken under rather
bad seeing (see p. 36), Therefore the seeing is not the main
factor determining the qualities of plates and images.

In this connection it seems worth mentioning that most
plates were taken under good and excellent or even ,.perfectquot;
conditions of seeing (see p. 40).

The average ntunber of images per plate is about 25, the
maximum and minimum numbers are 146 and 1 respectively.

The qualification of the plates was obtained by examining
the plates after development, using a magnifying glass of low
power. The numbers of images were taken from the sheets
with the measurements.

An attempt was made to obtain fairly equal numbers of
doubles, plates and images for the different distance ranges

in the first column. In view of the dependence of the observer
on the atmospheric conditions the result is satisfactory.

Table 6,

e = excellent,
g = good,
fg = fairly good.

As developer Carbonal (Hauff) was used. Plates 1—6
were developed in a tank, the solution being

Carbonal.......Vz oz.

Water........64 „

Potassium bromide , . , 30 grains

Time: 30 minutes at 65° F.

Plates 7—123 were developed in a tray, the formula used
being as follows:

Carbonal

Water........8

Potassium bromide . . .
Time: 10 minutes at 65° F,

The formula of the fixing bath is:

^ i Water........

\' I Hypo........

/ Water........

] Sodium sulphite (dry) , .
Sulphuric acid C,P, . , .
Chrom alum......

A and B mixed in given proportion and rotation,
B poured in A while stirring so as to avoid
precipitation,

b) The 1929 material.

The plates used in the preliminary investigation, ment-
ioned in § 2 have been taken along in the present discussion.
The total number of images is small, the nvmibers of plates
and stars are relatively large,

Cramer Isochromatic plates were used throughout.
The arrangement of Table 7 is similar to that of Table 6,
The table is selfexplanatory.

Table 7.

Nearly all plates of this set were taken under excellent
seeing.

Various developers were used:

Developer

Hydrochinone

(Determinations of Stellar Parallax,
diss. Sten Asklöf)

[ Water......35 oz

A.nbsp;^ Hydrochinone . , . ,1%
f Sodium sulphite ... 1

/ Water......35

\\ Sodium carbonate (dry) 1

B,nbsp;/ Potassium carbonate , 3

Potassium bromide . . 1/4
Sodium sulphite , , , 3

lA and IB.

Elon Quinol (Eastman Kodak) 2 tubes
Water 8 oz,
70° F.

Elon Quinol (E, K.) 1 tube
Water 8 oz,
70° F.

quot;Special cartridgequot; (E. K.) 2 tubes
Water 8 oz,
65° F.

Elon Quinol (E. K.) 1 tube
Water 8 oz.

Potassium bromide 1 : 16 60 drops
62° F.

Elon Quinol (E. K.) 1 tube
Water 8 oz.

Potassi^ bromide 1 :16 60 drops
63° F.

Plate

25922—3—4

25946—7—8

25968—9

26008—9

26011

26026—7—8—9

26030—1—2

26044—5—6

26060—1—2—3—4

26150—1

26181

26198—9

25849—50

25851—2

25861—2

25879

25880

Elon Quinol (E. K.) 1 tube
Water 8 oz.

Potassium bromide 1 :16 15 drops
64° F.

MoHitt\'s developer

Elon...... .

A, } Sodium sulphite (dry) ,
Distilled water to make

^ Sodium carbonate (dry)

Potassium bromide . .
Distilled water to make

lA and IB.

■f It proved necessary to use 20 grains
in order to prevent fogging.

Hauff\'s tank developer

24004

25808—9

25830

25847—8

26023

26129

§ 4,
MEASURES.

a) The 1930 material.

The plates have been measm-ed on a Repsold measuring
engine. This instriunent, belonging to the Observatory of Leiden
and temporarily used at the Astronomical Institute of Amster-
dam, was kindly put at my disposal through the courtesy of
Professors Dr, W, de Sitter and Dr, A, Pannekoek,
A description of the instrument may be found in
Sande Bakhuijzen, van de. Mesure des Clichés
d\'après la méthode des coordonnées rectangulaires.
Bulletin du Comité international permanent pour l\'exé-
cution photographique de la Carte du Ciel, Tome I, p.
164—204, 1892,

N ij 1 a n d, A. A, Uitmeting van den Sterrenhoop G.C. 4410
(dissertation, 1897; Dutch).
The periodic errors of the micrometer screw have been
investigated by measuring the distance of two specks on a
plate about ,1 apart. Table 8 gives the results expressed in
thousandths of a revolution as a unit (1 = °\'quot;,085), The
first column contains the starting points on the screw, the
second one the corresponding distances, whereas the differenc-
es with the mean appear in the last column. The probable
error of a distance is 2,6 expressed in the same unit.

Each value in the second column is the mean of 2 distance
measiu-ements. In all cases 5 successive settings on a speck
have been made.

It is evident that the periodic screw errors can be neglected,
in agreement with the results obtained by Nijland As to the
progressive error, judging by Nijland\'s measures and taking
into account the small distemces to be measured, a redeter-
mination of this error seemed not necessary.
All measures were performed at Utrecht during the months

20
Table 8.

March till July of 1931. To illuminate the plate artificial
light was used only, the light source being an ordinary electric
bulb. Underneath the plate a piece of lense paper was placed
so as to diffuse the light reaching the plate. The magnifying
power of the microscope was about 35 times.

The plates numbered R 2, 10, 13, 17, 24, 28, 33, 40, 41, 43,
54, 83 and 89 were measured on a Gaertner measuring machine
in Virginia also. This long screw engine is described in
„Parallaxes of 260 Starsquot; by Mitchell, whereas the description
of a slightly different type may be found in Publications of
the Allegheny Observatory, Vol 3, No. 11; 1916.

The examination of the screw resulted in finding both
periodic and progressive errors to be negligible. The measures
were made from January till June of 1930, with the purpose
of getting some preliminary results. It was then found that a
magnifying power of about 30 times is the most suitable. The
grain structure of the image is well visible, whereas the itnage
is not too large for bisection.

As regards the Repsold machine its circle carrying the plate
was investigated for excentricity. The accuracy required in
the determination of position angles as an additional result is
relatively small. Hence excentricity errors must be large to
be of any influence. As this was not the case small errors,
if at all present, were neglected and one microscope read only.
The meEisurements were performed as follows.
Firstly the circle positions for the trail parallel to the
horizontal and vertical wire were read. After substracting
90 degrees from the vertical reading the mean was taken and
called trail readitig.

Then the plate was oriented in such a manner as to have
the line joining the centers of the images parallel to the
horizontal wire. The advantage of this method is that the
distances are always measured in a similar manner which is
not the case when measurements are made in rectangular
coordinates, e,g, in the direction of right ascension and declin-
ation, From a comparison of the residuals H off (1929)
foimd the measurements in distance to be more accurate than
the measurements made in rectangular coordinates.

For every suitable image the plate was oriented by hand
and the circle read. This was repeated after reversing the
plate 180 degrees. The mean of all these readings was taken
as the orientation of the plate for the distance measurements
of all images. The distances run from 1quot;.5 to 5quot;,5, 1 mm.
corresponding to 20quot;.8 on the plate. The error of an orient-
ation amounts to 0°,5 as determined from good normally
exposed images. Therefore any errors introduced in the
distances by applying this method are negligible.

Next the microscope was pointed at the millimeter scale
and the distance between the lines 61 and 60 determined in
thousandths of a screw revolution. The distance between the
components of the double thread is slightly larger than the
width of a line. This assures an acciu-ate setting. On each
line 3 settings were made. In the average 1 mm corresponds
to 11 quot;quot;.75.

Next the images were jexamined emd estimated excellent,
good or fairly good. As to the shape of the double image

a scale was used according to which the images were classified
as follows:

0 —nbsp;no blackened grains between the images,

a —nbsp;some ,,nbsp;„nbsp;n n n

b — a bridge of ,,nbsp;))nbsp;1» If 1» •

c — the images in „contactquot;,
d — „ „ „blendedquot;, i.e, overlapping.
Then all suitable images were measured. Each image was
bisected twice with the single thread and the screw was read
in thousandths of a revolution. This was repeated with the
plate rotated 180°. Furthermore in both positions of the plate
single settings were made on all 4 borders of the double image.
These measures were recorded in hundredths of a revolution.
The temperature in the room was kept at about 67° F. dxuring

all measurements.

All images having been measured the distance between the
lines 61 and 60 was measured once more-

Information concerning \'the error of bisection and the error
of a setting on a line of the scale will be found in the next
paragraph,

b) The 1929 material.

This series of plates was measured on the above mentioned
Gaertner machine. The method of measurement was the same
as that applied to the 1930 material.

§ 5.
ERRORS,

1. The errors of measurement are classified, as follows:

a)nbsp;The error of bisection

Investigation of the material giVes for the groups of
excellent, good and fairly good images as the probable
error of one bisection ,54, .65 and .74 respectively,
the weighted average being .66{jl.

Thus in the distance measurement of one image
probable errors are introduced amounting to ,38, ,46
and ,52 respectively, the weighted average being .47 jjl,

b)nbsp;The error of setting on a border

This error has been determined from measures of the
distance between the outer borders Do, The error
introduced in the measurement of one Do by the error
of one setting on a border is equal to the latter.
The probable values determined are 2,5, 2,7 and
3,4 (jL respectively, the weighted average being 2,9 jji,,

c)nbsp;The error of setting on a line of the millimeter
scale fj.

The probable error of one setting on a millimeter line
amounts to quot;quot;,0061, Thus a probable error of quot;^0035
or ,3 % is introduced in the value of a 1 mm interval
as expressed in screw revolutions.

The unpublished results of a determination of the scale
value of the McCormick plates were kindly put at my
disposal by Dr, Vyssotsky.

The value used is 1 mm = 20quot;,748, the value of the probable
error being about quot;,0005,

2. Image and plate errors.

The systematic errors are discussed in full in the next
paragraph, A table of corrections has been derived by
investigating all available material. Application of the cor-
rections for the images of a same plate will introduce an
error which may affect both image errors s^ and plate
error fp. This will be readily seen as the corrections C
have been derived from all plates.

Regarding the remaining errors after correction as purely
accidental the error of one image may be expressed by

s^ representing the other errors of measurement namely
and the errors of the micrometer screw.

A comparison of the corrected distances on a same plate
gives the internal error

s^ is small with respect to the other errors and can be
neglected.

Thusnbsp;_~nbsp;represents the image

error after correction in which expression is small as
compared with the pure image error.

As to the plate error, for its determination a large munber
of plates on one and the same star is needed. However the
largest number occurring is 4. Therefore neither £p, the
pure plate error, nor the plate error which is inherent in
the corrected measures can be determined with sufficient
accuracy.

The intercomparison of curves of different plates on a
same star has been made relative to the corresponding
values of A (see p. 37). A marked dependence on A has
been shown.

Correcting the curves by means of this relation offers the
opportunity to derive the order of magnitude of the pure
plate error fp.

For the construction of the table of corrections in § 6, e
the material has been devided into 3 groups of A. Thus
slight errors are introduced which are partly responsible for
the errors e .

Finally the order of magnitude of the pure image error £j
may be determined with sufficient accuracy from the
distances between individual points and curve on the plots
mentioned on page 27.

DISCUSSION OF THE MEASURES.

a) The relation between p and Di.

If there is such a phenomenon as the interaction of two
neighbouring images, a reasonable assumption is that this
interaction depends upon

1.nbsp;the distance of the inner borders Di,

2.nbsp;the distance between the centers p,

3.nbsp;the sharpness of the image.

The third factor is governed mainly by the seeing or defin-
ition and may be expressed numerically, e.g. by using a
personal scale from 0 to 5, 5 representing the condition of
perfect seeing, i.e. maximum sharpness. Since however not the
seeing itself but its effect on the plate is the essential
criterium, preference mvist be given to the A scale, A being
the growth in microns of the diameter of an image with
doubling of the exposure time (see p. 3),

For one and the same plate A is assumed constant. Hence
it seemed advisable ito investigate graphically the relation
between p and Di, each plate giving a plot.

As has been stated the presence of at least three influences
may be expected. The attracting forces are the turbidity and
gelatine effects, respectively due to the interaction of the
light of the two images and to the contraction of the image
during its drying process. The first increases with decreasing
Di, the second is mdependent thereof. The repulsing force is
caused by the developer, the latter being deficient in between
the two images. This repulsion grows also with decreasing Di,

As to the developer effect one seems justified to assume
that it will be negligible in the case of underexposed images.
Hence for these images systematic errors, if any, will be
negative — i,e, pph—pM lt; o* ^^ ^ matter of fact the plots
show this phenomenon in many cases. It appears that already

for fairly blackened images the developer repulsion outgrows
the attractions and this difference continues to increase with
increasing exposure time, i, e, with approaching adjacent
borders. However, when the exposure time is such that the
condition of contact or slight overlap is reached, the rate of
increase of the measured distance diminishes and the ciu-ve,
instead of keeping its resemblance to an exponential function,
starts to bend down in the direction of the Di axis.

It will be readily seen that not every plate gives a curve like
the sinuous one just mentioned. In fact many different types
have been found. If the number of images and the range of
exposure times are sufficiently large all close pairs show the
above mentioned relative increase of p with\' decreasing Di,
This may then in the simplest case be a linear relation. As to
the absolute dimensions of the errors these are uncertain for
a single plate as a consequence of the uncertainty in the extra-
polated micrometer distance.

In Fig, 1 the plot of R 61 is shown. This plate on 44 Bootis
was taken on the 26th of April, 1930,

The seeing was estimated to be 4—5, the transparency of
the atmosphere was called 3 on a scale on which 5 denotes
maximum transparency. The sky was called „clearquot; and the
thermometer read at 51° F,

The total number of images amounts to 146 of which 42
images are excellent, 56 good and 48 fairly good.

The probable error of a single image, derived from the
deviations of the plotted points from the curve, amounts to
3,0 fjL, The exposure times have a range from 12 to 120 sec.
The value of A derived from 67 images is

A = 28{i.,

In both coordinates the unit is 1 micron = quot;,02075,
The distance determined from micrometer observations is
^M = 3quot;.06 ± quot;,014
or \'quot;■quot;,1475 on the plate.

The excellent, good and fairly good images are represented
by black, half black and open circles. The relative increase of

•00

B s B

jSp^^witli decreasing Di is very evident and is numerically shown
by Table 9.

The values of Di have been computed by means of the
relation

Di = 2 P^-Bo.
Table 9.

Unit: 1 micron.

An attempt will now be made to give a qualitative explanation
of the most complicated type of p-Di curve found. The
explanation is tentative only, owing to the mixing up with
personal errors which very likely will be dependent upon
Di also.

Starting with the underexposed images it is evident that
if the borders are sufficiently close, e.g. Di lt; 80 [ji, for
A = 30 fjL, the images will be elongated at the inside. Bisect-
ions will be made on two areas being reinforced at their
adjacent sides and appearing of homogeneous density to the
eye. Hence the distances will be measured too small.

With an increase of exposure time the images grow,
involving a growing attraction. At the same time the increase
of intensity will result in having a gradual decrease of the
density from the centre outwards. To the eye the image
appears to have a nucleus of maximum density. In view of
the fact that bisections are made on such a nucleus, if
present, the measures will get freed from the turbidity
influence. Moreover the latter is strongly decreased by the
behaviour of the developer which is deficient in between
the two images.

Continued increase of exposure time involves a steady
growth of the images, i,e, a decrease of Di, and at the same
time an increase in size and density of the nucleus.

Assuming the developer effect to increase with increasing
exposure time the adjacent sides of the images will suffer
more and more from this deficiency of the developer. Several
observers have noted the apparent flattening of the images.
The result in the measures is shown by a steadily growing
distance.

Suppose the exposure time be pushed that far that the
maximum density on the plate is reached. Having passed this
stage the gap between the flattened borders will gradually be
filled. Thus the rate of increase of p will gradually diminish
and the curve will bend towards the Di axis.

As has been stated no attempt has been made to give a
quantitative analysis of ithe p-Di curve. The table of cor-
rections to be given (§ 6, e) has been derived by comparing

the curves with standard values (see p, 32, 33), Due to the
uncertainty in the measurement of Di, the inner borders
being moreover systematically displaced, in practice p has
been plotted against Do and finally for each plate each Do
has been converted into Di by means of the standard
value p J,,

The greatest range in p ,^on a single plate is 31,6 microns,
corresponding to a range in Di of 160 microns, or to a range
in exposure time of 1 to 45.

b) A. The growth A (in microns) of the diameter of an
image with doubling of the exposure time has been chosen for
a classification of the plates according to seeing or definition.
The values of A have been derived for all plates on which
the number of images ib sufficiently large. The results are
unreliable for such plates as were taken through clouds or
under progressively changing seeing.

The average A amounts to 29 microns, the maximum and
minimum A are 69 and 12 microns respectively. There is a
pronounced correlation between A and the estimated seeing
at the telescope, wliich is shown by Table 10 and its graphical
representation in Fig. 2,

Table 10.

n is the number of plates.

It appears furthermore that for the condition of excellent
or perfect seeing A approaches to a limiting value. This
could be expected as for these conditions A depends mainly
on the turbidity of the plate,

c) The adopted standard system.

As has been mentioned on page 9 micrometer measures were
taken as the standard values for comparison. All errors were
considered to be accidental ones, thus neglecting personal
or systematic errors. The dependence of the quality of the
observations on the size of the instrument is of little signi-
ficance as has been pointed out by van den Bos (1925),
Baize (1929) and others. Therefore this factor was
neglected in assigning weights. The observations were weighted
according to the number of nights only, A measurement on 1 and
a mean of 2 nights were given weight 1, a mean of 3, 4, 5 and
6 nights was given weight 2, whereas all values derived

from measures on. more than 6 nights were given weight 3.
As a rule the measures were collected by going backwards
chronologically, starting with the very recent ones. Thus an
average of 25 observations per star was obtained. For most
cases the number of measures made during the last 15 to 20
yeafs was sufficiently large, for the remaining part measures
had to be taken back to 1900 or still fiurther back yet. For
the latter Lewis\' Catalogue of 2-stars and Burnham\'s Gener-
al Catalogue were used. In a few cases 25 observations
could not be found, even in going back as far as William
Herschel\'s measures. As to the modem observations these
were collected from a large number of different publications,
some of them listed on pages 77 and 78, Though completeness
is not claimed the number of overlooked recent observations
will probably be small.

For each star the measures were plotted chronologically
and the extrapolated value determined on the assumption
of a linecir relation. This seems justified as the interval of
time is short for the rapidly changing — and therefore fre-
quently observed — pairs, whereas in the cases of a long
interval of time the distance changes very slowly. An except-
ion was made for a few stars showing clearly a curved relat-
ion due to fast orbital motion. In those cases a smooth curve
was drawn by hand, fitting the plotted points as well as
possible.

For some stars orbits are available. Nevertheless these
stars were treated in the same manner as the others so as
to apply one and the same method to all stars. Their orbits
are not based on the most recent observations. Moreover
they happen not to fit the modem observations. Thirdly ob-
servations may have been rejected, others corrected for
personal error. The standard system which has been adopted
here might indeed be spoiled by including one or a few values
computed from orbits.

The plates taken on C Cancri had to be omitted in the
general discussion, i, e. in the derivation of the table of
corrections. The observations did not allow to determine the
variability of the distance to any degree of accuracy,

The total number of observations collected is 1843 on 73
stars, an average of 25 observations per star.

The average probable error of the extrapolated value
amounts to quot;.025, the average probable error of a single ob-
servation is quot;,11,

d) Photographic effects.

A very elaborate discussion has been given by Ross (1924)
whereas several other observers have considered the matter
to some extent. Plate errors rather than physiological effects
are the cause of the occurrence of systematic errors in the
photographic distance measures of close pairs.

Owing to the change in the original working plan the in-
vestigation of artificial pairs (§ 8) has reached a preliminary
stage only. It is evident that photographic effects should be
studied in the laboratory. It is suggested to investigate photo-
metrically the intensity distribution of enlarged images. This
would yield the relative effect of the developer and would
furthermore show to which extent the erroneous bisections
must be ascribed to the personality of the observer.

The theory of the turbidity action as given by Ross seems
to be essentially correct. There is some doubt however
whether its influence on the bisections is as simple as assum-
ed. Particularly in those cases for wich a notable density
has been reached it seems doubtful whether the Kostinsky
repulsion can be calculated by simply correcting the observ-
ed difference by means of the computed turbidity effect.
The effect of the gelatine contraction as determined empiric-
ally on the other hand may readily be accounted for.

The turbidity effect is dependent upon A and Di, For the
latter Ross uses the measured distance between adjacent
borders. For large values of A the borders get more and
more diffuse. Moreover the values of Di obtained in this
manner are too large due to the incomplete development at
the adjacent sides of the images.

The second one of the three effects considered by Ross is
the gelatine effect, a shrinkage of the image as a whole
during the process of drying. With the exception of pyro

metol the same ntimerical result was obtained for all classes
of developer, within the errors of the experiment. Further-
more the contraction appears to be constant between Di = 0
and Di = 80 (X, amounting to — 1.6 [a for doubles of separation
of »quot;.1 and less.

As to the above mentioned Kostinsky effect this is very
likely caused by the developer reaction known as the Eber-
hard effect. Whatever be its chemical or physical explanation
the existence of the Eberhard effect merely is sufficient
to account for the Kostinsky effect observed in measures of
close doubles.

The results obtained for a possible dependence upon the
class of developer are not conclusive. From 11 plates
developed in various solutions Ross finds a pronounced
retrocession of centers amounting to 9,6 {a for Di = -f 10 p,.
The object measured was an artificial double star of
separation. The ranges in exposiu-e time, Di and image
diameter were 1 to 240 sec,, 96 to 10 {jl and 76 to 171 res-
pectively, the corresponding A being 12,5 [jl.

Taking into account the influence of both gelatine con-
traction and turbidity attraction the repulsion due to the
developer alone is even larger than the value given above.

From Table 13a (p, 41) iit appears that the systematic error
as derived from the telescopic material for Ai, pu = 175 [x
and Di = 0 amounts to -f- 4,8 |jl, in good agreement with the
results obtained by Ross,

In § 8 a comparison between Ross\' and my laboratory
results is given.

e) The systematic errors.

For a statistical discussion the material was treated in the
following manner. Each curve may be represented by

1.nbsp;its slope with respect to the Di axis,

2.nbsp;the amount of ppj^ — p^^ for Di = 0, i,e, the case of
contact, to be denoted by „zeropointquot;.

For most plates the plots are such as to allow a straight
line to be drawn through the points. In those cases in which
a marked curvatiu-e is present it was decided to use that

part of the plot for which the curvature is smallest Thus
either the underexposed or the overexposed images or both
were neglected and a straight line was drawn fittmg the
remaining points as closely as possible.

The dependence of the slope and zeropoint on p^ and A
was investigated. Moreover the coefficients for the correlation
between A and p,^ and the one between slope and zeropoint

were computed,nbsp;, , inbsp;.r

The dependence of A on p^ was investigated with the

only purpose to determine quantitatively the value of the
correlation coefficient. As a matter of fact the dependence is
qualitatively a mere consequence of the observational selection.
The closest pairs cannot be photographed unless the seeing
is excellent. On the other hand for the wider pairs a wide
range of seeing is allowable. Moreover in view of the depend-
ence of photographic effects on A a number of plates on
wide pairs was purposely taken under rather poor seemg.
The following correlation coefficients were found:

1.nbsp;zeropoint and p^.....r = . 600 ± ,048 (p, e,)

2,nbsp;zeropoint and A...... = . 234 ± , 075 „

3nbsp;slope andp^...... = - . 362 . 061 „

4nbsp;slope and A.....^ = . 074 ± , 068 ..

5nbsp;A andp^.....r= .592 ,052 „

6, slope and zeropoint, . r = . 059 ± . 086 „.

1nbsp;The first result shows the marked increase of zeropoint
with p„ or the increase with increasing diameter. This is a
manifestation of the Kostinsky effect which assumedly

increases with increasing diameter,

3 The third correlation coefficient indicates the tendency
of the slope to decrease with growing p^. This result can be
readily explained by the fact that for the larger distances the
curves in the average do not extend to such small values of
Di as are reached for the closer pairs. Hence photographic

effects will be smaller for the first,

2nbsp;In the second case there seems to be no pronounced
correlation. This is a remarkable fact since the intercompar-
ison of plates on a same star indicates a pronounced depend-
ence as will be shown later (p, 37), The correlation coefficient

may be statistically explained as follows. The correlation (5)
shows the prevalence of large values of A for the larger
distances, which could be expected a priori (see p, 36),
Combining this with the coefficient found in case (1) a corre-
lation coefficient for case (2), if of any significance, must be
of positive sign,

4,nbsp;No correlation between slope and A was found. In view
of the correlation between A and p^j, relative to the corre-
lation (3) one might expect to find a slight correlation between
slope and A- This would then be such as to show a tendency
of the slope to be smaller for larger A-

6, No correlation is present between zeropoint and slope.
The first is clearly related to pjjas has been shown in (1),
the relation being such as to have zeropoint increasing with
increasing pjj. The less pronounced correlation between
slope and pj^ shows a tendency of the slope to diminish with
increasing p^i- Therefore this result does no need any
further comment either,

5,nbsp;This correlation has been mentioned in connection with
case (2),

The dependence of ppjj on A was investigated as follows.
The curves representing different plates on a same star were
compared relative to their corresponding values of A- This
intercomparison is free from the errors of the standard
values. An examination showed at first sight that ppj^ de-
creases with increasing A in the average.

Denoting dp as the change in ppj^ corresponding to an
increase in A of 1 (jl, it is evident that dp must be governed
by two factors acting in the same direction. The first is the
differential Kostinsky effect. Let Ai and A2 belong to plates
(1) and (2) on a same star, Ao being larger than Ai. The
images on (1) and (2) with equal diameters — i, e, equal
values of Di — are differently acted upon by the Kostinsky
effect. The images on (2) are of smaller density than the
corresponding ones on (1). Hence they will be less influenced
by the repulsive developer reaction.

Thus the differential Kostinsky effect causes:

_ p^ lt; 0 for A2 gt; Ar

The second factor is the differential turbidity action. The
turbidity attraction increases with A- In the case of contact
it amounts to V2 A (see p, 3).

Thus e.g.:

P2 —Pi = —for As —Ai = 10[i,.

For increasing Di this difference decreases, the rate of
decrease being dependent upon A«

A value of dp has been determined from each set of — i.e.
2 to 4 — plates on a same star.

Next the dependence of dp on Di has been investigated.
The individual values of dp have been foimd from the differ-
ences between corresponding parts of the curves, i.e. over-
lapping iin Di. Thus each dp is related to a certain Di, for
which the average Di for the overlapping parts of the curves
was taken.

Disregarding the weights the large dispersion among the
individual values of dp can be accounted for by the cases
for which the range in A is relatively small. Assigning
weights however allows a fair determination of the relation
between dp and Di. dp is found to be negative, jdpj decreasing
with increasing Di, in excellent agreement with the depend-
ence of both differential Kostinsky action and turbidity
effect on Di. Table 11 contains the values of dp, dt and
dK = dp — dt.

Table 11.

Unit : 1 micron.

The order of magnitude of the probable error of each dp
in the second column is .05 {x.

The third column contains the differential turbidity effect
at A = 30 {A as a function of Di, The lasit column contains the
differences between the values in columns (2) and (3).

In view of this result and the coefficient found for the cor-
relation between zeropoint and p^j the assumption made on
p, 26 proves to be justified. Thus the work was carried out
on this principle — i,e. grouping the plates according to pjj
and A.

Each curve was read ait points differing 10 f^ in Di, Thus for
each plate a set of differences pp^ — p^^ was obtained relat-
ive to their corresponding values of Di. The differences
were weighted taking into account the error of the standard
value and the error of the curve, derived from the deviations
of the individual points from the curve.

Weighting according to -j-^—^ would perhaps be prefer-

^M ^Ph

able from a theoretical standpoint. It would however cause
the curves of smallest weight, though significant as separate
observations, to be of practically no influence. Therefore it

was decided to assign weights proportional to

1/

Ph

The numbers of plates for different values of A are given
in Fig. 3,

The grouping according to A is shown by the following
Table.

Table 12.

In Fig|, 4 the results are plotted with respect to Di, each
curve belonging to a certain pj^ (see Table 13),
The unit is 1 micron.

Fig, 4,

Fig, 4 shows that on any vertical line for corresponding
curves, i, e, curves belonging to the same p^j^

fAi gt; f Aa gt; ^Aa (see p, 37).

Converting the errors into correctibns by reading the cvirves
and reversing ithe sign yields 3 sets of corrections, given in
Table 13 a, b, c.

The values marked : are less accurate than the others.
As to the latter the value of their probable error is about ,5 |jl.

Table 13a.

Ai

Unit : 1 micron.

Table 13b.

A.

Unit: 1 micron.

Table 13c.

As

Unit: 1 micron.

RESEARCHES BY OTHERS.

Some of the investigations dealing with the subject have
been mentioned in § 1.

It may be of interest to give the results of a comparison
with the „standardquot; visual system. Only those investigations
were considered for which the number of coincidences with
the present series is sufficiently large.

Hertzsprung\'s measures yield the following result:
For Pm lt; 3quot;.o /Jph -PM = -quot;.076 ± quot;.010 (p.e.) from 11 stars.
For piA gt; 3quot;.o /Jph -PM = -quot;001 ± quot;.Oil (p.e.) from 16 stars.

The probable errors of one difference are quot;.033 and quot;,045
respectively. From Hertzsprung\'s published errors and the
errors of the micrometer measures as derived by me the
average probable errors of one difference amount to quot;,022
and quot;,027 respectively.

The discrepancy is easily explained by the fact that both
Hertzsprung\'s errors and the errors of the standard values
are but measures of the internal agreement in the two cases.
It is probable however that the difference is mainly due to
systematic errors of the standard values.

The result shows that in the average the distances of
Hertzsprung\'s close pairs are too small. This is in good
agreement with the results published in Pop, Astr, 38, 406;
1930,

The scale value of the Potsdam plates is 1 mm = 16quot;,39.

O s g o o d\'s measures do not show a pronounced negative
difference ,,photographic minus standardquot; for the close pairs.
This is not surprising as the scale value of his plates is
1 mm = 8quot;,24, whereas all pairs considered have distances
larger than 2quot;,3 excepting one double of separation 1quot;,85,

The differences for 25 stars yield:

For PiA lt; equot;.onbsp; quot;.007 ± \'\'.013 (p.e.),

the probable error of one difference being quot;,065.

As derived from Osgood\'s errors and the errors of the
standard values the average probable error of one difference
is quot;,030,

The measures of Przybyllok and Labiitzke treated
in a similar manner yield:

Yotpu lt;4quot;.onbsp;= -quot;.096 ±quot;.030 (p.e.) from 7 stars.

For pu gt; 4quot;.o Pph-PM = - quot;.011 ± quot;.030 (p.e,) from 9stars.

The probable errors of one difference are quot;,080 and quot;.068
respectively. The order of magnitude of the errors of the
photographic measures was derived. Combined with the
errors of the standard values the average probable errors of
one difference were found to be quot;.023 and quot;,027 respectively.

The scale value of the plates is 1 mm = 41quot;,84.

In this connection the laboratory experiments of the
authors must be mentioned. No evidence of photographic
errors was found. It must be kept in mind however that this
may have partly been caused by the difference in magnitude
of the components and the relatively large distances of the
centers. It is likely that in this case photographic effects are
small, maximtun effects occurring for components of equal
magnitude.

Van den Bos has shown from comparisons with visual
measures that for close pairs his distances are measured too
small,

A comparison with the standard system yields:

For Pu lt; 6quot;.o /Jph - /^M = - quot;.180 ± quot;.029 (p.e.) from 8 stars.

the probable error of one difference being quot;,082.

As derived from van den Bos\' errors and the errors of the
standard values the average probable error of one difference
amounts to quot;,057.

The scale value of the plates is 1 mm = 39quot;.37.

The comparison of the measures of Marriott and Pit-
man with the standard values gives:

For Pmlt;5quot;5 /\'pk -/\'m^ - quot;.183 ± quot;.034 (p.e.)
from 10 stars, the probable error of one difference being quot;,108.

For the photographic measures the order of magnitude of
the errors was determined. Combining with the errors of the
standard values the average probable error of one difference
was found to be quot;,057.

The scale value of the Sproul plates is 1 mm = 18quot;.74.

The coincidences of H o f f\'s measures with the standard
values give the following result:

For ^M lt; 5quot;.o/Jph —/\'M quot;.150 quot;.033 (p.e.) from 9 stars,

the probable error of one difference being quot;,098,

The average probable error of one difference was derived
from Hoff\'s errors as estimated by me and the errors of the
standard values. It was found to be quot;.029 approximately.

The scale value is 1 mm = 29quot;.26,

S h a j n has compared his measures of doubles taken with
the normal astrograph of the Poulkovo Observatory with
visual observations. The images were overexposed. The results
are in good agreement with Ross\' laboratory data. Arranged
according to distance p the repulsion is largest for the closest
pairs. The differences decrease when the images taken with
the longest exposures are omitted. The Kostinsky effect is
shown most clearly by grouping the differences with respect
to Di.

Shajn finds a repulsion of 4,5 [x in the case of contact
and a maximum effect of 9,7 ^ for Di about — 60 (/„ If the
relative decrease for still more overlapping images shown by
a repulsion of 7,2 {jt, for Di = — 120 is real, it would be
in excellent agreement with the frequently occurring type of
curve found in the present investigation and the qualitative
explanation attempted thereof.

It was suggested by Shajn and others to cut down the
exposure times as much as possible. As far as reduction of

the troublesome Kostinsky effect is concerned this is undoubt-
edly advisable. It must be remembered however that in this
manner one is likely to introduce the errors due to attracting
causes to their full extent. They may be of considerable size
too, particularly so under mediocre conditions of seeing.

The results of Kostinsky®) were the first chronologically,
so far as I am aware; the repulsions noted by several other
observers later on were named after him.

In view of all recent results his measures can easily be
explained. Relative to the imequal magnitudes of the com-
ponents the question is put forward to which extent his
measxures may have been affected by a magnitude error.
Assuming both Kostinsky effect and turbidity action to reach
a maximum for components of equal magnitude, Kostinsky\'s
results may loose slightly as to their quantitative importance.
Yet the order of magnitude of the effect agrees very well
with the data of others. The repulsion reached a maximum
value of 17 (ji, for Di = — 40 [x, being zero for Di larger
than 80 p, and amounting to 10 [ji, in the case of contact.

The results obtained by L a u ®) were found by a different
method. Possible errors inherent in the method were already
mentioned by Ross but thought to be negligible as to their
probable size.

The measures show a good agreement with those of
Kostinsky,

The complicated combination of repulsive and attracting
forces offers the possibility of observing the distances unaf-
fected by systematic errors. This case seems to be present in
the measures of Krueger 60 by Mitchell and Olivier ®).
The distances were compared with Barnard\'s visual measures.
Yet one objection seems worth being raised namely as
regards the comparison with one visual observer only. Lately
the accuracy of Barnard\'s micrometric work has been
doubted by van den Bosch Aside from possible personal
errors the accidental errors render the detection of small
systematic errors of the photographic measures impossible.

As to the measures of Olivier on parallax plates and
so-called D-plates, the number of comparisons with the
standard system is 6.

The result is:

For/JMgt; 2quot;.5 PPK-Pu = \'M5± quot;.067 (p.e.) from 5 stars.
For/5Mlt;2quot;.5 /jph —= —quot;.19nbsp;from 1 star.

the probable error of one difference for the first comparison
being quot;.12. From the estimated photographic error and the error
of a standard value this error is calculated to be quot;,06.

The number of comparisons is too small particularly for
the closer distances to have much confidence in the values
derived. It would therefore be of interest to have a detailed
account of the author\'s statement regarding the absence of
systematic errors in his measures found from comparison with
visual ones. Unfortunately this was not given, A critical
discussion of systematic errors present in some of Olivier\'s
measures has been given by van den Bos ^o) (1927),

V y s s o t s k y\'s data obtained from measures of Espin
doubles as compared with Espin\'s measures show strong
evidence as to the effect of the tiurbidity action for weak
images. The manner of comparison being similar to that
applied in the case of Krueger 60 the results are subject to
the same objection as has been raised therefor.

The discordance shown by the investigation of B e 11 amy
namely the apparent attraction for overlapping images seems
more difficult to explain. The cause must be sought for either
in the photographic measures, as regards their accuracy, or
in the micrometer distances used for comparison. Yet a third
possibility must be considered also, i.e, the images being
weakly exposed in spite of their blended shape.

The other photographic determinations will not be discussed
here, the ntunber of comparisons being too small, or Hhe
epoch of the observations being too early. As to K i n g\'s

measures e.g. there are many stars in common with) the
present list. However, owing to the early epoch of King\'s
plates, the number of stars suited for a comparison is too
small.

As has been shown in view of recent data various results,
in fact nearly all, though disagreeing among each other at
first sight, can be plausibly accoiuited for,

A discussion of data obtained from similar investigations
on spectral lines will not be given, notwithstanding the subject
possibly being equally interesting as the one considered here.
It seemed preferable to limit myself to the case of double
stars exclusively. A limitation which proved justified a
posteriori since so much work remains to be done on this
subject.

ARTIFICIAL DOUBLE STARS.

There is little doubt that in order to obtain good know-
ledge about the effects governing the behaviour of close
images on a photographic plate, artificial star images must
be investigated. The true distance being known one is able
to find the absolute amount of attraction or repulsion,
whereas from ordinary double star exposures relative effects
are found only.

An apparatus for producing artificial double stars need not
be complicated. Therefore it seems advisable for the double
star observer in the case of photographing close pairs to
make some additional experiments on artificial pairs, using
the same observing conditions as regards plates, developer
etc.

With the purpose of making a more or less extensive series
of measurements on artificial double stars an apparatus was
constructed in the Physical Laboratory of Utrecht under
careful supervision of Dr, M, G, J, Minnaert, I am greatly
indebted to him for his help and interest in the work and
wish to express my gratitude to the director Prof, Dr, L, S,
Ornstein for giving me the opportunity of making use of the
splendid equipment of his Laboratory,

In spite of the fact that no definite results were obtained,
due to the unavoidable discontinuation of the work, it seems
worth while to give at least a description of the apparatus
constructed.

Firstly it will be readily understood that the experimental
conditions in the laboratory should approach the observation-
al ones at the telescope as closely as possible. The star-
like images have to be produced in such a manner as to
obtain the same distribution of intensity as in the case of
the star images. Since in the formation of the latter the

scintillation is the main factor the light distribution must be
Gaussian (M, G, J, Minnaert, Onregelmatige Straalkromming;
diss,, Dutch),

As light source L (Fig, 6) a large Philips Argenta bulb
(300 Watts, 220 Volts) was used. A brass plate S (Fig, 6),
15 cm, square, placed close to the lamp, was pierced with
holes arranged in such a way as to have the number of holes
from the centre towards the edges decreasing as a Gaussian
fimction. To obtain this distribution concentric circles were
drawn at equal distances and for each ring between two
successive circles the computed number of holes bored. The
final shape of the holes is indicated by the section view in
Fig. 5,

Fig, 5,

The holes were coned out so as to reduce the „shadow
effectquot; of the holes near the edges. The total number of holes
in all 12 rings, each of which has a width of 5,5 mm,, amounts
to 1024,

Before entering into any more details a schematic view of
the mounting is shown by Fig, 6,

The thin brass plate A is pierced with circular holes of
0,7 mm, diameter arranged as indicated in Fig, 7 (Section
view in Fig, 8), each pair representing a double star. Each
hole gives a pinhole image of the diaphragm S on the piece
of ground glass d. These pinhole images resemble diffuse
star images. They are sharpest for d close to A, the
sharpness decreasing with increasing distance d-A, The
latter may be read on a scale. By means of this device any
condition of seeing can be imitated, the reproducibility
making this method preferable above others.

The images on the ground glass are photographed with the

-e-ih

^-^

z.s

2. a

-iy

-é-

Fig. 7.

Fig. 8.

camera C and reduced in the ratio 20 to 1. Hence the size
of the components and their mutual distance are comparable
with those of the telescopic images.

To this simple apparatus some improvements had to be
made so as to be sure of obtaining a light distribution in the
image strictly comparable with the theoretical one.

1),nbsp;The first requirement is the following.

Let „corresponding pointsquot; of two images on d, forming
a pair, be two points at equal height and having exactly the
same mutual horizontal distance as the two holes in A, As
seen from the camera objective which is pointed at d, two
such corresponding points must have the same quantity of
light when closing either one of the two holes in A, This was
achieved by placing the lenses and I2, having focal
lengths of 20 cm, and 4 m, respectively, in the path of the
rays. The adjustment is such that S is placed at the focus
of 1^. Thus each hole of S throws a beam of parallel rays
on to A, two parallel beams of which will reach the corre-
sponding points on d. The place of I2 is such that its focus
coincides with the camera objective. Hence the two beams
reaching the objective from corresponding points will have
left d in precisely the same direction,

2),nbsp;Secondly care must be taken to have in each image
the light distribution as computed theoretically.

In the first place it is necessary to investigate the intensity
distribution of the light coming from the left hand side of L.
Some photographs were made providing an intensity scale
also, the densities measured on an Ica Sensitometer and the
intensity determined for each point on the surface. The
measures resulted in finding the surface intensity distribution,
some areas having an intensity of only 50 % of the maximum.
This wide range is more than could be expected from a visual
examination only. It seems probable that this unequal distri-
bution is caused by local irregularities in the thickness of
of the glass. The niunbers of holes in S were then corrected
so as to neutralize the effect of the heterogeneous light
giving disc.

Furthermore it is readily imderstood that the holes of S,
as seen from A, are not equally large but so much the
smaller the larger their distance from the centre. Therefore
allowance should be made for the remaining „shadow effectquot;
(Fig. 9).

For a central hole let the angle be A^o • o^®
centre A«i . then we have:

unbsp;, A p\' cos a

^ and

A^i_p^ cos cx,

A«„nbsp;D

As h = dtga,

p\' = (p — dtga) cos

Thus, substituting in (1):

A«i (p — dtga) cos^ OLnbsp;, d .

—-= ^--= cos^ oc--sin a cos

A«onbsp;pnbsp;p

The distance D is 200 nun,, the width of the holes 1,1 mm.
Let the effective depth of a hole be 0,7 mm, in the average,
then we get correction factors running from 0,98 between
ri == 5.5 mm, and rg = ILO mm, down to 0.72 for the ring
between r^ = 60,5 mm, and r^g = 66,0 mm. The arrangement
of the holes in S was altered accordingly.

There still remains one effect to be corrected for, i. e. the
scattering of the light by passing through the piece of ground
glass d. The light distribution of the images on d is altered
by the peculiar law of scattering of the ground glass which
transmits less of the incident light the larger the angle
between the transmitted and the infalling beam. The effect
was determined photographically and corrected for.

In order to shield the camera from stray light a set of
diaphragms was used indicated by D in Fig, 6, F is a
yellow filter.

With this arrangement a number of plates was taken, Ilford
Rapid Chromatic plates were used throughout. The formula of
the developer is

Carbonal.......2 cc.

Water........64 „

Potassium bromide 10 % . . 5 „

Time: 15 min, at 65° F,

The formula of the fixing bath used is the same as given
on page 16,

Alltogether 34 plates were selected for measurement, the
total number of images being 102,

The „truequot; distances were derived from photographs taken
with d close to A, The following values (in microns) were
obtained:

1.nbsp;83.7.

2.nbsp;114.1.

3.nbsp;133,2,

4.nbsp;154,8,

5.nbsp;204,2,

6- 265,6,

As to the other plates, these were taken with 6 different
distances d-A, thus reproducing 6 different conditions of
seeing. The corresponding values of A were found to be
15, 16, 19, 24, 30 and 37 microns.
The differences p pj^ — p,^^^ are given in Table 14.

The values marked : are uncertain.

Notwithstanding the small number of images the qualitative
agreement with the previous results (see p. 40) is very good.
With the exception of a few values Table 14 exhibits the same
characteristics as shown by Fig, 4, For instance the decrease
Pph— Ptrue increasing A for corresponding values of
P truenbsp;the same Di is pronounced.

As to a quantitative comparison, herefor the average values
of Ai, Aa and As. as given in Table 12, may be used.
will then be seen that the numerical agreement is satisfactory.
The agreement with Ross\' results is very good. This may
be seen by comparing Ross\' measures (Table 30, p. 179)
with the values in columns 4 and 5 of Table 14 a, b, c of the
present publication.

It may be remarked in this connection that the artificial
images are of high quality compared with the telescopic ones.

It is my intention to continue the experiments in the way
as indicated above and to obtain an extensive series of
measures, A matter of great importance is the separation of
photographic and physiological errors. It has been suggested
to investigate photometrically the enlarged double images.

The results may be of interest to those applying photography
in the determination of positions of double stars.

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§ 9.
CATALOGUE.

Tables 15a and 15b contain some information for both
series of plates, respectively for the R-series (1930 material)
and the ^-series (1929 material).

Column (2) gives the range in exposure time,
Coliunns (3), (4) and (5) contain the numbers of measured
images.

Column (6) gives the values of A- Some of these were
derived with the aid of the curve gjiven in Fig, 2 (p. 31).

Colimin (10) of Table 15b contains the openings of the
rotating sector.

For instance for sector 5 the angle of the opening amounts to

X 360°, i, e, 5 % of the infalling light is transmitted.

REMARKS
(Table 15a).