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UNIVERSITY OF CALIFORNIA PUBLICATIONS
Determination of The Constant of
Refraction from Observations made
with The Repsold Meridian Circle
of The Lick Observatory
DISSERTATION IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE
DEGREE OF DOCTOR OF PHILOSOPHY IN THE UNIVERSITY OF CALIFORNIA
PRESENTED IN IQOI BY
RUSSELL TRACY CRAWFORD
[Reprinted from the Proceedings of the California Academy of Sciences,
Third Series; Math.-Physics; Vol. I, No. 8.]
DETERMINATION OF THE CONSTANT OF REFRACTION
FROM OBSERVATIONS MADE WITH THE
REPSOLD MERIDIAN CIRCLE OF THE
LICK OBSERVATORY.
BY RUSSEI.L TRACY CRAWFORD.
OF THE
UNIVERSITY
CONTENTS.
PAGE.
INTRODUCTION . . - . 105
1. The Meridian Circle 105
2. The Room 107
j. Meteorology 108
4. Plan for Observing 114
OBSERVATIONS 1 18
/. List 118
2. Details of Observations 119
j. Reduction of Observations 122
4. The Cons/ant of Refraction 190
j. Latitude 191
CONCLUSION 192
ADDENDUM 193
INTRODUCTION.
i. The Meridian Circle. The instrument with which
these observations for refraction were made has been fully
described by Astronomer Tucker in Volume IV of the
" Publications of the Lick Observatory, 1900." For the
sake of completeness, however, it will be described again
in this paper.
The instrument was made by Messrs. Repsold and Sons,
and was described by Professors Auwers and Krueger to be
" in its construction in every way suited to be the chief
instrument in an observatory of the first class/' (cf. Vol. I,
" Publications of the Lick Observatory.")
The aperture of the object glass, which was made by
Clark and Sons, is 6.4 inches. Its focal length is 6 feet
IO6 CALIFORNIA ACADEMY OF SCIENCES. [PROC. 3D SER.
4 inches. The tube of the telescope is in two parts, each
of which is attached to a central cube. Their diameters
decrease from 8.1 inches at the cube to 6.5 inches near
their outer ends. An eyepiece giving a power of 90 and a
field of 12' was used for these observations. The star
images formed are not exactly round, but are slightly elon-
gated in a direction parallel to the horizontal (declination)
thread. There being no component of this elongation
parallel to the vertical threads, it can have no effect upon
observations for zenith distance.
The axis is 3 feet 2^4 inches long, the distance between
the counterpoises being 2 feet 2 inches. The pivots are
3.6 inches in diameter and are protected by brass covers.
The telescope is furnished with clamps which, however,
were never used during these observations. After the
telescope was once set for a star it was not moved again to
make the bisection, this being done by means of the
declination micrometer. The value of one revolution oi
the screw of this micrometer is 48". 10. This value has
been adopted as the result of many determinations made in
past years. The micrometer thread is single.
The instrument has two circles, one of which can be
rotated about the axis of the instrument while the other is
rigidly fixed to it. They are both graduated to 2'. The
degrees, as numbered, increase counter-clockwise. The
diameter of the silver circle, upon which the graduations
are marked, is 26 inches. There are 130 graduations to
the inch. The fixed circle was used throughout these
observations. ,
The four reading microscopes on each side are alike in
all respects. They are 26.5 inches long and have clear
aperturqs of 0.55 of an inch. Their powers are 40 and their
fields are nearly one degree. The objectives are 5 inches
from the circle and their eye ends project 8 inches from
the frame holding them. The micrometer heads are divided
into 60 parts. One revolution of a micrometer head carries
the threads over:ne minute of arc of the circle. There
M.-P. VOL. L] CRAWFORD CONSTANT OF REFRACTION. 107
are two pairs of threads in every micrometer, but one of
which is generally used.
There is a separate broken telescope for setting. This
is supported on wyes attached to either pier and is at the
level of the lower rim of the circle. By means of this the
circle can be seen either from the north or from the south,
so that the settings can be made very conveniently.
The illumination for both the field of view and for the
circles under the microscopes is furnished by a Rochester
lamp placed in a cylindrical case 9 feet from the axis of the
instrument. This light also illuminates the heads of the
microscope micrometers. Most of the heat from this lamp
is carried out of the room by a pipe which extends from
directly over the lamp through the roof to the outside air.
A simple mechanism enables the observer to change the
system of illumination from a bright field with dark wires to
a dark field with bright wires and vice versa; he can also
reduce the amount of illumination at will.
The brick piers supporting the instrument are 34 inches
by 44 inches at the floor of the room and 22 inches square
at the top. The sides next to the telescope are vertical.
They are cased in wood with a layer of felt between the
surfaces. The platforms for the microscope reader are
entirely disconnected from the casing of the piers.
The microscope bearers are 23 inches in diameter and
17 inches long. The wyes for the pivots of the instrument
are attached to the inner faces of these frames.
The weights of the counterpoises hang from levers
26 inches long. The fulcra are in the centers of the levers
and are 6 inches from the inner faces of the microscope
bearers.
Two collimators, of same aperture and focal length as the
Meridian Circle, are suitably mounted. The collimator
micrometers are 35 feet 6 inches apart.
2. The Room. The Meridian Circle house on Mount
Hamilton has been most admirably designed. Its efficiency
will become apparent from the meteorological data to be
given later.
(2) May 5, 1903-
108 CALIFORNIA ACADEMY OF SCIENCES. [PROC. 30 SER.
The observing room is 43 feet long (north and south) and
38 feet wide. All of the walls are double. The outer of
the two is a louvre-work of galvanized iron which prevents
the sunlight from touching any part of the building proper.
The inner wall is of California redwood, and is separated
from the outer by a two foot air space. The ceiling is
also of redwood. It is about 16 feet above the floor.
Above the ceiling is an air space 8 feet high at the observing
slit and sloping to meet the east and the west walls.
The observing slit is slightly over three feet in width.
The covering for the slit is in four parts which open out-
ward. The ends are closed by shutters, each of which is
in two parts opening inwards. Each end is also provided
with a single shutter which slides up and down. For stars
at zenith distances greater than, 72 degrees these shutters
have to be lifted. When down they are very efficient wind
breaks.
There is a large canopy which can be rolled over the
instrument to serve as an additional protection in stormy
weather or when the instrument is not in use.
For a more detailed account of the instrument and room
see Astronomer Tucker's account of them in Volume IV
of the " Publications of the Lick Observatory, 1900."
j. Meteorology. To make quite sure of the condition
of the atmosphere at any time during the observations, the
thermometers were read, on the average, three times an
hour (at nearly equal intervals); and the barometer was
observed every hour. The reading of the wet bulb ther-
mometer was also taken when the dry was read. The
relative humidity has not been introduced into the reduc-
tions, but it was thought desirable to have it for possible
future reductions.
The barometer, Green 2839, nan g s on the north wall of
the observing room. It reads to one two-hundredth of an
inch. The dry and the wet bulb thermometers (F) hang in
the air space between the north walls. . The dry bulb ther-
mometer, used to indicate the external temperatures, is
Green 494. This thermometer has been calibrated at the
M.-P. VOL. I.] CRAWFORD CONSTANT OF REFRACWON. 109
Yale Observatory. The corrections which have been
applied to all the readings have been taken from the
following table sent from Yale Observatory:
/(Fj
Cor.
+o.i
32
Q w 2
52:!
! .1
, N
j
112
j . 1
The table which follows contains the unconnected temper-
atures (t), the readings of the attached thermometer (T),
of the barometer (B), and the times at which they were
taken. The readings of the wet bulb thermometer are not
given here.
no
CALIFORNIA ACADEMY OF SCIENCES. [PROC. 30 SER.
vO
M
IT)
Tl-
vo
M
if)
vO
M
tO
00 io o ON <S O ON 000 00 00 00 vO O
CSrOMfOfOMCSMNCS
OO CO O
<* -<t -tf-
10 tr>
00 00
o io
ovo t^co co oc co co
OO CO t^ \O
t^ t*. - t^ f
M t * M M
to io 10 10 10
ON CO
vO vO
O CO CM rf r^CO t~ M O to to to O
t-^ t^-co
vO vO VO
vO vO vO
OOvor^iOC*OOM<D ONCO io
to
vo
t^. vO
vO
t^ q
4 to
. M Tt t^ q
00 ' ' O\
s
co"
to
00 CO CO OC
O io O >O
iT'
1 >
vo VO VO vO vo
O r^ t^ ONCO coco M o OVOOOCQCO
vO vO vO VO ^O vO ^D vO vD vO ^O VO vO ^
*
0_
IO
t^ vO to M
vO vO vO vO
M M M M
IO to to to
M
co
VO
CO CO t^ VO
vO vO vO vO
J2>
<N ^t O
tOOCNMOONMM T^-VO CO
00 CO CO t^ t^ r^ r^.vO OvO VO vO vO vO
vO vO vo vO vO vO VO vO vO vO vO vO vO vO
CO
00
CO CO VO fO
M
*o
to m io io
i
SjN NIN ^ NN
to io to VO vO
vO vO VO vO vO
rj- if) tovO tOVO vOvOvOvOvOvOvOvO
vO vO vO vO vO vO vO vO vO vO vo vo vo vO
>0
N ON t^ io
co I s * r-. r^
to io io io
ON
s
t^ vO vO vO
O to to io
>
t^CO ^t fO rO ON io ^OO M O W O -rf-
o |^^ i^.vrt
to to to
VO vo to to to tovO vO vo t^vO
toiO'OtoiOioiotO'O'OtO
00
^
?
ON ON ON ON
to >o to 10
s h
3
i > ^
VO^
M vOOO
O O O ON
t^ t^ t> vo
rj- ON ON ON ONVO to (S ON lOCO
RRR
O O O O O O ON ONCO ONCO
S3
t^ O fO
O ON rOvO O ^ t>. M rj- t^ O
& 4 jo
VO t^- 00 ON
MM M M
M.-P. VOL. I.] C^^ WFORD CONST A NT OF REFRA CTION, III
3
t^ t^* t*> vo cO
M M M M M
vo vo vo vo vo
~ O ON t^ CO
t- t^. vO VO vO
M O O O O ONOO t^OO cO O 00 M ^t
**
M o t^ ON ON 00 CO t^ *t~>i t^ t^. r^-CO CO
tx, c^vO vo vO vO vo vO vO vO vO vO vO vO
:liJii|l|
"&ii&*
*
Tf VO M CO
vO vO vO VO vo
lO O vo vo vo
vo (*''
O t> t^OO OlNvOcOdOOvOOOcO
2= 8 S S S t r
'*!? 11 15
*l s Wl
8 -1 S 1 j
-s| S.rigs
U 7g.s|g
t^txt^t^t^t^t^t^t^t^t^l^t^t^
llrllitp
*'S) S -SSS
ttj^iWi
SQ
o
c
CO vo -rf N ON
iO vo vo vo vo
o co t>t t^ r^
t>, vo vo vO . *O
vOvNOOOOCO COCOW cOvorJ- T^CO vO
VO t^vO vo vovO vOvOvOvOvOvOvOvO
vOvOvOvOvOvOvOvOvOvOvOvOvOvO
^^'"o-S^S^
sffriiil?
g^l !!& s <
[ "s * 1 1 5 j > . c:
w n8~wS S '2
ftgfirtug-ng^
.*5i1liiall .
"(s
G
p
M to _ M O CO
C? I?
^O vO ^O ^O ^O
O O vN CO COVO CO VOCQ O ^ (N M t^
vO
3
o o oo co t^
l^ t^ vo vo vo
vo vo vo O iO
d ON ON ON CO
vo vo vo O *O
O ^VO MWOOOOMOJCHcOcOWO
ON O^CO CO ON ON ON O O O ON ON ONOO
vOvOvOvOvOvOvO t^C-^ i^vO vO vO vO
t*
CO 00 t- t^ t^. r^ t^CO CO CO CO 00 CO CO
vovovovovovovovovovovovovovo
CO
1**
CO ON vO t^ t^
CO OO CO CO CO
vo vo vo vo vo
t^ \yO vO vO vO
VO
3
lO vo vo iO *O
CO 00 C< CO O O O O O ON vo vo t*^ ^^
co co r- t^ t^vo vo t^-oo co co i>. t^ t^
vO vO vO vO vO vO vO vO VO vO vO VO vO vO
*^3 t
t^O covo ON covo Tf^M^.^0
T3 c.
t^i O cOvO ON cOvO O ^ t^^ ^ ^ t^ O
en
^ -rf vo vo t^ CO ON
MM MM M M
.;; CN
C^
^ ^- vo vO t->> CO ON
112 CA LIFORNIA A CA DEMY OF SCIENCES. [PROC. 30 SER.
In this table the unit of B is one two-hundredth of an
inch.
From this table the following data have been taken:
Maximum temperature = 74. o, July 3
Minimum temperature = 55. i, June 12 ,
Maximum range = 18. 9
Maximum barometer 5194, June 14
Minimum barometer = 5145, June 12"
Maximum range = 49.
During this period of observing, the maximum differ-
ence .between the dry and the wet bulb thermometers was
75. 5. 48. o = 22. 5. This was on June 29. The
minimum was 65. o 56. o = 9.o, which occurred
June 27.
Concerning the maximum temperature noted above,
74. o, it should be remarked that this was the first reading
of the period, and was taken several minutes before the
sun had set.
Besides the regular thermometers in the air space be-
tween the north walls, three other thermometers were sus-
pended from the ceiling of the observing room. All three
were swung under the observing slit, near the plane of
the meridian. One was directly over the instrument, and
three or four feet from the ceiling. The other two were
hung, one north and one south, about half way between
the instrument and the north and south walls respectively,
and at such a distance above the floor that the plane of the
axis of the instrument and the line of sight of the telescope,
pointed at about 83 zenith distance (north and south
respectively), would intersect the thermometers near their
bulbs.
Before being thus placed, these thermometers were
compared with Green 494, so that their readings could be
reduced for comparison with those of the external ther-
mometer (Green 494).
During the course of an evening's observations these
three thermometers were read just after reading the regular
thermometer. The average difference between the inside
and the outside thermometers was found to be the same
M.-P. VOL. I.} CKAWFORD CONS7*ANT OF REFRACTION. 113
for all three, and is o.3 (F). It is nearly always the case
(in this hemisphere) that the southern part of a room is a
trifle warmer than the northern. But this is not the case
on Mount Hamilton. The temperature of the air inside
is, on the average, very uniform and but very little (o.3)
warmer than the air outside. In his " Untersuchung liber
die Astronomische Refraction u. s. w.," Dr. Bauschinger
notes that the southern part of his observing room in
Munich was warmer than the northern, and that at night
the average difference between the inside and the outside
temperatures is i-3 (C). From his investigation, he con-
cludes that the temperature of the air within the observing
room should be taken into account.
Because of these difficulties, many observers have seri-
ously considered the idea of mounting their instruments
under a movable house, so that when at work the instru-
ment will be entirely out of doors, and thus completely
obviate this difficulty. But this would needlessly endanger
the instrument. To accomplish the same purpose, the
Meridian Circle house being built at Kiel is to be con-
structed in the shape of a cylinder whose axis coincides
with the axis of the instrument. This is undoubtedly the
best form of construction.
For the efficiency of the Meridian Circle house on Mount
Hamilton, the difference between the inside and the outside
thermometers can speak. As has been said, the average
difference (in the sense Inside-Outside) is -\- o.3 (F).
The maximum difference noted was one evening, a few
minutes before the sun had set, when the difference
was.+ i.i (F). The maximum difference noted here is
less than half the average at Munich. After this Meridian
Circle house has been completely opened for an hour and
a half, the temperature inside is practically the same as it is
outside.
During the months October to December, inclusive, a
similar set of observations was secured. For these months
the average difference between the inside and the outside
temperatures is even less than for the summer months.
But the range of the difference is much greater for the
114 CALIFORNIA ACADEMY OF SCIENCES. [PROC, 30 SER.
fall and the winter months. The maximum differences
observed were 2.o ( F) and -f- 2.i (F). There was
one still larger difference, viz. 3. 7 (F), which can
hardly be counted in the series, for it occurred on a poor
night, immediately after observing had been suspended
because of clouds and poor "seeing." The hot wave,
which caused the outside temperature to rise suddenly,
undoubtedly destroyed the "seeing." Although the
winter months present conditions not so favorable as those
of the summer months, nevertheless they also speak well
for the efficiency of the Lick Observatory Meridian
Circle house.
^. Plan for Observing. The method of determining
the refractions here may be stated as being a quasi con-
verse to Talcott's method of determining the latitude.
Instead of eliminating the refractions to get the latitude,
the method is to determine the refractions by eliminating
the latitude, as follows:
Let
z 8 = the zenith distance of a southern star,
z n = the zenith distance of a northern star,
z' g = the apparent zenith distance of the southern star,
z' n = the apparent zenith distance of the northern star,
S 8 = the declination of the southern star,
8 n = the declination of the northern star,
r s = the refraction of the southern star,
r n == the refraction of the northern star,
<p = the latitude of the Meridian Circle.
Then
=*+*=?+ (z'n+r n ) (i)
S s =? z 8 =v (z' 8 +r s ) (2)
Let
A=S n -S s (4)
B=z' s +z' n (5)
Then
A=B + r s +r n (6)
or
r s +r n =A B (7)
M.-P. VOL. I. ] CRA WFORD CONST A NT OF RE PR A CTION. 115
If now, the southern and northern zenith distances were
the same, and if, at the times of observing them, the condi-
tions of the atmosphere were the same, the two refractions
would be the same, /. e.,
r a =r n .
In this case we have
2r=A B (I)
In practice these ideal conditions are only approximately
satisfied. We therefore proceed as follows:
From (7) we have
2r 8 -r s +r n =A-B (8)
whence
2r.= (A B) + (r r.)
and
r. = #(A B) + #(r. r,,))
also >- (II)
r B =#(A B) + tf(r,, r.))
In case the northern star is at lower culmination we shall
have:
S n =i8o z n v (9)
S 8 =z s (10)
S n +S.=i8o_z u z. (ii)
^180 [ Z ' n + r n +z' 8 -fr 8 ]. (12)
Hence
r n -+r 8 =i8o [z' n +z' B ] -[ + .] (13)
and
2 r 8 = i8o-[ Z ' n + Z ' 8 ]-[A+ 8J+ [r. rj. ( 14)
Calling
A'=S n +S 8 (15)
and since
B=z'.+z' B (5)
we have
r 8=9 o-^ [A'+B] + y 2 [r -r D ] )
and > (III)
r=90 ^[A' + B] + ^[r n rj )
In order to obtain the refractions from (II) and (III) it
is necessary to know the declinations of the stars, their
apparent zenith distances (or rather the sums of the zenith
distances of the pairs of north and south stars), and the
differences between the refractions of the pairs. The
stars chosen for this work are all fundamental, and in a
first approximation their declinations are to be considered
1 1 6 CA LIFOKNIA A CA DEMY OF SCIENCES. [ PROG. 3 D SER.
absolute. The list of stars, given later, has been taken
from Professor Newcomb's "Catalogue of Fundamental
Stars for 1875 and 1900, reduced to an absolute System."
The apparent zenith distances, or the sums of the zenith
distances of the several pairs, are obtained from the
Meridian Circle observations; and the differences in the
refractions are found by computing the refractions from
some standard table. In this work the Pulkowa tables
have been used. The term ^(r s r n ) being of the nature
of a differential refraction, any error in the constant of
refraction of the table used will have practically no effect
upon this difference. The more nearly ideal conditions
(/. ., when r s =r n ) are approached, of course, the better the
determination of the refractions will be.
This method has both its advantages and its disadvantages.
Among the former, the most important are: first, the total
elimination of the latitude and hence also of its variation ;
second, the elimination of the nadir, since (z' s +z' n ) is
nothing more nor less than the difference between the circle
readings, and is therefore independent of the zenith point;
third, there is no wait of twelve hours or of six months in
order to observe a star at both culminations, as is usually
done; and fourth, the simplicity of the reductions.
The greatest disadvantage in this method lies in the fact
that the declinations of the stars have to be considered
known. But by taking fundamental stars, such as those
whose places are given by Professor Newcomb's new
Fundamental Catalogue, and by taking a large number of
these stars, this difficulty will be nearly completely eliminated.
Having now the new refractions, the correction to the
constant of the table used (Pulkowa) is found from the
following equation [eq. (701) pg. 672, Vol. I, Chauvenet,
" Spherical and Practical Astronomy''] :
dr=Ada + Bd,
where
A=I
a
and ,,- ~
r> -a 2 /^dQ Q
B = sm^z + - ( - -
\/3 W 2/3
M.-P. VOL. I.] CRAWFORD CONSTANT OF REFRACTION. 117
For this observatory, whose altitude is 4,209 feet and
where the mean annual pressure is less than 26 inches,
an investigation into the effect of the higher powers of
A /3 involved in the factor fi== i -) - = i -|
r> B B
(in Bessel's notation for r) was necessary. In his memoir,
" Untersuchungen iiber die Constitution der Atmosphare
und die Strahlenbrechung in Derselben," St. Petersburg,
1866, (jylden has neglected the squares and higher powers
of %-, since for places at low altitudes An is a very small
D ' . D
quantity. This investigation was made by Professor Corn-
stock (Vol. I, " Publications of the Lick Observatory").
From his investigation the conclusion is drawn that " the
Pulkowa Refraction Tables may be used for atmospheric
pressures as low as 25 inches without taking into account
the squares and higher powers of ^b, and the quantities so
neglected will not be sensible at zenith distances less than
80. " The minimum reading of the barometer during these
observations was 25.72 inches, so that in these reductions
no modification of the factor of the refraction depending
upon the barometer need be made.
This question having been disposed of, the assumption is
here made that all of the error in the refractions is due to
an error in the constant of refraction. This amounts to
assuming the constant j3 to be correct or that d/3=o. The
equation above then reduces to the very simple expression
dr Ada = da ;
hence
da dr
a r
or dloga = dlogr.
Having dlogr from the reductions, we thus have dloga, and
hence da.
This assumption would perhaps seem somewhat risky f6r
stars whose zenith distances are greater than 80. But at
the conclusion of the reductions, the value of dloga deduced
Il8 CALIFORNIA ACADEMY OF SCIENCES. [PROC. 3D SER.
from such stars was found to fit in very well with those
deduced from the other stars. Furthermore, down to 85
zenith distance the observing was very good. In con-
sequence of these facts it was decided to take into account
all the stars observed. The zenith distances of the stars in
this list range from 21 21' to 89 12' (apparent).
From 85 zenith distance down, the quality of the
" seeing" decreases quite rapidly. This can be seen from
the following table of average weights. These weights
were derived from the probable errors of the individual
determinations of dloga.
Z. D. Av. Wt.
20 tO 30
2.0
50 to 60
7-5
60 to 70
7-5
70 to 80
ii. 8
80 to 85
14.8
85 to 90
3-6
The small weight for the small zenith distances is due to
the fact that in the expression for da the refraction occurs
in the denominator. The small weight for the stars at
zenith distances greater than 85 is, of course, due to
uncertainties in observing at such low altitudes.
OBSERVATIONS.
/. List. The following list of 31 stars was observed on
seventeen nights, from 1899 June 7 to 1899 July 6,
inclusive, and have been reduced according to the plan
outlined in the preceding section. Eleven other stars were
on the same observing list, but they have not been used
here. They were put on to obtain data for determining
bisection error, and for other purposes.
The numbers of the stars are those of Newcomb's
" Catalogue of Fundamental Stars for 1875 and 1900,
reduced to an Absolute System."
M.-P. VOL. I.] CRAWFORD CONSTANT OF REFRACTION.
No.
a
(1900)
B i
1900)
948
14*
Sim
59*
42
43'
52". 30
190
2
57
33
+53
6
959
15
5
6
5 1
43
6 .62
968
977
15
J5
13
21
29
9
+67
+15
43
46
35 -08
46 -45
984
15
28
28
40
49
50 .61
225
3
33
28
+62
53
33 -74
997
15
39
21
+ 6
44
24 -53
1005
15
47
32
19
52
5 -65
1009
15
50
+15
59
1 6 .46
1019
16
I
+58
49
56 .19
264
4
5
6
+85
17
29 .06
1032
16
12
21
49
54
36 -79
282
4
24
6
+53
37 -37
1084
1094
16
17
52
8
56
30
+ 9
+65
50
49 -32
15 -88
1105
17
15
52
24
53
59 -07
IIIO
17
20
58
29
46
35 -61
349
5
26
21
+74
58
39 -95
356
5
2 9
54
+85
8
49 .60
U35
17
40
35
40
5
17 -65
377
5
46
28
+55
i .68
1156
17
58
51
50
5
53 -20
1162
18
3
48
-45
58
18 .07
406
6
10
48
+59
2
50 .18
1179
18
19
34
-46
I
24 -50
1182
18
21
48
25
28
37 -40
424
6
29
10
+79
40
22 .10
438
6
45
29
+77
6
17 -47
444
6
48
37
+58
33
14 .18
1225
19
42
27
48
59 -80
2. Details of Observations. A night's program consisted
in observing the above list, together with three nadirs, one
before, one during, and one after the observing of the stars.
As has been pointed out, the nadirs are not necessary for
the refraction determinations, but, were taken for the
reduction of the latitude, which is a problem practically
inseparable from the main one undertaken here.
No transits were observed during these observations, the
whole attention being devoted to the observations for zenith
distance. The telescope was set to the nearest 2' and not
disturbed until the observation had been completed. The
bisection was made (with but a very few exceptions) at the
central transit wire, by means of the declination micrometer.
For the sake of uniformity every star was bisected but once
during its transit. Because of unavoidable circumstances a
few of the stars had passed the meridian before the bisection
120
CALIFORNIA ACADEMY OF SCIENCES. [PROC. 30 SER.
could have been made. In these cases the readings have
been reduced to the meridian.
For the position of the circle four microscopes were read.
Settings were made upon two scratches under every micro-
scope. The circle microscopes were usually read after the
star had been bisected. In a few cases, because of a
following star culminating very soon, the microscopes were
read before the bisection. In such cases the position of the
circle was quickly checked after the bisection.
The correction for funs for a night was obtained from all
of the microscope readings of the night. This correction
has been applied to all of the observations. Its values for
the several nights of observing are given in the following
table:
Date
R
Date
R
Date
R
June 7
+o".o6
June 19
-J-0".02
June 30
-f o" . 06
8
-j-o .08
21
+o .03
July 3
H-o .07
9
+o .08
22
+0 -03
4
+o .08
12
+o .05
27
+o .04
5
+o .05
13
+o .03
23
+o .07
6
-fo .08
14
+o .07
2 9
+ .06
These corrections were applied to the circle readings to
reduce them to the mean position of the two scratches; so
that for a reading of o" the correction is -J-R, for 6o v it is o,
and for 120" it is R.
In the few cases where the bisections were made a little
late the reductions to the meridian were computed from the
formula,
, sin 2 \ (r m) ,
S = 8 : sin 20
sin i
The horizontal flexure in this instrument is very small.
In his work published in Vol. IV, " Publications of the Lick
Observatory," Astronomer Tucker adopts the correction
o".isin Z.- D., which was determined from a series of
observations extending over two and a half years. In this
work but two observations for flexure were made, one on
1899 June 3, and the other, 1899 July 8. The mean of
M.-P. VOL. I.] CRA WFORD CONSTANT OF REFRA CTION. 121
the two gives the correction o".oisin Z. D.; so that for
these observations the flexure correction has been considered
zero. The mean of the values of one revolution of the
declination micrometer, determined at the same time, is
48". 05. The value adopted, as noted before, is 48". 10.
For the computation of the preliminary refractions
(called r' in the reductions) the Pulkowa tables have been
used. The reductions for the barometer, for the attached,
and for the external thermometers were taken from Vol. I,
" Publications of the Lick Observatory."
The graduation errors of the i divisions of the fixed
circle have been determined by Aetronomer Tucker. His
results are given in Vol. IV, " Publications of the Lick
Observatory." He says there, in part: "The probable
error of a reading upon four divisions of the fixed circle
due to graduation may be adopted as o".i5. * * " *
There is some evidence of periodic character in the errors,
and it may be assumed, in absence of further data, that
the probable error due to errors of graduation is not
diminished by reading upon two adjoining divisions under
each microscope. * * * The largest error measured is
o".7 for the mean of four divisions."
The errors are not sufficiently systematic to warrant
interpolating for undetermined divisions, so that no correc-
tion for division error has been applied.
Three nadirs were observed every night. The changes
during a night were usually very small. The following
table gives the means of the three determinations on the
several nights:
Date
Nadir
134 57'.
t
Date
Nadir
134 57'
t
June 7
22". 87
62
June 27
20". 95
66
8
22 .18
66
28
21 .32
67
9
22 .14
6 9
29
21 .40
6 9
12
24 .41
' 57
3o
21 .70
66
13
22 .70
62
July 3
21 .43
72
14
21 .6l
70
4
21 .46
69
19
23 .81
57
5
22 .91
61
21
22 .36
66
6
22 .10
58
22
21 -59
67
122 CALIFORNIA ACADEMY OF SCIENCES. [PROC. 30 SER.
All of the observations were taken with the fixed circle
west. Had more time been available the instrument would
have been reversed.
Weights, ranging from 5, the highest, to I (occasionally
j^), the lowest, were arbitrarily assigned to all the obser-
vations. Judgment on a weight was formed from the
steadiness of the image during the observation. These
weights have been applied all through the reductions.
j. Reduction of Observations. The first thing done
on the reductions was to take the means of the microscope
readings and to apply the micrometer corrections, giving
the circle readings (called C' in the tables following).
The means of the microscopes were checked by taking
the difference of every microscope reading from the mean
of .the four. If the sums of these differences for the two
opposite pairs of microscopes was the same, the mean was
correct. The corrections for the micrometers were checked
by duplicating this part of the work.
From the readings C 7 the quantity B [equations (II) and
(III)] is obtained. The terms A and A' of these equations
are obtained from the declinations.
The declinations have been reduced to 1899.0 by means
of the data furnished in Newcomb's Catalogue. The
reductions to apparent places were computed by using the
Besselian Star Numbers from the American Ephemeris.
The factors a', b', c' and d' were computed from the
American Ephemeris data. The reductions to apparent
places for the first night (June 7) were computed by means
of the Independent Star Numbers also. The places for
the remaining nights were checked by differences. The
apparent declinations are placed in the columns S of the
tables given later.
The following table exhibits the stars' approximate zenith
distances and the stars with which they are grouped in the
reductions for the refractions :
M.-P. VOL. I.] CRAWFORD CONSTANT OF REFRACTION.
I2 3
STAR No.
Z. D.
SOUTH
Z. D. NORTH
GROUPED WITH
STAR No.
948
79
59-9
. /
225 /. c.
190 /. c.
89 12.0
959
959
88
45-5
{ 282/1^.
968
30 22.9
997
977
21
33-2
1019
984
78
6.6
225 /. c.
948
225 /. c.
79 41-9
984
1135
997
30
35-5
968
1005
57
"3
f 264 /. c.
1009
21
20.7
1019
1019
21 29.3
f 977
\ 1009
264 /. c.
57 21.0
1005
1032
87
3-1
377 / c.
282 /. c.
88 40.0
959
1084
27
48.1
1094
1094
28 29.4
1084
1105
62
12.9
424 /. c.
IIIO
67
349 /. c.
349 / c.
67 39.0
IIIO
356 /. c.
57 29.5
1005
H35
77
22.1
225 /. c.
377 /. c.
86 47-2
f 1032
11156
1156
87
13-9
377 /. c.
1162
83
12.4
[ 406 /. c.
\ 444 /. c.
406 /. c.
83 30-2
f 1162
\ii79
1179
83
15-5
/ 406 /. c.
\ 444 I.e.
1182
62
47-5
424 /. c.
424 /. c.
62 57-5
{1105
\Il82
438 /. c.
65 31-4
1225
444 /. c.
83 59-3
/ Il62
1 1179
1225
65
7-7
438 /. c.
It will be noticed from this table that some of the stars
are grouped with two others and that one is grouped with
three others.
( 3 > May 6, 1903.
124 CALIFORNIA ACADEMY OF SCIENCES. [PROC. 30 SER.
The following tables show the reductions for the new
refractions. The column ^ contains the means of the
weights of the pairs of stars. The other columns have
already been explained. In the grouping of the pairs on
the several dates the northern star is written first and the
southern star below it. The numbers of the stars given at
the tops are arranged in this same order. The pairs which
have their northern stars at upper culmination are placed
first. It will be noticed that the headings of the columns
for these pairs are slightly different from the later ones
containing the lower culmination stars.
Because of very bad "seeing" or of occasional accidents,
some of the stars were not observed on some nights. In
such cases blanks appear after the dates. No observations
have been rejected.
M . -P. VOL. I . ] CRA WFORD CONS TA NT OF REFRA CTION. 125
r*
^^. ^^. ^co M M MM COCO OCO VOVO
IO O CS CS CO CO
vO vO M co O CS r^ ON ON M CO CS co ON ON C^
v ON M CS ^~ VO GO cO ^^ ON CS VO ON ^"VO O CS
CS CO M cO OO CS
ON M vo CO CO M
k
COON ONON CO GO ONON COON COCO O^ ON ONON
CSCS CSCS CSCS CSCS CSCS CS CS CSCS CS CN
<8 33 3^
v o o
g
vO CS M co O O vO CO
^ ?l 8
3
ON ON CO ON ON CO ON ON
cscscscscscscscs
ON CO ON
CS CS M
M
o
v
2 s a ^8 = 2 s> 8-
CO M CS
s
oooooooo
000
+ + 4-
5 vScg 3 3 Jo co 5 ^ ^cS c^S 8c? g,^
o t^ co o 10 o
cO >O *sf t">. TJ- t>.
X
k
CO CO CO CO CO CO CO 00 CO OO CO CO ON ON CO CO
CSCS CSCS CSCS CSCS CSCS CSCS CSCS CSCS
CO CO OO CO 00 00
cs cs cs cs cs o
^00
IOVO M Tj-fOlOONCS
ON vO vO
^ iO O
CS CS cOCS cOrfcO^
cscscscscscscscs
rj- IO 10
cs cs cs
05
CO
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vO
v 10 <o ^co CSON IOM o *$ csco o*-< COON
Tf CO Tt O VO CS
ONCS COO t^-O OcO COM vOO COM lOON
N ^O CS *O CS ^O CO ^O CS - IO CS IO CS IO CS ^3"
^"oo ~cs co COQO
CS ^ CS Tt" CS ^ -
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CO cO
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vOO O M >OVO t^fO r T
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cscscscscscscscs
cs cs cs
vg
M cO CO I s *" CS CO O ON T}~ M M 10 t^vO CO "^~
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IOVO CS <O M T^-
CO t~ CS CS r}- CO
t^^vo t^vO CO vO CO t~> ON t~> ON t^ O CO M oo
^cs TJ-CS ^cs ^cs ^j-cs ^~cs iocs iocs
M CO cs ON CS ON
IO CS IO CS IO CS
v CO Tj-
,
t^CO ON CS.cO * ON M
CS t^ CO
cs cs cs
q
a
126 CALIFORNIA ACADEMY OF SCIENCES. LPROC. 3D SER.
*,
cO cO
^^ ^
k
: H
NM CNCS CNCM M(N
v
1
CO
O 10 cO iO
CO 00 ON ON
CN CM CN CN
*
v a
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M M . M M
6 d d 6
ir
+
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ONCN CN-3-voco CO M
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CO 00
CN CN
l^CO CO CO 00 CO CO ON
CNCN CNCN MCN CSCJ
v
;
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CN CN CN CN
3
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V
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cs 1 ^- *% cT^P c?^
^ CO
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TJ- rt -rf IO
^
c?
CO CO cO cO
N CN CN CN
s
d CO
COCO vOCN con- <O"d-
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v N ON
cOO cOO cOO cOO
iO CO tocO O CO toco
1
ON O
CO ^t *O VD
q
3
>
M.-P. VOL. I.] CRAWFORD CONSTANT OF REFRACTION. 127
*
^" ^J" Tt" ^3" *O ^O
MM MM COCO COCO COCO COCO 10 0404
a\ t^ ON in 10 M -
0404 VOO4 CO^ ONIO cOON O<N rOON COON
lOvO VO t>. ' ^ iO lOvO cOcO MM coco 0404
^
O^ ^^ O^ Q\ O > * s *
ONON ONON ONON ONON ONON ONON ONON ONON
v o o
q
cO 04 CO
^04 "3- O
iO vO 'O vo cO M cO C^
1
ON ON ON
ON ON- ON ON ON ON ON ON
5
v O
v a
V
odd
iO co cO cO cO M cO co
OOOOOOOO
d d d d o" o d d
v ^oT 8^ 8?8
MM CQIO QvO Mt^ COO ^tt^ 04ON O4OO
O> O^ O^ O^ OO O^
ON ON ON ON ON ON ON ON ON ON ON ON ON ON ON ON
v
10 ON o
M 00 t^
V -4 1 CO rj-
T^ co ^~ ^* iO vo vO vO
o
^
-
vO >-> t^vO cO cO
cO co cO
^ OO O
04 CO
ON cO
O4 CO
ONON rj-cO O4O OOvO MCO CO'* 1 lOiO vOvO
cO CO cO cO ^O cO iO cO *O CO vo cO
00 t^
04 04
vO t>* CO
04 04 04
04 cO ^O M CO ^^ O ^
cOcOco^-'rJ-'rJ-iOio
^
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v 04 VO lOCO 00 ON
v3 o>^ SR ^vS- ^8 vS? JC2?. 8c^
cO O co O co O
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v O VO
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IO M
1
t^ 00 ON
1
> 1
04 CO^ONM O4 t^CO
MMMMO404O404
ON t^
M 1^
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128
CALIFORNIA ACADEMY OF SCIENCES. [PROC. 30 SER.
ON t>-
M r^
O ON
*.
CO CO
^
CO CO >0 CO CO
CMC,
v ^
COCO
CO co M ON VO 00
MM CO CO f>- t^
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M.-P. VOL. I.] CRA WFOKD CONSTA NT OF REFRA CTION.
I2 9
*
**
^-^- COCO MM d d COCO COCO ^"^f Tf ^ OIO CSfN
d CO
v O CO
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^
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130
CALIFORNIA ACADEMY OF SCIENCES. [P^oc. 3D SER.
^
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M.-P. Voi>. I.] CRAWFORD CONSTANT OF REFRACTION.
*,
10 10 ^^ toto MM cscs toto co to
rtTt r^-^- IO>O CSCS
O vO *O ' ^"00 vO O tO ON CO ^t" to M
v VO CO ON CS to iO iOCO iO t^ O to CO M
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v vO to vO to VO to VO to vO to VO to VO vO
cscs cscs cscs cscs cscs cscs cscs
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to to M 10
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cs cs cs cs cs cs cs
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to to
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132
CALIFORNIA ACADEMY OF SCIENCES. [PROC. 3D SER.
CO CO
CO CO IO IO
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vO *O vO
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cs cs
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<% <& <&
odd
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10 co
M.-P.-VOL. I.] CRAWFORD CONSTANT OF REFRACTION. 133
*,
^ ^
fOtO WM 0404 tOtO
H\M\ M\-t\
fOtO -J- ^t fOtO IOIO 0404
t^ ON tO iO
tOON lOt^ IOM <O>O
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140 CALIFORNIA ACADEMY OF SCIENCES. [PROC. 3D SER.
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M.-P.-VOL. I.] CRAW FORD- CONSTANT OF REFRACTION. 167
The following tables contain the reductions for dlogr or
its equivalent dloga. The second column contains the
logarithms of the computed refractions; the next column
contains the logarithms of the observed refractions; the
fourth the difference between the two preceding, in the
sense of Observed Computed; the column^ contains the
weights and the last column the weighted differences.
The residuals and their weighted squares are not given.
Log \_-pw~\ is given in every case, as is also the resulting
probable error of the weighted mean of every set. All of
the results in the following tables have been checked.
STAR No. 948.
Date
log. r '
log. r
A
/
/A
June 7
2.42742
2.42617
0.00125
4
0.00500
8
2.42399
2.42119
280
4
1 120
9
2.42126
2.41762
3 6 4
3
1092
12 2.43095
2.42727
368
i
3 68
13
2.42658
2.42490
1 68
2
336
14
2.42169
2.41838
33i
3
993
19
2.43214
2.42889
325
3
975
21
2.42478
2.42185
293
4
1172
22
2.42149
2 . 42042
107
3^
375
27
2.42459
2.42243
216
5
1080
28
2.42313
2.42147
166
2^
4i5
29
2.42262
2.42014
248
3^
868
3
J"iy 3
2.41600
2.41678
+ 78
2^
+ 195
4
2.41916
2.4l8l6
IOO
5
500
5
2 . 42644
2 . 42605
39
3
117
6
2.43042
2.42602
440
l#
660
I 0.00205
[p] = 50^ ; logpw\ = 5-8653
p. e. = 0.00015
1 68
CALIFORNIA ACADEMY OF SCIENCES. [PROC. 3D SER.
STAR No. 190 /. c.
Date
log. r '
log. r
A
P
/A
June 7
9
3.09609
3.08699
0.00910
3
0.02730
12
3.10852
3-09598
1254
i
1254
13
3.10231
3 . 10302
+ 71
%
+ 35
H
3.09619
3.09129
490
3
1470
19
21
3.10009
3-09349
660
4
2640
22
3-09543
3-09387
156
^
546
27
3-09851
3.09629
222
5
mo
28
3-09793
3.09046
747
3
2241
29
3.09748
3.08610
- 1138
3
34M
30
3.09728
3-09563
165
4
660
July 3
4
3.09289
3.08925
364
5
1820
I
3.10261
3-097I3
548
3
1644
::= 38;
= 6.6II2
A 0.00513
p. e. =
0.00047
STAR No. 959. (With 190 /. c.)
Date
/>. r '
log. r
A
P
/A
June 7
O
9
3-03783
3.02741
0.01042
3
0.03126
12
3.05008
3-0357I
H37
i
1437
13
3-04374
3-04454
+ 80
/^
+ 40
14
3-037I4
3-03I75
539
3
1617
21
3.04205
3-0345I
754
4
3016
22
3.03782
3-03605
177
619
27
3.04138
3-03886 252
5
1260
28
3.04032
3-03I77 855
3
2565
29
3-03986
3.02685 1301
3
3903
3
3-03983
3-03795
188
4
752
July 3
4
3 . 03667
3-03252
415
5
2075
5
3.04442
3-03815
627
3
1881
6
A I
o . 00584
[p ] = 38 ; log
= 6. 7298
P-e.= 0.00053
M.-P. VOL. I. ] CRA WFORD CONST A NT OF REFRA CTION. 1 69
STAR No. 959. -(With 282 /. c.)
Date
,
log. r
A
P
/A
June 7
3.04492
3 . 04068
0.00424
M
0.01908
8
3.04160
3.03886
274
3^2
959
9
3-03783
3-03050
733
3
- 2199
12
3 . 05008
3-04703
35
i
305
13
3-037I4
3-03633
81
3
243
19
3-05165
3.04787
378-
3
21
3.04205
3-03741
464
4
1856
22
3.03782
3-03645
137
3/^
479
27
3.04138
3-037I7
421
5
2105
28
3.04032
3.03228
804
2 /^
2OIO
29
3.03986
3-03043
943
3 t
2829
3
3-03983
3.03611
372
1674
July 3
4
3.03667
3.03112
555
5
2775
5
3.04442
3.03910
532
3/^
1862
6
3.04920
3-04347
573
2 /^
1432
| 0.00462
= 5i# J log[pvv] = 6.3662
p. e. = 0.00027
STAR No. 968.
Date
/qg\ r '
log.r
A
P
/A
June 7
1.45651
.46180
+ 0.00529
4
-f- 0.02116
8
.45383
46553
+ 1170
4
4680
9
I.45H9
45637
488
3
1464
12
.45985
.46790
805
i
805
13
456i4
46225
611
I#
916
M
.45172
.45758
586
3
1758
19
. 46276
46879
603
3
1809
21
-45485
.46374
889
3K
3111
22
.45181
.46120
939
3^
3286
27
45453
45652
199
5
995
28
.45407
.46060
653
2^
+ 1632
29
45340
45984
644
3^
2254
3
July 2
44653
45347
+ 694
3
-f 2082
4
.45114
.45408
294
5
1470
5
45656
1.46835
1179
3
3537
6
.46066
1.46850
+ 784
ig
+ 1176
0.00662
[P } = 5 ;
= 6. 6307
p. e. = 0.00036
1 70 CALIFORNIA ACADEMY OF SCIENCES. [PROC. 30 SER.
STAR No. 977.
Date
**;<
log. r
A
*
/A
June 7
i . 28488
. 28488
^ o.ooooo
4
^ o.ooooo
8
1.28218
. 28892
-f- 674
4
+ 2696
9
.28019
.28126
107
3
321
12
.28796
. 29270
474
i
474
13
. 28439
.29491
+ 1052
1^2
1578
. 28022
.29092
1070
3
3210
19
.29163
173
3
519
21
.28336
.28758
422
H77
22
. 28043
.28149
106
3/^
37i
27
. 28302
.28758
456
5
2280
28
. 28288
28533
245
612
29
. 28206
.28691
485
3^2
1697
30
. 28204
. 28648
444
4
+ 1776
July 3
.27518
.28171
653
3
1959
4
i .28003
.28758
755
5
3775
5
1.28512
29623
mi
3
+ 3333
6
i . 28948
. 28870
- 78
2
156
I + 0.00476
= 54 1 A ; log [pvv} = 6.7951
STAR No. 984.
p. e. =
0.00040
Date
/0g\ r '
log.r
A
/
/A
June 7
9
-
12
2 . 35626
2 -35 I 99 0.00427
I
0.00427
J 3
2.35336
2.35114 222
2^
555
14
2.34902
2.34616 286
3
858
19
2.36071
2.35971
IOO
3
300
21
2.35175
2.35042 133
3
399
22
2-34937
2.34805 132
3^
462
27
2.35175
2.34951 224
5
1 1 20
28
2.35162
2.35176 + 14
2
+ 28
29
2 . 35060
2.34874 i 86
4
744
3
July 3
2.34417
2.34616
f 199
3
+ 597
4
2 34844
2.34713
131
5
655
5
2.35414
2.35319 95
3
- 285
6 1 2.35871
2.35581 290
i#
435
A
0.00142
[pvv] = 5.8091
p. e. = ^E 0.00017
M.-P. VOL. I.] -7 CRA WFORD CONSTANT OF REFRA CTION. 171
STAR No. 225 /. ^r. (With 948.)
Date
%" f '
log. r
A
/
/A
June 7
2-41352
2.41224
0.00128
4
0.00512
8
2.41100
2.40812
288
4
1152
9
2.40895
2.40523
372
3
1116
12
2.41618
2.41237
381
i
38i
13
2.41359
2.41187
172
2
344
H
2.40930
2 . 4059 1
339
3
1017
19
2.42102
2.41769
333
3
999
21
2.41181
2 . 40880
301
4
1204
22
2.40967
2.40858
109
3^
38i
27
2.41188
2 . 40966
222
5
IIIO
28
2.4H75
2.41007
168
2^
420
29
2.41072
2.40815
257
3^
899
3
July 3
2.40463
2.40542
+ 79
2^
+ 197
4
2.40845
2.40741
104
5
520
5
2.41441
2.41400
4i
3
123
6
2.41907
2.41457
45o
I#
- 675
0.002II
[/ 1 = 50^ ; log [pvv ] = 5.8809
STAR No. 225 /. c. (With 984.)
p. e. =
0.00015
Date
r.r-
log.r
A
>
/A
June 7
8
9
12
2.41618
2.41246
0.00372
i
0.00372
13
2.41359
2.41165
194
2 %
485
2.40930
2 . 40678
252
3
756
19
2.42102
2.42014
88
3
264
21
2.41181
2.4IO66
115
3
345
22
2.40967
2 . 40849
. 118
413
27
2.41188
2.40983
205
5
1025
28
2.41175
2.41186
+ ii
2
+ 22
29
2.41072
2.40914
158
4
6 3 2
3
July 3
4
2 . 40463
2.40845
2.40637
2.40729
4- i74
116
3
5
+ 522
580
5
2.4I44I
2.41357
84
3
252
6
2.41907
2.41652
255
382
| 0.00126
[p ] = 39^ ; log [pvv 1 = 5-6934
p. e. =
0.00015
(6)
May 9, 1903.
172 CALIFORNIA ACADEMY OF SCIENCES. [PROC. 3D SER.
STAR No. 225 /. c. (With 1135.)
Date
log. r '
log. r
A
P
/A
June 7
2.41352
2.41299
0.00053
4^
0.00238
8
2.41100
2 . 40928
172
4
688
9
2.40895
2.40601
294
3
882
12
2.41618
2.41416
202
i
202
J 3
2.41359
2.4II05
254
2
508
14
2.40930
2.40724
2O6
3
618
19
2.42102
2.41858
244
3
732
21
2.41181
2.4IIOO
81
4
324
22
2.40967
2 . 40882
85
4
340
27
2.41188
2.40981
207
5
1035
28
2.41175
2.4IIOO
2^
187
2 9
2.41072
2.40744
328
4
1312
3
July 3
2.40463
2.40488
+ 25
3
+ 75
4
2.40845
2.40691
154
5
770
5
2.41441
2.41437
4
3^
14
6
2.41907
2.41547
360
2
720
= 5.7856
A I
0.00159
P> e >
0.00013
STAR No. 997.
Date
/cjg-. r '
log.r
A
/
/A
June 7
1.45932
1.46479
+ 0.00547
4
-f- 0.02188
8
I.45705
1.46879
1174
4
4696
9
1.45504
1.45969
465
3
+ 1395
12
1.46180
1.46967
787
i
787
13
1-45953
I-46553
600
i#
900
14
1-45544
i .46120
576
3
1728
19
i . 46676
1.47261
585
3
1755
21
45774
i . 46642
868
3^
3038
22
45588
1.46509
921
3^
3223
27
45791
1.45984
193
5
965
28
45782
1.46419
637
2^
+ 1592
29
45671
1-46315
644
3^
+ 2254
3
July 3
1.45099
1-45773
-f 674
3
-|- 2O22
4
I.45436
1.45712
+ '276
5
I 3 80
5
i . 46049
1.47217
1168
3
3504
6
i . 46492
1.47261
+ 769
i#
+ U53
[p ] = 50 ; log \_pvv] = 6.6325
A I + 0.00652
p. e. = Jz 0.00036
M.-P. VOL. I.] CRAWFORD CONSTANT OF REFRACTION. 173
STAR No. 1005. (With 264 /. c.)
Date
/<. r '
log.r
A
P
/A
June 7
.87711
1.87518
0.00193
4
0.00772
8
.87496
1.87186
310
4
1240
9
.87269
.86700
569
3
1707
12
.87989
.87697
292
i
292
13
.87719
.87361
358
2
716
H
.87307
87454
+ H7
3
+ 44i
19
88455
.88138
3!7
3
95i
21
22
.87581
.87378
: 86964
348
414
4
4
- 1392
1656
27
-87582
.87489
93
5
465
28
87565
.87093
472
2
944
2 9
.87436
.87256
180
4
720
30
.87545
.87489
56
4
224
July 3
.86915
.86847
68
3
204
4
.87220
.87157
63
5
3*5
5
1.87863
.87823
40
3
1 20
6
1.88269
.87881
- 388
2
- 776
= 56 ; log
= 6.2452
A I 0.00215
P. e. =
STAR No. 1005. (With 356 /. c.)
Date
log. r '
log. r
A
P
/A
June 7
9
.87269
87233
0.00036
3
0.00108
12
.87989
.87800
189
i
189
13
.87719
87547
172
2^
43
14
.87307
87355
+ 48
3
144
19
-88455
.88502
+ 47
3
+ HI
21
.87581
87413
168
4
672
22
.87378
.87268
no
4
44o
27
-87582
.87743
-f 161
5
+ 805
28
87565
87425
140
2
280
29
30
.87436
87545
.87512
.87714
+ 76
+ 169
4
4
+ 304
+ 676
July 3
86915
.86788
127
3
381
4
.87220
.87326
+ 106
5
+ 53
5
.87863
.87547
3i6
3^
1106
6
.88269
.88064
205
2^
512
A I 0.00031
[P ] = 49 % ; log [pvv] = 6.0442
p, e. =
0.00019
174 CALIFORNIA ACADEMY OF SCIENCES. [PROC. 3D SER.
STAR No. 1009.
Date
&#. r '
log.r
A
P
/A
June 7
.27967
.27600
0.00367
4
0.01468
9
27759
27515
. 28149
.28149
390
+ 634
4
3
+ 1560
4- 1902
12
. 28250
. 28240
10
IO
13
.27963
28307
+ 344
2
+ 688
14
27547
. 28262
7i5
3
2H5
J 9
. 28706
.28825
119
3
357
21
27843
27989
+ 146
4
22
. 27648
27346
302
4
1208
27
27834
.28511
+ 677
5
+ 3385
28
.27819
1.28126
307
2
614
29
. 27674
1.28149
475
4
1900
30
.27815
1-28375
560
4
2240
July 3
4
.27187
27473
1.27300
1.27807
U3
334
3
5
339
1670
5
1.28132
i . 28466
334
3
1 002
6
1.28519
1.29003
+ 484
2
+ 968
= 56 ; log [pvv] = 6.7629
I + 0.00298
p. e. = zt 0.00038
Star No. 1019 (With~977.)
Date
log. r '
log.r
A
P
/A
June 7
.28286
. 28307
+ 0.00021
4
-(- 0.00084
8
28075
.28758
68 3
4
2732
9
.27851
. 27987
136
3
408
12
.28578
. 29048
470
i
470
13
.28283
29358
1075
I*
1612
H
.27867
28959
1092
3
3276
19
- 29036
. 29203
I6 7
3
501
21
.28165
. 28623
458
3^
1603
22
. 27970
.28103
133
3^
465
27
.28158
. 28623
465
5
2325
28
.28158
.28398
240
2^
600
29
. 27989
. 28466
477
3^
1669
30
.28139
. 28601
462
4
1848
July 3
27536
.28171
635
3
1905
4
27798
28578
780
5
3900
5
. 28468
29579
-j- mi
3
+ 3333
6
.28837
. 28780
57
2
114
=. 54 /^ i log[pw] = 6.7903
A I + 0.00488
. e. = 0.00040
M.-P. VOL. I.] CRA WFORD- CONSTA NT OF REFRA CTION. 175
STAR No. 1019 -(With 1009.)
Date
/0-. r '
log. r
A
P
/A
June 7
. 28286
.27921
0.00365
4
0.01460
8
. 28075
. 28466
391
4
+ 1564
9
.27851
. 28466
+ 615
3
+ 1845
12
.28578
.28556
22
i
22
13
.28283
.28623
340
2
-f 680
H
.27867
.28578
711
3
2133
19
. 29036
.29137
101
3
303
21
.28165
.28307
142
4
+ 568
22
. 27970
.27669
301
4
1204
27
.28158
.28825
+ 66 7
5
+ 3335
28
.28158
.28443
285
2
57o
29
27989
.28466
477
4
1908
3
.28139
.28691
552
4
-j- 2208
July 3
27536
27623
87
3
261
4
. 27798
.28126
328
5
1640
5
. 28468
. 28780
312
3
936
6
28837
.293H
+ 477
2
+ 954
A
-f- 0.00290
\.p} = 56 ; log [pvv ] = 6.7654
STAR No. 264 /. c.
P- = it 0.00038
Date
log. r '
log. r
A
P
/A
June 7
.87981
87783
'0.00198
4
0.00792
8
.87779
.87466
313
4
1252
9
.87564
.86994
570
3
1710
12
.88285
.87996
289
i
289
J 3
.87988
.87628
360
2
720
H
.87560
.87697
+ 137
3
+ 411
19
.88743
.88423
320
3
960
21
.87852
.87500
352
4
1408
22
87657
87245
412
4
1648
27
87853
.87754
99
5
495
28
.87878
. 87408
470
2
940
2 9
87673
.87489
184
4
736
30
.87825
1.87766
59
4
236
July 3
.87237
87163
74
3
222
4
87492
.87425
67
5
335
5
.88164
1.88121
43
3
129
6
.88517
1.88133
- 384
2
- 768
A
0.00218
[p ] = 56 ; log [pw} = 6. 2338
p. e. = -r 0.00020
176 CALIFORNIA ACADEMY OF SCIENCES. [PROC. 30 SER.
STAR No. 1032.
Date
log. r '
log. r
A
P
/A
June 7
8
9
12
13
2 . 85820
2.86091
-f 0.00271
i
-j- 0.00271
14
2 . 85280
2.85044
236
3^
826
*9
2.86657
2.86178
479
3
1437
21
2-85637
2.85442
195
4
780
22
2.854II
2.85258
153
4
612
2
2 . 85620
2.85690
2.85429
2.85286
191
404
\x
955
IOIO
29
2.85421
2.84821
600
3^
2IOO
3
2.85600
2.84956
644
4
2576
July 3
2.84957
2.84596
36i
3
I08 3
4
2.85239
2.85174
65
4^
2 9 2
5
2.86022
2.85728
294
4
1176
6
2.86417
2.85807
610
2j^
1525
| 0.00317
[p] = 44% ; log [pvv] = 6.2854
STAR No. 282 /. c.
p. e. =
0.00029
Date
%.r'
log.r
A
P
PA
June 7
3-03250
3.02825
0.00425
4^
O.OI9I2
8
3.02963
3.02682
281
3#
983
9
3 . 02804
3-02054
750
3
2250
12
3.03690
3.03376
314
i
3H
13
14
3.02661
3-02556
105
3
315
19
3.04241
3-03855
386
3
H58
21
3-03063
3.02586
477
4
1908
22
3.02814
3.02674
140
3/^
490
27
3.03018
3.02586
432
5
2l6o
28
3.03140
3.02319
821
2 /^
2052
29
3.02815
3.01847
968
3 x
2904
30
3.02989
3 . 02608
381
1714
July 3
4
3.02636
3 . 02069
567
5
- 2835
5
3-035II
3.02968
543
3/^
I9OO
6
3.03907
3.03320
587
2^
1467
A | 0.00473
log [pvv] = 6.3770
p. e.
0.00027
M.-P. VOL. I.] CRAWFORD CONSTANT OF REFRACJ^ION. 177
STAR No. 1084.
Date
log. r '
log. r
A
p
/A
June 7
I-40959.
1.41263
-\- 0.00304
5
-f- 0.01520
8
.40788
1.40157
63i
4
2524
9
.40678
.40790
+ H2
3
+ 336
12
41235
.41162
73
i
13
.41026
.41145
+ 119
2
+ 238
14
40551
.40381
170
3
510
19
.41774
.41681
93
3
279
21
.40831
.40976
-f J 45
4
+ 1256
22
.40704
.40432
^272
4
1088
27
.40883
. 40926
+ : 43
5
+ 215
28
.40783
. 40892
' 109
2
218
29
.40587
.40500
- I '87
3
261
3
. 40780
.41010
' 230
4
+ 9 20
July 3
.40181
39863
318
3
954
4
40565
40552
13
5
65
5
4II59
.40449
710
4
2840
6
.41433
40993
440
3
1320
A I o.ooioi
[/] = 58; log[pw] =6.7152
STAR No. 1094.
p. e. =
0.00035
Date
log. r '
log. r
A
P
/A
June 7
i . 42207
i . 42488
+ 0.00281
5
-f 0.01405
8
. 42036
1.41414
622
4
2488
9
41943
. 42062
+ 119
3
+ 357
12
. 42492
.42423
69
i
69
13
.42275
42374
+ 99
2
+ 198
14
.41809
.41631
178
3
534
19
.43008
.42894
114
3
342
21
. 42082
.42210
+ 128
4
, + 5i2
22
.41979
.41714
265
4
1060
27
42185
.42226
+ 4i
5
205
28
41995
.42095
+ 100
2
+ 200
29
.41807
.41714
93
3
279
30
42033
42243
210
4
+ 8 4 0.
July 3
.41401
41095
306
3
9l8
4
.41844
.41830
14
5
70
5
.42416
4i73i
68 5
4
2740
6
1.42679
42259
420
3
I26O
A I
0.00104
p. e. 0.00034
178 CALIFORNIA ACADEMY OF SCIENCES. [PROC. 3D SER.
STAR No. 1105.
Date
/<#-. r '
log. r
A
P
PL
June 7
o
9
1.96122
1.95861
- 0.00261
3/2
0.00913
12
T 3
.96464
.96209
255
2
510
14
.96010
.96468
+ 458
3^
+ 1603
!9
.97190
97257
+ 67
3
4- 201
21
-96285
96i37
148
4
592
22
96i73
.96114
59
4
236
27
.96404
.96161
243
5
1215
28
.96169
.96223
+ 54
3
+ 162
29
9599
.95985
5
3
15
3
.96218
.96142
76
4^
342
July 3
95599
1-95650
+ 5i
3
153
4
.96028
.96099
+ 7i
5
+ 355
5
.96610
1.96577
33
4
132
6
.96874
.96876
+ 2
3
+ 6
=6.1881
A
0.00029
p. e. 0.00023
STAR No. mo.
Date
/<?. r '
log. r
A
P
/A
June 7
2.05864
2.05998
+ 0.00134
5
-f- 0.00670
8
2.05683
2.05790
+ 107
4
+ 428
9
2.05574
2 . 05342
232
3
696
12
2.06194
2.O6OI7
177
i
177
13
2.05916
2.05888
28
i
28
14
2.05485
2.05778
+ 293
3
+ 879
19
2 . 06659
2 . 06446
213
3
639
21
2.05744
2.05637
107
4
428
22
2.05644
2.05319
325
4
1300
27
2 . 05892
2-05775
117
5
585
28
2.O5622
2-05599
23
2
46
29
2.05450
2.05385
65
4
260
30
2.05679
2.05427
252
4^
1134
July 3
2 . 05066
2.04895
171
2^
427
4
2.05488
2 . 05484
4
5
20
5
2 . 06079
2 05964
H5
4
460
6
2.06344
2.o6lI9
225
3
- 675
I 0.00084
= 58 ; log
= 6.1535
p. e. =
0.00018
M.-P. VOL. I.] CRAWFORD CONSTANT OF REFRACTION. 179
STAR No. 349 /. c.
Date
/<?f . r '
log. r
A
/
/A
June 7
2.07053
2.07177
-f- 0.00124
5
-f- 0.00620
8
2.06871
2.06974
4- 103
4
412
9
2.06761
2.06539
222
3
666
12
2.07385
2.07210
175
i
175
13
2.07104
2 . 07078
26
i
26
14
2 . 06690
2.06971
-f 28l
3
+ 843
19
2 . 07824
2.07613
211
3
633
21
2 . 06933
2.06826
107
4
428
22
2 . 06834
2.06517
317
4
1268
27
2.07091
2.06974
117
5
585
28
2.06804
2.06781
2 3
2
46
2 9
2 . 06647
2 . 06580
67
4
268
30
2 . 06870
2.06622
248
4>
1116
July 3
2.06268
2.06104
164
2^
410
4
2.06687
2.06685
2
5
10
5
2.07272
2.07159
H3
4
452
6
2-07535
2.07316
219
3
- 657
A I
0.00084
[p] = 58; log [pvv] = 6.1255
STAR No. 356 /. c.
p. e. =
0.00018
Date
/0\ r '
log. r
A
/
/A
June 7
o
9
.87922
1.87881
0.00041
3
0.00123
12
.88536
.88349
187
i
187
13
.88248
.88076
172
2^
430
H
.87854
.87898
44
3
+ 132
19
.88965
.89009
44
3
+ 132
21
.88077
.87910
167
4
668
22
.87968
.87858
no
4
440
27
.88234
88395
-|- 161
5
+ 805
28
.87948
.87806
142
2
284
29
.87811
.87881
+ 70
4
4- 280
30
.88005
.88173
+ 168
4
+ 672
July 3
.87414
.87280
134
3
402
4
.87840
87938
+ 98
5
+ 49
5
.88413
.88098
315
3^
IIO2
6
.88677
.88474
203
2^
507
I 0-00033
\.P ] =
log [pvv ] = 6.0359
p. e. = 0.00019
l8o CALIFORNIA ACADEMY OF SCIENCES. [PROC. 30 SER.
STAR No. 1135.
Date
/eg-, r '
log. r
A
P
/A
June* 7
2.32700
2.32638
0.00062
4K
0.00279
8
2.3 2 535
2.32327
208
4
832
9
2.32443
2.32087
356
3
1068
12
2 . 33060
2.32816
244
i
244
13
2.32766
2.32457
309
2
618
14
2 . 32400
2.32149
251
3
753
19
2.33465
2.33169
296
3
888
21
2.32578
2.32479
99
4
396
22
2.32463
2.32362
101
4
404
27
2.32747
2.32496
251
5
1255
28
2.32461
2.32368
93
2^
232
2 9
2.32347
2.31946
401
4
1604
30
July 3
2.31931
2.31962
+ 3i
3
+ 93
4
2.32378
2.32193
185
5
925
5
2.32932
2-32927
5
3 1 A
17
6 | 2 . 33200
2.32760
44
2
880
~\ = 5-9589
A
0.00193
. e. = 0.00016
STAR No. 377 /. c. (With 1032.)
Date
&JT- * '
log.r
A
P
/A
June 7
8
9
12
13
2 . 83400
2.83705
+ 0.00305
i
-f 0.00305
14
2.82985
2.82736
249
3^
871
19
2 . 84207
2.83701
506
3
1518
21
2.83180
2.82974
206
4
824
22
2.83075
2.82914
161
4
644
27
2.83356
2.83148
208
5
1040
28
2-83035
2 . 82600
435
2^
1087
29
2.82931
2.82296
635
3^
2222
30
2.83107
2.82425
682
4
2728
July 3
2 . 82480
2.82096
384
3
H52
4
2 . 82968
2 . 82900
68
4^
3 06
5
2 . 83608
2.83298
310
4
I24O
6
2.83912
2.83265
647
2^
l6l7
A I 0.00336
[p] =
6.2716
p. e. =
0.00028
M.-P. VOL. I.] CRAWFORD CONSTANT OF REFRACTION. l8l
STAR No. 377 /. c. (With 1156.)
Date
/qf. *" '
log. r
A
/
/A
June 7
2.83328
2.83115
0.00213
5
0.01065
8
2.83152
2.82838
314
4
1256
9
2.83045
2.82720
325
3
975
12
13
2 . 83400
2.83306
94
%
47
14
2.82985
2 . 82607
378
3^
!3 2 3
19
2 . 84207
2.83464
743
3
2229
21
2.83180
2 . 83048
132
4
528
22
2.83075
2 . 82840
235
4
940
27
2.83356
2.83081
275
5
1375
\j i \j
28
2.83035
2 . 82647
388
3
1164
29
2.82931
2.82312
619
4
2476
30
2.83107
2.82833
274
4
1096
July 3
2 . 82480
2.82124
356
3
1068
4
2.82968
2 . 82730
238
5
1190
5
2.83608
2.83239
369
3^
1291
6
2.83912
2 83502
410
2^
1025
A I O.OQ334
= 57 ; log [pvv] = 6.0815
STAR No. 1156.
p. e. =
0.00018
Date
#. r '
log.r
A
P
/A
June 7
2.87524
2.87330
0.00194
5
0.00970
8
2.87296
2.87010
286
4
1144
9
2.87172
2.86876
296
3
888
12
13
2-87557
2.87471
86
tf
43
H
2.87138
2.86795
343
3^
1 200
19
2 . 88372
2.87698
674
3
2022
21
2.87302
2.87182
120
4
480
22
2.87193
2 ..86980
213
4
852
27
2 . 87448
2.87197
251
5
1255
28
2.87189
2.86837
352
3
1056
29
2 . 87078
2.86516
562
4
2248
3
2 . 87246
2.86996
250
4
IOOO
July 3
2.86594
2.86271
323
3
969
4
2.87134
2.86918
216
5
1080
5
2-87773
2.87437
336
3^
1176
6
2 . 88028
2.87655
373
2^
.933
= 57 ; log [pw} = 6.0105
I 0.00304
p. e. = it 0.00016
182 CALIFORNIA ACADEMY OF SCIENCES. [PROC. 30 SER.
STAR No. 1162. (With 406 /. c.)
Date
/#-. r '
log. r
A
P
/A
June 7
Q
O
9
2.57666
2-57349
0.00317
3/2
0.01109
12
13
2.57998
2.57897
IOI
%
50
14
2.57649
2-57339
310
3 1 A
1085
19
2.58742
2.58196
546
3 - 1638
21
2.57789
2.57491
298
4
1192
22
2.57681
2-57474
207
4 828
27
2.57924
2.57728
196
5
980
28
2.57699
2-57364
335
3^ ! 1173
29
2.57604
2.57302
302
4
1208
3
2-57739
2.57226
513
4
2052
July 3
2-57156
2.56791
365
3^
1277
4
2.57727
2.57417
310
5
1550
5
2.58212
2.58006
206
3^ 72i
6
2.58448
2.57905
543
3 l6 29
0.00330
= 50 ; log [pvv] = 5.8169
STAR No. 1162 (With 444 /. c.)
P> e. = 0.00015
Date
&. r '
log.r
A
P
/A
June 7
8
9
2 . 57666
2.57219
0.00447
3 1 A
0.01564
12
13
2.57998
2 . 57648
350
X
175
14
2.57649
2.57545
104
2^
260
19
2.58742
2.58178
564
3
1692
21
2.57789
2.57518
271
4
1084
22
2.57681
2.57583
98
4
392
27
2.57924
2.57694
230
5
1150
28
2.57699
2.57306
393
4
- 1572
2 9
2.57604
2.57358
246
3/ 2
86 1
30
2-57739
2.57309
430
4
1720
Jly 3
2.57156
2 - 56904
252
3
756
4
2.57727
2.57438
289
5
H45
5
2.58212
2.58035
177
3^
619
6
2.58448
2 . 58043
405
2
810
v] = 5-8851
A I 0.00297
p. e. db 0.00017
M.-P. VOL. I.] CRAWFORD-CONSTANT OF REFRACTION. 183
STAR No. 406 /. c. (With 1162.)
Date
/cg-. r '
log.r
A
P
/A
June 7
Q
O
9
2-59357
2.59052
0.00305
3$
0.01067
12
13
2.59683
2.59586
97
l /2
49
14
2.59350
2.59052
298
3^
1043
19
2 . 60425
2.59900
525
3
1575
2r
2-59477
2.59191
286
4
H44
22
2.59366
2.59i 6 5
2OI
4
804
27
2 . 59602
2.59413
I8 9
5
945
28
2.59420
2.59097
323
3^
1130
2 9
2.59315
2.59022
293
4
1172
30
2.59432
2-58939
493
4
1972
July 3
2.58842
2.58491
35i
3^
1229
4
2.59297
2.58997
300
5
1500
5
2.59909
2.59711
198
3^
693
6
2.60148
2.59625
523
3
1569
I 0.00318
= 50 ; log [pvv} = 5-7810
STAR No. 406 /. c. (With 1179.;
P> e- = db 0.00015
Date
/< r '
log. r
A
P
/A
June 7
2-59730
2-59537 0.00193
4
0.00772
8
2.59456
2.59219 237
4
948
9
2-59357
2.59002 355
4
1420
12
13
2.59683
2.59691 + 8
%
+ 4
14
2.59350
2.59039 3ii
4
1244
19
2 . 60425
2.60003 4 22
3
1266
21
2-59477
2 . 59104 373
4
1492
22
2.59366
2.59077 289
4
1156
11
2.59602
2.59420
2.59413
2.59084
I8 9
336
5
3^
945
1176
29
2.593 r 5
2.59041
274
3 l /2
959
30
2.59432
2 . 59002
43
3*/2
1505
July 3
2.58842
2.58574
268
3/2
938
4
2.59297
2.59II2 185
4^
832
5
2.59909
2 . 59686 223
4
892
6
2 . 60148
2 59683 465
3
1395
A
0.00292
= 5-6978
p. e. =
o. oooi i
184 CALIFORNIA ACADEMY OF SCIENCES. [PROC. 30 SER.
STAR No. 1179. (With 406 /. c.)
Date
log. r '
log. r
A
P
*>A
June 7
2.58409
2.58211
0.00198
4
0.00792
8
2.58167
2.57922
245
4
980
9
2-57955
2.57590
365
4
1460
12
13
2.58282
2 . 58290
+ 8
%
+ 4
14
2 - 57953
2.57633
320
4
1280
19
2.59007
2.58573
434
3
1302
21
2.58069
2.57682
387
4
- 1548
22
2-57955
2.5/657
298
4
1192
27
2.58185
2.57990
!95
5
975
28
2.58049
2.57703
346
3#
I2II
29
2.57918
2.57635
283
3^
991
30
2.58015
2.57569
446
3^
1561
July 3
2.57417
2.57142
275
3^
962
4
2.57852
2.57661
191
4^
860
5
2.58493
2.58263
230
4
920
6
2.58735
2.58255
480
3
1440
0.00301
[p. 1 = 58 ; log [pvv} = 5-7112
STAR No. 1179 (With 444 /. .
Date
log. r '
log.r
A
P
/A
June 7
2.58409
2-58351
0.00058
3
0.00174
8
2.58167
2.57807
360
4
1440
9
2 - 57955
2.57462
493
4
1972
12
13
14
2.58282
2-57953
2.58043
2-57837
239
116
#
3
348
19
2.59007
2 58554
453
3
1359
21
2.58069
2.57709
360
4
1440
22
2 57955
2 . 57766
189
4
756
27
2.58185
2.57956
229
5
U45
28
2-58049
2.57646
403
4
1612
29
2.57918
2 - 57692
- 226
3
678
3
2.58015
2.57654
361
3/2
1264
July 3
2.57417
2.57254
163
3
489
4
2-57852
2.57681
171
*y*
769
5
2-58493
2.58293
200
4
800
6
2-58735
2 - 58392
343
2
686
= 54 T A ; log[pvv] = 5-9 I2 5
0.00276
p. e. = 0.00015
M.-P. VOL, I.] CRAWFORD CONSTANT OF REFRACTION. 185
STAR No. 1182.
Date
/>. r '
log.r
A
P
/A
June 7
.97645
1-97543
0.00102
3
0.00306
8
.97288
1.97230
58
4
232
9
.97180
.96923
257
4
1028
12
J 3
.97496
.97520
+ 2 4
2>^
+ 60
H
.97208
.97690
482
4
1928
19
.98178
.98268
90
3
270
21
.97296
97359
63
4
252
22
.97167
.97248
4- 81
4
+ 324
27
.97413
.97382
31
5
155
28
.97291
.97313
+ 22
4
+ 88
2 9
97153
.97179
+ 26
3
+ 78
30
.97242
.97128
114
3/2
399
July 3
1.96655
.96918
+ 263
3
+ 789
4
.97073
97058
15
5
75
5
1.97694
97520
174
4
696
6
1.97923
.97855
68
3
204
OJ = 59; log [pvv] = 6.2272
{- O.OOOI2
p. e. =
0.00020
STAR No. 424 /. c. (With 1105.)
Date
log.r'
log. r
A
P
/A
June 7
9
1.97474
1.97216
0.00258
3 1 /*
0.00903
12
13
.97816
97571
245
2
490
14
.97502
.97941
439
3/2
+ 1536
19
.98471
.98534
+ 63
3
1 80
21
.97609
.97465
144
4
576
22
97473
.97414
59
4
236
27
.97727
.97488
239
5
1195
28
.97613
.97658
+ 45
3
+ 135
29
.97468
.97465
3
3 ,
9
3
97549
.97470
79
4/2
356
July 3
.96971
.97021
+ 5o
3
150
4
97371
97437
+ 66
5
+ 33
5
.98000
.97964
36
4
144
6
98238
.98236
2
3
6
I 0.00031
= 6.1588
p. e. =
0.00022
1 86 CALIFORNIA ACADEMY OF SCIENCES. [PROC. 3 D SER.
STAR No. 424 /. c. (With 1182.)
Date
/-. r '
log. r
A
P
/A
June 7
1.97982
.97882
o.ooioo
3
0.00300
8
97599
97534
65
4
260
9
97474
.97220
254
4
1016
12
13
.97816
.97841
+ 25
2^
+ 62
14
.97502
.97982
+ 480
4
-f- 1920
19
.98471
.98556
85
3
255
21
.97609
.97672
63
4
+ 252
22
97473
97552
+ 79
4
4- 316
27
.97727
97695
3 2
5
160
28
.97613
97635
+ 22
4
+ t-88
29
.97468
97493
+ 2 5
3
+ 75
30
97549
97433
116
3 1 A
T4o6
July 3
.96971
.97225
+ 254
3
+ [762
4
97371
97354
17
5
85
5
1.98000
.97823
177
4
708
6
1.98238
.98164
74
3
222
I + o.oooio
= 59 ; log [pvv ] = 6. 2248
STAR No. 438 /. c.
p. e. =
0.00020
Date
/<#. r '
log. r
A
/
/A
June 7
2 . 02896
2.02882
0.00014
3
0.00042
8
2.02529
2.02288
241
4
964
9
2 . 02369
2.02263
106
4
424
12
13
2.02753
2.02727
26
i#
39
M
2.02398
2.02841
+ 443
2^
+ 1107
19
2.03351
2.03234
117
3
35i
21
2 . 02530
2 . 02690
+ 160
4
640
22
2.02385
2.O242O
+ 35
4
+ HO
27
2 . 02640
2.02592
48
5
240
28
2.02535
2.02702
+ 167
4
668
29
2 . 02403
2.02415
12
3^
42
30
2 . 02436
2.02547
III
4
444
July 3
2.OI9OO
2 . 02057
157
3
471
4
2.O2276
2.02333
57
5
285
5
2.029T5
2.02958
43
4
172
6
2.03160
2.03338
+ 178
2
+ 356
A
-f 0.00040
[p ] = 56^ ; log [fiw] = 6.0647
P. e. = i 0.00017
.: I.] CRAWFORD CONSTANT OF REFRACTION. 187
STAR No. 444 /. c (With 1162.)
Date
log. r '
log. r
A
P
/A
June 7
o
9
2.62193
2.61791
0.00402
3 1 A
0.01407
12
T 3
2.62622
2 . 62306
316
%
158
H
2.62223
2.62129
94
*X
235
!9
, 2.63245
2.62736
509
3
1527
21
2,62367
2.62123
244
4
976
22
2.62220
2.62132
88
4
372
27
2.62478
2.62271
207
5
1035
28
2 . 62369
2.62016
353
4
1412
29
2.62213
2.61992
221
ZY*
774
3
2.62278
2.61891
387
4
1548
July 3
2.61701
2.61475
226
3
678
4
2.62082
2.61819
263
5
1315
5
2.62782
2.62622
160
3^
560
6
2.63053
2.62688
- 365
2
730
=47% I log[pvv] 5-7941
I 0.00268
P. e. =
0.00015
STAR No. 444 /. c. (With 1179.)
Date
log. r '
log. r
A
P
/A
July 7
2.62762
2 . 62709
- 0.00053
3
0.00159
8
2.62363
2.62036
327
4
1308
9
2.62193
2.61745
448
4
1792
12
13
2.62622
2.62405
217
%
108
14
2.62223
2.62118
105
3
315
19
2.63245
2.62834
411
3
1233
21
2.62367
2 . 62042
325
4
22
2.62220
2.62048
172
4
688
27
2.6-478
2.62270
208
5
1040
28
2.62369
2 . 62003
366
4
1464
29
2.62213
2 . 62OO7
206
3
618
3
2.62278
2.61950
328
2.Y*
1148
July 3
2.61701
2.61553
148
3
444
4
2 . 62082
2.61927
155
4^
698
5
2 . 62784
2.62599
185
4
740
6
2-63053
2.62743
3'Q
2
620
A | 0.00251
; log
= 5-8266
p. e. =
0.00013
1 88 CALIFORNIA ACADEMY OF SCIENCES. [PROC. 30 SER.
STAR No. 1225.
Date
^
log. r
A
P
/A
June 7
2.02116
2.02103
0.00013
3
0.00039
8
2.01757
2.01515
242
4
968
9
2.01589
2.01481
108
4
432
12
13
2 . O2OO4
2.01978
26
i l 4
39
*4
2.01668
2.02119
-f 45i
2/4
-f 1127
J 9
2 . 02602
2 . 02486
116
3
348
21
2.01728
2.01891
+ 163
4
-f 952
22
2.01609
2.0I64I
+ 32
4
-f 128
27
2.01853
2.01804
- 46
5
230
28
2.01726
2.01895
+ 169
4
+ 676
29
2.01634
2.01645
+ ii
3%
39
30
2.01658
2.01770
-}- 112
4
448
July 3
2.0II55
2.01322
4- 167
3
SOT
4
2.01453
2.0I5II
58
5
290
2.02135
2.O2l8l
+ 46
4
184
6
2.02390 j 2.02576
+ 186
2
+ 372
I + 0.00042
= 6.0780
p. e. =
0.00018
The next table contains the results collected from those
preceding. The weights given in the column^ have been
derived from the probable errors as given in column r.
The remaining columns are self-explanatory.
M.-P. VOL. I.] CRA WFORD- CONSTANT OF REFRA CT1ON.
189
Star
A
r
log. r 2
log. p
p
PA
948
- 205
15
2.3522
1.0964
12.5
0.02562
190 /. c.
513
47
3 3442
0.1044
!-3
667
959(D
- 584
53
3.4486
o.oooo
1.0
584
9592)
462
27
2.8627
0.5859
3-9
1802
968
-f 662
36
3 . i i 26
0.3360
2.2
+ 1456
977
+ 476
40
3.2041
0.2445
1.8
+ 857
984
142
17
2.4609
0.9877
9-7
1377
225(1)7.*.
211
15
2.3522
1.0964
12.5
2637
225,2) /. c.
126
15
2.3522
1.0964
!2-5
1675
225*3) I- C.
997
10051)
- 159
+ 6 5 2
215
i
21
2.2279
3.1126
2.6444
I . 2207
0.3360
0.8042
16.6
2.2
6.4
2639
+ 1434
1376
1005(2,
3 1
19
2-5575
0.8911
7-8
242
1009
1019(1)
+ 298
f 488
38
40
3^596
3 2041
o . 2890
0.2445
i.-9
1.8
+ 566
878
1019:2)
+ 290
38
3-1596
o . 2890
1-9
+ 55 1
264 /. c.
218
20
2.6021
0.8465
7-o
1526
1032
3*7
29
2 . 9248
0.5238
3-3
1046
282 /. c.
473
27
2.8627
0.5859
39
1845
1084
101
35
3.0881
0.3605
2-3
232
1094
- 104
34
3.0630
0.3856
2.4
250
1105
29
23
2.7235
0.7251
5-3
154
I IIO
- 84
18
2.5105
0.9381
8.7
73i
349 l - c -
- 84
18
2.5105
0.9381
8-7
73i
356 /- c.
33
19
2-5575
o . 89 1 1
7-8
257
H35
193
16
2.4065
I .0421
n .0
2123
377d) I. c.
-336
28
2-8943
0.5543
3-6
1210
377(2 I.e.
334
18
2-5'o5
0.9381
8.7
2906
1156
34
16
2.4065
.0421
II.
3344
Il62;i)
- 33
15
2.3522
.0964
12.5
4125
Il62 (2)
297
17
2 . 4609
0.9877
9-7
2881
406,, /. c.
-318
15
2.3522
.0964
12.5
3975
406,2, /. c.
292
n
2 . 0828
.3658
23.2
6774
ii79(D
301
n
2.0828
-3658
23.2
6983
1 179 2)
-276
15
2.3522
.0964
12.5
3450
1182
+ 12
20
2. 6O2I
0.8465
7-o
+ 84
424(1) /. c.
31
22
2.6848
0.7638
5-8
180
42412) LJC.
+ 10
20
2. 6021
0.8465
7-o
+ 70
438 /. c.
+ 40
17
2.4609
0.9877
9-7
+ 388
444D /. c.
268
15
2.3522
1.0964
12.5
3350
444(2) /. c
251
13
2.2279
I . 2207
16.6
4167
1225
+ 42
18
2.5105
0.9381
8-7
+ 365
A I 0.00180
= 340.6
[pVV ] = O.OO
A = 0.00180
0.00019
190 CALIFORNIA ACADEMY OF SCIENCES. [PROC. 30 SER.
4. The Constant of Refraction. The value of a deduced
by Gylden for the Pulkowa Tables, as given in his "Unter-
suchungen iiber die Constitution der Atmosphare u.s.w.," is
a =0.00027985 = 57". 723.
This is for B = 29.5966 inches at o and / = 7. 44 R.
The Pulkowa Tables used here, however, are Gylden's
with JJL systematically reduced by 0.00124. Combining
this with the value found for A, the correction to Gylden's
constant becomes
and a = 57". 548.
This reduced to the condition of 760 mm. pressure at o
and o C temperature gives
a= 60". 159.
To this value of a correspond the following:
c = 0.00029182
and ^=1.00029178.
For the sake of comparison, the most important deter-
minations of the constant of refraction are given below.
These values are for the conditions B = 760 mm. at o C
and external thermometer = o C. (These values are taken
from Professor Bauschinger's * 'Untersuchungen iiber die
Astronomische Refraction u.s.w.").
a /A
1. Fund. Astr 60". 320 1.00029257
2. Tab Reg 440 29315
3. Tab. Pulk 268 29232
4. FuSS .122 29161
5. Greenw. 1857-1865 .. .120 29160
6. Pulk. 1865 .209 29203
7. -Greenw. 1877-1886. . .192 2 9 I 95
8. Pulk. 1885 058 29130
9. Miinchen .104 29152
M.-P.-VOL. I.] CRA WFORD- CONSTANT OF REFRA CTION.
The first and second of these are determinations by
Bessel; the third by Gylden; the fifth by Stone; the
sixth by Nyren; the seventh by Newcomb; the eighth by
Nyren; and the last by Bauschinger.
Bauschinger gives weight zero to each of Bessel's
determinations; to the first, because there was considerable
uncertainty in Bradley's meteorological instruments; to the
second, because of the uncertainty in reading the Meridian
Circle (read by vernier to one second). He gives equal
weight to the last seven, and gets for a mean
a = 60". 1 53 and i*> = 1.00029176.
5. Latitude. The following table gives the value of
<f deduced separately from the southern and from the
northern stars. All of the stars of the list down to
84 Z. D. were used.
V --= + 37 20'
Date
V*
P
*fcs
?N
P
P9x
June 7
25-38
4
101.52
24.89
4
99.56
8
25-88
4
103-52
24.71
4
98.84
9
26.49
4
105.96
24.27
4
97.08
12
26.08
i
26.08
24.96
i
24.96
J 3
25-99
2
51-98
25.27
2
50-54
14
25.88
4
103.52
25.26
3
75.78
19
26.55
4
106.20
24-54
3
73-62
21
25-99
5
129-95
24.66
4
98.64,
22
25-65
5
128.25
24-54
4
98.16
27
25-67
7
179.69
24-59
5^
135-24
28
26.48
4
105.92
24.87
3
74.61
29
25.10
5
125-50
24.89
4
99-56
30
26.08
5
130.40
24.80
4
99.20
July 3
25.60
4
IO2 . 40
24.91
3
74-73
4
26.03
7
182.21
25.22
5^
138.71
5
25-95
5
129.75
25.07
4
100.28
6
26.80
3
80.40
24.60
3
73-8o
2 \ 73
I893-25
61
1513-31
Weighted mean <p
25-93
24.81
Applying the new refractions found here, the latitudes
become from the
Southern Stars <p =25''. 55
Northern Stars <p = 25 .19
giving for the mean <p at this epoch (1899 June 22),
f -4 37 20' 25". 3 7.
192 CALIFORNIA ACADEMY OF SCIENCES. [PROC. 30 SER.
The remainder of the difference between the values of <p
as found from the northern stars and from the southern stars
(o".36) is probably due to slight errors in the declinations
of the stars used, and to bisection error.
CONCLUSION.
In conclusion it is desired to state that limitations of time
have prevented the complete reduction of these observations
and of the series taken during the fall months (1899
Oct. -Dec.). It is hoped that, in the near future, time will
be available in which to carry out these reductions by
correcting the declinations used and then repeating such
portions of these computations as will be necessary. It is
also desired to make reductions which will include the
relative humidity and a term depending upon the zenith
distance.
It will be noticed from the table (p. 189) that there is a
large range in the values of A> viz., from 0.00584 to
-f- 0.00662. This discordance is due partly to the values of
the declinations adopted, but is also very clearly a function
of the zenith distance. By introducing a term depending
upon the zenith distance, and re-solving by Least Squares,
this discordance can be greatly diminished.
From this investigation the following conclusions can be
drawn:
1 . That this preliminary reduction gives for the Constant
of Refraction
a = 60". 159
for B = 760 mm. at o (C) and / = o (C).
2. That for the epoch 1899 June 22, the latitude of the
Lick Observatory Meridian Circle was
v = + 37 20' 25". 3 7.
3. That the final reduction will show that the Constant
of Refraction of the Pulkowa Tables is too large.
4. That the observing room of the Lick Observatory
Meridian Circle is of a very good design, and that there is
no need of mounting Meridian Circles in the open air.
M.-P. VOL. I.] CRAWFORD CONSTANT OF REFRACTION. 193
ADDENDUM.
The table on page 189 shows a large range in the values
of A, viz., from -{-0.00662 to 0.00584. Upon plotting
these values, using the zenith distance z for abscissa, and
A for ordinate, it is easily seen that A varies quite uniform-
ally with the zenith distance. A straight line, inclined
about 145 to the zenith distance axis, and cutting'it at z =
about 55, appears to represent A very well. Therefore,
assuming Z to be the zenith distance for A = o, we can set
up an observation equation of the following type for every
star :
loga=loga -[- [Z z]x,
or
loga Ioga = A = Zx zx= D zx ,
where
and where a is the a of the tables used (Pulkowa).
Equations of this kind were, accordingly, formed and
solved for Z and x by the method of Least Squares.
CALIFORNIA ACADEMY OF SCIENCES. [PROC. 30 SER.
Equations of Condition.
= zx.
No.
Star
D zx
A
P
i
948
D 80.00 x
= o . 00205
12.5
2
190 1. e.
89.20
513
3
959
88.76
= - 487
4-9
4
968
30-38
= 4- 662
2.2
5
977
21-55
= 4- 476
1.8
6
984
78.11
= 142
9-7
7
225 1. c.
79.70
= 167
41.6
8
997
30-59
= + 652
2.2
9
1005
57- J 9
= 114
14.2
10
1009
21.34
= + 298
ii
1019
21-49
= + 386
3-7
12
264 I.e.
57-35
= 218
7.0
13
IO}2
87.05
= 317
3-3
14
282 1. c.
88.67
= 473
3-9
15
1084
27.80
= 101
2-3
16
1094
28.49
= 104
2.4
17
1105
62.21
= 29
5 3
18
IIIO
67.08
84
8.7
19
349 I- c.
67.65
= - 84
8.7
20
356 1. c.
57-49
33
7-3
21
H35
77-37
= 193
II.
22
377 Lc.
86.79
= 335
12/3
23
1156
87.23
= 304
II
24
1162
83.21
22.2
25
406 1. c.
83-50
= 301
35-7
26
1179
83.26
292
35-7
2 7
1182
62.79
12
7.0
28
424 1. c.
62.96
9
12.8
29
438 1. c.
65-52
= 4- 40
9-7
30
444 1. c.
83 99
= - 258
29. i
31
1225
65-13
= 4- 42
8-7
To reduce the number of equations, those nearly alike
were combined, as follows: Equations No. i, 6, 7 and 21;
2, 3 and 14; 4 and 8; 5, 10 and n ; 9, 12 and 20; 13, 22
and 23; 15 and 16; 17, 27 and 28; 18 and 19; 24, 25, 26
and 30; and 29 and 31, giving the n equations:
No.
i
2
3
9
10
ii
79.20
8S.78
30.48
21.47
57-31
87.03
27-I5
62 75
67.36
83 49
65.34
x =
I
i
P
.00174
74.8
485
IO. I
657
4-4
385
7-4
117
29.0
320
26.6
I0 3
4-7
7
25.1
84
17.4
291
122.7
18.4
8.6
3 2
2. I
2.7
5-4
5-2
2.2
50
4.2
II. I
4-3
M.-P.-VoL. I.] CRAWFORD-CONSTANT OF REFRACTION. 195
Weighted Observation Equations.
fo.
a
b
n
I
8.6 D
681.1 x
=
0.01496
2
3-2
284.1
=:
1552
3
2.1
57 9
=
+ 1248
4
2-7
58.0
=
-j- 1040
5
5-4
309-5
=
- 632
6
5-2
452-4
S=
1664
7
2.2
59-7
=
227
8
50
3I3-7
=
35
9
4-2
282.9
=
353
10
II . I
926.7
t=
- 3230
ii
4-3
281.0
==
+ 176
; . ; - ' . , ' 'V i - '
To render these more nearly homogeneous, let D=D;
loox y and multiply the absolute term by 100. Then we
have the following
Weighted Homogeneous Observation Equations.
Vo.
a
b n
i
8.6 D
6.811
y = '
1.496
2
3-2
2.841
1-552
3
2. [
o 579
i
1.248
4
2-7
0.580
_|_
i .040
5
54
3 095
=
O.6}2
6
5-2
4-524
1.664
7
2.2 .
0-597
=
0.227
8
5-o
3-137
=
0.035
9
4.2
2.829
=
o-353
10
II. I
9.267
= ;
3-230
ii
4 3
2 8lO
- +
0.176
Combining these by the method of Least Squares we
obtain the following
Normal Equations.
+ 341.28 D 254.512 y= 61.7188
254-5 1 -fipV-JS 1 -f53-4383
Solving these, remembering that the absolute terms had
been multiplied by 100, we have
log 7.75694; log y=8. 00376 or log x=6. 00376.
Now since D=Zx, we have log Z = 1.75318,
Whence x= -{-0.0001009 and Z=56
Substituting the values of D and x, thus found, in the
Weighted Observation Equations, we find \_pw~\ =
196 i CALIFORNIA ACADEMY OF SCIENCES. [PROC. 3D SER.
0.00024690, from v^hjch the following probable errors have
been deduced:
^ <S V. v/.
r x =,^f 0.0000130 and r = 0^031 = oi'52".
*?.V
We, ther^fbrej have from this solution
Z=5638'.8i'.9 and' x+o.oooioi 0.000013,
giving
loga=loga -\- o.oooioi [5638'.8 z] .
We are, ; therefore, led to the conclusion that the so-called
Constant of Refraction needs not only a correction, but a
Correction for 'every zenith distance. In other words, the
formula from which refractions are computed needs to be
modified. Or, the formula may be retained unaltered, and
the desire^ result pbtained by correcting the log p table of
the refraction tables used (Pulkowa) by the amount
A log/*=p ; oopioi [56 38'.8 z].
R. T. C.
ranTcrd-
Determination of the
onstant o:? refraction
YD 04994