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TRANSAOTIONS ‘ THE DETROIT OBSERVATORY,
UNIVERSITY OF_ MICHIGAN.
\
- ’ PART I.
DETERMINATION OF THE ABERRATION CONSTANT FROM
ZENITH DISTANCES OF POLARIS MEASURED WITH
' ' THE WALKER MERIDIAN CIRCLE,
_BY
(
ASAPH HALL, JR., DIRECTOR OF THE OBSERVATORY.
[Reprinted from the Fourth Report of the Michigan Academy of Science, 1904.]


A—l—R



I .—I ntro duction.
The Detroit Observatory of the University of Michigan was built about
1854-through the efforts of President Tappan, money .for the purpose
being raised in Detroit. Mr. Henry N. Walker of Detroit was especially
interested in the project and gave funds for the purchase of the meridia
circle. 7 . \ _
The observatory building is of the usual old-fashioned type, a central
part, on the top of which is the dome for the equatorial, and east and west
wings, the meridian circle being in the east wing and the library in the
west. All the walls are of heavy masonry, so that the temperature in the
observing rooms changes slowly.
In addition to the Walker meridian circle the observatory was equipped
at first with a 12%-inch equatorial constructed by Fitz, and a clock by
Tiede~of Berlin. The equatorial has the old German style of mounting
with a wooden tube. As far as I can find out the driving clock was never
of any use. Also, it is rather difficult to manage the illumination of the
micrometer, so that with it few systematic observations were made. The
object glass is a fair one. With this instrument Professor Watson dis-
covered twenty-one_ asteroids. A number of these were observed but a
few times and are now lost. .The difliculty in using' the micrometer is
probably the reason for the small number of observations of them made
at Ann Arbor. _ ' —
Observations of comets and asteroids were also made with this instru-
ment by Dr. Briinnow, Professor Watson and Messrs. Schaeberle, Camp-
bell, Hussey, and Townley. I believe that several comets were discovered
with it.
The Tiede Clock has now an irregular rate. .
About 1880 a small observatory was erected near the large building,
designed especially for practice work. In it were placed a 6-inch, equa-
torial with a Clark glass, and mounting by Fauth, and a 3-inch Fauth
meridian transit. _
The object glass of the equatorial is good, with the sharp definition
characteristic of the Clark glasses. The mounting is fair, though the
driving clock, having a Foucault governor, is too weak.
With this equatorial observations of comets and asteroids have been
made by Messrs. Schaeberle, Campbell, Hussey, and ToWnley. - "
The object glass of the meridian transit is poor. AUrsae Min0ris cannot
be seen with a bright field. The pivots rest on wide and flat agate bear-
ings, an arrangement which is wrong mechanically, and may account for
the existence of two azimuths. ‘
The observations made at Ann Arbor have been published in the various
astronomical journals and in the American Journal of Science. In the
way of records there is very little. ' ' - '
" The observatory building is on a hill south of the Huron River, on cla'
\
w
38 MICHIGAN ACADEMY OF SCIENCE.
soil. Along the river runs the Michigan Central Railroad and the passing
of the trains sometimes makes it difiicult to determine nadirs. The pre-
vailing Winds are westerly. The best seeing is usually in the spring and
summer, though there is fine weather also in October, December, and
January. There is considerable dampness.
The instruments of this observatory were in bad condition when they
came into my hands. It was necessary to take apart and clean the object
glasses. Tackles were rigged in the slits of the domes, and the tubes,
axes, and bearings of the axes were taken down, and the accumulations
of oil and grease removed.
2.—Latitucle and Longitude of the Detroit Observatory.
Asto the latitude no record of an accurate determination can be found.
From the discussion which follows of observations of Polaris the latitude
can for the present be assumed
‘ +42° 16’ 48.8".
The value +42° 16’ 48.0” as printed in the ephemerides was, I think, an
approximate determination, +42° 16’ 48”, the .0 being finally added by
accident.
The best determination of longitude is probably that found by connect-
ing with Hamilton College. Clinton, New York. Dr. Briinnow observed at
Ann Arbor and Dr. Peters at Clinton. The difierence of. longitude was
found to be
33m 17 .69s.
Hamilton College had been previously determined with respect to Cam-
bridge, and was found to be west of Cambridge '
17m 6.48s.
Thus the Detroit Observatory is west of Cambridge
50m 24.21s.
See Briinnow’s Astronomical Notices, numbers 15 and 27.
,Also, Ann Arbor was twice connected with Detroit, and Detroit was
connected directly with Cambridge. See pp. 716, 717, 869 of Professional
Papers, Corps of Engineers, U. S. A., N o. 24, also the Spherical Astronomy
of Briinnow, one of the examples under the Method of Least Squares.
From thesedeterminations Detroit is west of Cambridge.
47m 41.17 s. ‘
and Ann Arbor is west of Detroit
‘ ' 2m 43.10s.
In the second exchange of longitude signals between Ann Arbor and
Detroit apparently there was no telegraph line running to this observa-
tory. The signals from Ann Arbor seem to have been sent from a chro-
nometer which was carried to the telegraph office. ‘ ‘
3.——The Walker M Circle.
~ '4 An investigation, of -_ {of :~the fine circle of this instru~
ment was published in Briinnow’s Astronomical---N.0tices.- I cannot find
that anything else. has.iieen.vprinted:regareing it.1-;-:-.-.~.-;.-. . 1
HALL, ABERRATION CONSTANT. 39
In the Notices are given, also, the determinations of the places of a
number of comparison stars for asteroids and comets. Several of the
older graduates have told me that Briinnow made with this meridian
circle an elaborate series of observations of the Bradley stars, the records
of which he took to Europe for reduction, by permission of the University
authorities. I cannot find out anything regarding such observations.
Professor Watson, after taking charge of the observatory, seems to have
been interested in the construction of ecliptic charts and the discovery of
minor planets, and not to have made any regular use of the meridian
circle. It was employed by Professor Schaeberle, however, for the observa-
tion of latitude stars, Struve double stars, and planets. See report of
Professor Harrington to the Regents, 1881. A list of 155 stars observed
by Professor Schaeberle was printed in the “Publications of the Wash-
burn Observatory.” They were reduced, it is stated, differentially, but
none of the constants of reduction are given.
After some experience at the Naval Observatory under Professor East-
man, I became interested in meridian circle work, and on coming to this
place resolved to make such observations. A new micrometer was pur-
chased from the Repsolds, a chronograph from Saegmiiller, and a clock
from Howard. The object glass was taken to the Clarks’ shop and a
spring was put in the cell to act against the glass. The instrument was
taken to pieces and carefully cleaned. Observations were begun of a list
of Bradley stars, including a number to be used for latitude at the George-
town College Observatory. ‘
On looking up the latitude of this place no record could be found of an
accurate determination, so that observations were made of Polaris, both
for the purpose of determining latitude and with the idea of obtaining the
amount of latitude variation at Ann Arbor. Also, an examination was
begun of the division errors of the fine circle, to test the permanency of
the values given by Dr. Briinnow. The reduction of the nadirs was kept
up, and they seemed to show that the instrument was steady and the
work good. During term time of the University it was necessary to
neglect the other reductions. As soon as they could be brought up the
work was shown to be not first rate. The reduction of the observations
of the Bradley stars are pretty well completed. They can be used, I think,
if they are made strictly differential.
On looking the instrument over again the following trouble was found
which had probably existed since it was first mounted. To support our
meridian circle two brass cones with lugs attached are let into the stone
piers, and to the cones are screwed heavy brass discs. The discs support
the wye blocks which carry the pivots, and to the discs, also, are clamped
the microscope arms. _ The cones were found to be loose in their packing.
This packing was what seemed to be mortar mixed with brick dust, the
brick dust being added, I suppose, to make the mixture hydraulic. See
the older hand books of engineering under cements. The packing when
removed was a fine, dry dust. -
I attempted to mount the cones in the piers first with lead and then
with plaster of Paris. Finally Portland cement was used and with it
they seem steady. We are under obligations to Mr. Fecker, superintend-
ent of Warner and Swasey’s instrument department, and to Messrs,
Warner and Swasey for the remounting of the instrument. Mr. Fecker
called my attention to the fact that the object glass cell fitted loosely in
A-2—R
40 MICHIGAN ACADEMY OF SCIENCE.
\
the telescope tube, so that its weight came entirely on the three collima-
ting screws. A new cell was made, therefore, with a bell flange, fitting
tightly in the tube and having a better spring to work against the object
glass. I have wondered whether the curious flexures shown by some
meridian circles might not be produced in this way, by the bending of the
collinating screws on account of the object glass cell resting on them.
After the instrument was remounted it was necessary to take up some
work that should test it. Also, the reductions could not be too heavy, for
it would not do to allow them to fall behind. Finally it was decided to
begin again observations of zenith distances of Polaris with the idea of
determining the aberration constant, since a number of the values found
according to the method'of Kiistner differed considerably.
4.—Description of Meridian Circle.
This instrument was constructed by Pistor and Martins in 1854. It is
of brass with steel pivots. It is unsymmetrical with respect to the cube,
the cone carrying the object glass being 4 feet 11/2 inches long, while the
length of the eye end. cone is 3 feet and 1% inches. The total focal length
i approximately 8 feet 31/; inches. A lead ring is placed inside the tube,
near the micrometer, to balance the greater weight of the object glass end.
- The length of the axis is 3 feet 5% inches. The diameter of the objective
is 6.3 inches. The object glass and eye ends of the telescope cannot be
interchanged.
The instrument is mounted between sandstone piers as described in Art.
3. The piers are not covered with wood or felt. The substructure is brick.
The dimensions of the observing room are. north and south, 26 feet 3
inches; east and west, 17 feet 81/2 inches; height, 13 feet 31/2 inches; width
of opening, 2 feet 6% inches. The room istoo small. There is hardly
sufficient space for reflected observations, and there is no proper arrange-
ment for ventilation so that the temperature inside shall follow quickly
the changes of the outside air. Moreover, being built on as a wing to the
main building, the heating and cooling of this might produce refractions
different from those of the tables. '
5 .—The Object Glass.
This is rather poor, containing tree-like formations. The rays of light
are not brought sharply to one focus. Still the images are pretty fair,
and round all the way across the field.
6.4—The M icrometer.
The micrometer has a right ascension screw, with the Repsold device
for automatic registration of transits. The value of one revolution is ap-
proximately 3.640s. There is no zenith distance screw, and I may have
made a mistake in not having it. But I had become suspicious of some '
of the complicated arrangements at the eyeends of the large meridian
circles, and determined to make the zenith distance pointings with the
tangent screw of the telescope.‘
With this micrometer can be used only a bright field. The light is
thrown down the axis of the instrument, and reflected by a large mirror in
the cube, the mirror being pierced in the center by a circular opening in
order to let through the cone of rays from the object glass. The amount
HALL, ABERRATION CONSTANT. 41
of light falling on the mirror is regulated by opening or closing slats
placed in the axis of the telescope.
As the Repsolds had only the old Pistor and Martins micrometer to
work from they declined to attempt any arrangement for lighting the
wires, for fear, I suppose, of producing an unsymmetrical illumination.
For all observations the same eye-piece has been used, magnifying 160
times. This is about as high a. power as it is possible to employ over the
nadir basin. A number of attempts were made to use higher powers, but
the-nadir could not be obtained with them except when the air was quite
steady.
7.—The Pivots.
The pivots are approximately 1.819 inches in diameter. They must have
been very carefully made. Professor Schaeberle cleaned them, I under-
stand, with graphite and oil before beginning work with this instrument.
They were polished afterwards, also, by Professor Asaph Hall, in 1894,
with fine pumice stone and watch oil. The rust which had formed on
them had made etchings apparently, but had not injured their form. I
think they are as round now as when they were made. ,
It was not possible to test the pivot inequalities with the hanging
level, since the wye blocks are so large that the level wyes cannot be placed
over the bearings of the pivots. To examine the pivots, therefore, I had
the observatory purchase frOm Saegmiiller a spherometer caliper. A de-
scription of this is given in Doolittle’s Practical Astronomy. Though
exceedingly delicate measures can be made with it the results are not
very definite, as it is now constructed, for the upper and lower bearings
are not in the same vertical plane. It merely shows in a general way
whether or not the pivots are good.
Before taking the measures the two telescope ends and the circles were
removed from the cube, and it was placed on a wooden support like that
of the reversing carriage. Settings of the caliper were made on those
parts of the pivots on which the wyes bear, and on which the level wyes
are usually placed. Eight positions of the cube were taken: eye-end up
and down; edge of cube near 1854 in vertical, up and down; side inscribed
Berlin, horizontal, two positions; edge near Pistor and Martins, in verti-
cal, up and down. These positions were 90° apart.
Twenty settings of the caliper were made in each position. From 1[2 inch
and 1/4 inch steel blocks furnished by Brown and Sharp, one revolution
of the spherometer screw was found to be
' 0.00974754 in.
From the settings on the pivots we have the following results:
BEARINGS ON Y’S.

Fine Coarse
circle end. circle end.




Eye-end . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0.3823r 0.3718r
Edge 1854 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 0.3938 0.38l8
Side Berlin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 0.4214 0.3847
Edge Pistor and Martins . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 0.4298‘ 0.4231
Means . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 0.4068r 0.39041“

6
42 MICHIGAN ACADEMY OF SCIENCE.
Thus we find a shape slightly elliptical. One half the difference of the
means is 0.0082r, or 0.000082 in. Since the length of the axis of the me-
ridian circle is 41% inches, this would produce an inequality of 0.4051”
or 0.0270s, the coarse circle end being the bigger.
BEARINGS OF LEVEL.

Fine _Coarse
circle end. circle end.




Eye-end . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . 0.3706r 0.3658r
Edge 1854 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 0.3698 0.3524
Side Berlin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 0.3698 0.3714
Edge Pistor and Martins . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 0.3625 0.3634
Means . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 0 . 3682r 0.3632r

One half the difference of the means is in this case 0.0025r, or 0.000025
in., producing an inequality of 0.1235” or 0.0082s.
The weight on each pivot is approximately 34 lbs.
8.——The Circles.
There are two circles, one divided to 2’ and one to 10’. Each is read by
four microscopes to 0.1". Both circles were cleaned by me with fine
whiting in 1893. Evidently both had been cleaned a number of times be-
fore, but the lines on the coarse circle are in better condition than those
on the fine circle. On the fine circle they are faint in several places. As
originally cut the lines must have been rather fine and delicate. The
more modern method of making them heavy is better, and the heavy marks
can be pointed on just as accurately, as far as I can see.
The circles are approximately 371/2 inches in diameter. Each is sup-
ported by ten ribs running from the central hub. The ribs and the circles
themselves are rather light, so that there is some distortion by gravity.
The ribs are numbered I, II, through X. The fine circle is not
figured. I have considered the degree mark opposite X to be 0°, that
Opposite I to be 36°, and so on. Opposite 72° I placed a scratch on the
silver band. Afterwards it was found that a cross had been placed oppo-
site 314°, which perhaps had been used on Polaris.
The fine circle was investigated by Dr. Briinnow to every fifth degree.
These results are reprinted here from the Astronomical Notices, both to
show the character of the circle, and for possible use with any old obser-
vations. The coarse circle is on the side of the clamp.
. Examination of the Divisions of the Ann Arbor M ericlian Circle.
The Ann Arbor Meridian Circle was originally furnished with two
divided circles; but as the one on the side of the clamp was found to be
slightly bent when it arrived at Ann Arbor, it is now used merely for set-
ting the instrument, and only the one on the opposite side of the axis
is used for reading the zenith distances. The four microscopes for read-
ing the circle on each side are fastened by strong arms to a solid circular
disc, which is firmly screwed to a solid brass piece let into the stone‘
pillar. This disc supports at the same time the Y-pieces, so that the
center of the axis coincides with its center. The edge of this disc is dove-
\
HA LL, ABERRATION CON STAN T. 43
tailed; and when the three screws which clamp the arms of the micro-
scope are loosened, the arms can slide smoothly around the whole disc,
and may be fastened with the greatest ease and with perfect stability to
any point of the disc. By reason, however, of the width of the part of the
arm which is clamped to the disc, the smallest distance within which any
two microscopes can be brought is about 30°. .
WVith the microscopes in their usual position, 90° distant from each
other, I determined first the error of the line 180°, taking that of the line
0° equal to zero; and by bisecting the two arcs between the line 0° and the
line of 180° corrected, 1 found the errors of the lines 90° and 270°. Then
one microscope was placed at a distance of exactly 45° from the first; and
by means of these two, and the other three microscopes at the respective
distances of 90°, 180° and 270° from the first, I found the errors of the
lines 45°, 135°, 225° and 315°, by bisecting arcs of 90° and 270° corrected
according to the former observations. These observations of the lines at
a distance of 45° were taken on eight different days, in temperatures rang-
ing from 20° to 46° Fahrenheit. For each line, two observations were
made, one immediately after the other; and the errors given in the follow-
ing table are each deduced from the mean of two observations.
The errors of the lines distant 45° from each other, thus obtained on the
different days mentioned, are as follows :—






1857. 45° 900 135° 180° 2250 2700 3150 Temp.
November 25 ............ .. +3.15" +5.90" +7.3 " +7.60" +7.62" +2.35" -0 25" 19°
26.. . 3.56 6.08 7.15 7.72 8.16 2.41 0.25 23
3.75 5.90 6.93 7.57 8.17 2.33 0.53 28
3.02 5.30 7.04 7.70 7.90 2.55 0.50 36.5
29 3.27 5.30 6.78 6.99 7.52 2.13 1.04 .45
December 2 ............ .. 3.17 5.64 7.37 7.95 8.72 2.65 0.30 45.2
2 ............ .. 3.20 5.31 7.63 7.62 8.32 2.66 0.09 43.8
3 ............ .. 3.01 5.62 7.46 7.70 7.88 2.63 0.04 32.7
_ 3 ............ .. 3.27 . 5.80 7.58 7.77 8.60 2.56 0.09 .327
4 ............ .. 3.12 5.34 7.35 7.47 8.19 2 37 0.42 315
Mean ................. .. +3.25" +5.62" +7.26" +7.61" +8.11" +2.46" -0.35"








The differences in the errors of the same line, found on different days,
must have'been caused by the diiferent action of the temperature on
different parts of the circle.
The same observations were repeated in the same manner, but in posi-
tions of the circle 180° different from those in the former series; and the
following results were obtained, each result being the mean of two obser-
vations :—






1858. 45° 90° 1351) 180° 225° 270° 3150 Temp.
Januaryl ................ .. +3.59" +5.55" +7.49" +7.43" +7.34" +2.15" -0.73" 35°
1 3.64 5.55 6.89 7.25 7.22 1.85 0.43 35.2
3.59 5.08 6.48 7.30 7.04 1.53 0.42 33.3
3.51 5.02 6.79 7.02 6.68 1.51 0.55 35.2
3.39 5.39 7.00 7.47 7.16 2.02 0.69 41.7
3.38 5.47 7.18 7.77 7.65 2 32 0.59 44.5
3 33 4.76 6.86 7.32 7.00 1.94 0.61 38.5
3.78 5.76 7.30 7.55 7.73 2.52 0.22 39.0
3.39 5.24- 7.32 7.32 7.17 1.66 1.09 35.2
3.19 5.24 7.13 7.48 6.87 2.02 0.79 36.0
+3.48" +5.30" ‘ +7.04" +7.39" 7.19" +1.95" —0.61"









44 MICHIGAN ACADEMY OF SCIENCE.
The mean errors of the seven lines, resulting from the two series of
observations, are therefore :—

45° 90° 135° 180° 225° 270° 315°

Error . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. +3.36” +5.46” +7.15" +7.50” +7.65" +2.20” —0.48"








In order to find the errors of the intermediate lines for intervals of 15°,
I placed two microscopes exactly 105° apart: by means of these positions
I divided arcs of 315° into three equal parts, beginning successively with
the lines 0°, 45°, 90°, etc., and applying always the corrections for the
seven principal lines found before. These observations were made on four
days in one position of the circle, and on four other days in positions
always 180° difierent. The same errors were found also by another series,
with two microscopes placed 75° a art, arcs of 225° being divided into
three equal parts: these observationv‘ere likewise made on four days, and
repeated on four other days in positions of the circle which differed always
180° from those in the former series. The following tables show the re
sults found for the different errors on the different days :—
MICROSCOPES 105° APART.








Mgi _‘§ 15° 30° 60° 75° 105° ‘ 120° 150° 165° Temp.
December 12.... +0.45" +0.80" +3.21" +5.45" +6.57" +6. " +6.97" 8 21" 320°
14.... 0.42 0.94 3 08 5.52 6.94 6.33 7.37 8 41.5
15.... 0.17 0.94 3.28 5.52 6.31 6.46 7.64 8 44 43.7
January 7 ..... .. 0.62 1.24 3.14 6.58 6.21 6.13 7.64 2 32.0
Mean ...... .. +0.41" +0.98" +3.18" +5.77" +6.51" +6.35" +7.40" +8.29”
195° 210° 240° 255° 285° 300° 330° 345° Temp.
December 12.... +7.23" +6.85" +4.62" +4.29" +1.0 " +0.29" -0.30" - 1.51" 320*
14.... 7.36 7.38 4.72 4.49 1.01 0.46 +0.03 1.31 41.5
15.... 7.43 6.81 4.92 4.52 1.01 0.69 -0.37 1.11 43.7
January 7 ..... .. 6.93 6 31 5.02 4.52 1.31 0.19 +0.17 0.61 32.0
Mean ...... .. +7.24" +6.84" +4.82" +4.45" +1.10" +0.41" -0.14" -1.13"










CIRCLE 180° FROM ITS FIRST POSITIONS.


15° ) 30° 60° 75° 105° 120° 150° 165° Temp.
December 17. . .. +1.05" +1.77" +3.31" +5.78” +7.27" +6.90" +7.54" +7.91" 40.3°
18.... 1.15 1.50 3.88 ' 6.28 7.64 7.40 7.41 8.54 38.5
19.... 1.42 2.20 3.34 6.52 6.84 7.03 7.41 7.58 31.0
19.... 1.85 2.14 3.72 6.5 6.84 7.60 7.54 8.06 30.3










Mean . . . . . . .. +1.37"‘ +1.90" +3.56" +6.27" +7.15” +7.23" +7.47" +8.0"

HALL, ABERRATION CONSTANT.
45









































195° 210° 240° 255° 285° 300° 330° 345° Temp.
December 17.... +6.76" +6.65" +4.79" +4.12" +2.18" +0.26" +0.17" —1.08" 403°
18.... 6.86 6.78 4.49 3.75 1.65 0.06 -0.43 1.68 38.5
19.... 6.56 6.68 4.26 3.95 1.65 0.56 +0.63 1.75 31.0
19.... 6.49 6.28 4.42 3.72 1.91 0.33 +0.83 1.31 30.3
Mean ...... .. +6.67" +6.60" +4.49" +3.88" +1.85" +0.30" +0.30" _1.45"
MICROSCOPES 75° APART.
15° 30° 60° 75° 105° 120° 150° 165° Temp.
December 12.... +0.02" +1.45" +3.93" +6.28" 6.97" +6.17" +7.07" +8.31" 332°
14.... 0.56 1.48 4.27 6.58 7.04 6.24 7.47 7.68 44.0
15.... 0.72 1.35 4.10 6.05 6.67 5.74 7.60 8.18 47.7
January 7 ..... .. 0.91 1.38 4.27 5.95 7.04 5.80 7.40 7.81 32.4
Mean ...... .. +0.56” +1.41" +4.14" +6.21" +6.93" +5.99" +7.38" +7.99"
195° 210° 240° 255° 285° 300° 330° 345° Temp.
December 12.... +6.69" +7.37" +4.47" +4.09" +1.58" -0.41" _1.33" - 2.08" 332°
14.... 6.92 7.20 4.60 4.19 1.65 -0.25 1.23 2.02 44.0
15.... 6.82 7.67 4.90 4.65 1.78 _0.01 0.19 1.85 47.7
January 7 ..... .. 6.56 7.27 5.07 4.52 2.08 +0.75 0.46 1.42 32.4
Mean ...... .. +6.75" +7.38" +4.76" +4.36" +1.77" +0.02" —0.80" -1.84"
CIRCLE 180° FROM ITS FIRST POSITIONS.
15° 30° 60° 75° 105° 120° 150° 165° Temp.
December 17.... +1.59" +0.65" +3.67" +5.65" +6.27" +6.47" +7.70" +7.88" 40.8°
18.... 1.69 1.28 3.83 5.38 7.04 5.87 7.47 8.11 38.3
19.... 1.76 0.95 4.50 5.12 6.57 5.94 7.63 7.88 29.9
19.... 1.52 0.68 4.30 5.45 6.34 6.17 7.70 8.05 30.3
Mean ...... .. +1.64" +0.89" +4.07" +5.40" +6.55" +6.11" +7.62" +7.98"
195° 210° 240° 255° 285° 300° 330° 345° Temp
December 17.... +6.49" +6.44" +3.50" +4:~ " +1.61" +1.32" +0.37" _1.02" 40.8°
. 18.... 6.29 6.37 3.77 4.52 2.08 1.72 0.54 1.08 38.3
19.... 5.92 6.54 3.90 4.12 1.71 1.75 0.54 0.55 29.9
19.... 6.19 6.34 3.83 4.12 1.61 1.59 0.34 0.65 30.3
Mean ...... .. +6.22" +6.42" +3.75" +4.26" +1.75" +1.59" +0.45" —0.82"










,_E-_~__.-_'-
46 MICHIGAN ACADEMY OF SCIENCE.
Taking the mean of the results obtained in the two opposite positions
of the circle, we find the following errors :—










15° 30° 60° 75° 105° 120° 150° 165°
Microscopes 105° apart. +0.89" +1 .44" +3.37" +6.02" +6.83" +6.79" +7.43" +8.15"
Microscopes 75° apart... 1.10 1.15 4.10 5.80 6.74 6.10 7.50 7.99
Mean . . . . . . . . . . . . . . . .. +1.00" +1.30" +3.73" +5.91” +6.78" +6.45" +7.46” +8.07"
195° 210° 240° 255° 285° 300° 330° 345°
Microscopes 105° apart... +6.95” +6.72" +4.66” +4.16" +1.48" +0.35" +0.08" --1.29"
Microscopes 75° apart... 5.49 6.90 4.26 4.31 1.76 0.81 —0. 18 1.33
Mean . . . . . . . . . . . . . . . .. +6.77" +6.81" +4.46" +4.23" +1.62" +0.58" —0.05" —1.31"









I
The errors of the lines separated by 5° were determined similarly to
those for intervals of 15°, by placing the microscopes on four diiferent
days at distances of 85°, 95°, 100° and 110° apart; and thus arcs of 255°,
285°, 300° and 330° were each divided into three equal parts. The obser-
vations commenced successively with the lines 0°, 15°, 30°, etc, and the
corrections for the first and last lines of the arc were applied according
to the values given above. Thus the error ofleach line was found on dif-
ferent days by comparison with two different lines, so that the small un-
certainty remaining in the errors of the lines 15°, 30°, 45°, 60°, 75°, etc.,
will have very little influence on the determination of the errors of the
lines 5°, 10°, 20°, 25°, 35°, 40°, 50°, 55°, etc. These observations were
likewise repeated on four days, with the circle at each time in a position
180° distant from the corresponding position in the former series.
The following table shows the result of all these observations :—



5° 10° 20° 25° 35° 40° 50° 55°
December 21 .......... .. +0.96” —0.38" +0.42" +1.96" +2.7 " +1.77" +2.60" +4.06"
23 .......... .. 1.23 -0.45 0.52 1.14 3.18 1.02 3.25 3.85
26 .......... .. 2.10 +0.05 0.35 1:69 2.69 1.67 3.22 3.97
29 .......... .. 1.51 -0.66 0.47 1.56 2.59 1.84 3.21 3.82
22 .......... .. 1.67 0.35 1.07 1.76 3.26 2.11 3.19 5.05
25 .......... .. 1.68 0.29 0.32 2.26 3.83 1.90 3.57 4.75
28 .......... .. 1.88 0. 1.18 1.18 2.50 1.98 3.12 4.20
30 .......... .. 1.03 0.13 1.02 2.50 3.28 2.55 3.46 4.77
Mean ............... .. +1.51" -0 31" +0.67" +1.76" +3.00" +1.86" +3.20" +4.31"









HALL, ABERRATION CONSTANT. 47



















65° 70° 80° 85° 95° 100° 110° 115°
December 21 .......... .. +4.51" +3.57" +4.59" +6.28 ' +6.84" +4.61" +5.63" +6.51'
23 .......... .. 4.85 3.75 5.05 5.91 6.67 5.17 4.91 6.81
26 .......... .. 4.95 4.40 5.23 6.70 6.03 4.96 5.18 6.38
29 .......... .. 4.40 4.33 5.09 6.47 6.62 4.73 5.07 6.41
22 .......... .. 5.90 4.53 5.22 6.46 6.72 5.60 6.33 6.86
25 .......... .. 6.04 4.90 4.68 6.65 6.92 5.00 6.00 6.13
28 .......... .. 4.85 5.07 5.75 6.64 6.81 5.68 6.40 7.19
30 .......... .. 5.36 5.20 5.15 6.39 6.93 6.31 6.26 6.36
Mean ............... .. +5.11" +4.47' +5.10" +6.44" +6.69" +5.26" +5.72" +6.58"
125° 130° 140° 145° 155° 160° 170° 175°
December 21 .......... .. +6.37" +7.76" +7.26' +6.48" +8.75" +7.87" +8.04" +8.30"
. 23 .......... .. 6.11 7.43 7.35 6.66 8.70 7.72 7.42 8.70
26 .......... .. 6.70 6.51 6.37 7.06 9.31 7.66 8.25 8.89
29 .......... .. 7.01 6.58 7.10 6.37 8.43 7.92 7.72 9.07
22 .......... .. 6.35 7.63 6.73 7.06 8.08 8.10 6.78 8.40
2.- .......... .. 6.72 6 98 7.38 6.21 8.50 7.02 7.89 8.27
28 .......... .. 7.60 7.47 7.40 7.34 8.73 7.63 7.26 8.61
30..., ...... .. 7.64 7.04 7.87 7.41 8.82 7.92 8.18 8.21
4 Mean ...... ..4 ...... .. +6.81" +7.18" +7.18" +6.82" +8.66" 7.73" +7.69" +8.56"
185° 190° 200° 205° 215° 220° 230° 235°
~ +7.97" +8 28" +7.82" ' +7.25" +7.82" +6.05" +6.41' ' +7.25"
, 7.43 8 82 7.61 7.47 8.21 6.33 6.29 7.39
8.13 8.20 6.78 6.38 7.72 6.37 6.32 7.19
8.04 8 31 7.15 7.27 7.31 6.31 6.17 7.47
7.35 7.42 6.46 6.90 6.60 5.21 5.47 6.60
7.31 6.83 6.42 6.68 7.67 5.92 5.09 6.47
7.49 7.79 6.69 6.92 6.31 6.19 5.22 6.60
7.61 8.11 7.49 6.39 _ 6.99 5.61 5.55 6.29
+7.67” +7.97" +7.05" +6.91" +7.33" +6.00' +5.81" +6.91"
245° 250° 260° 265° 275° 280° 290° 295°
December 21 .......... .. +5.54" +3.97" +3.20" +2.67" +1.26" +2.69" +1.66" +2.16"
23 .......... .. 5.64 3.82 3.45 2.90 2.03 1.80 1.88 1.97
26 .......... .. 5.09 3.03 3.56 2.95 1.33 2.08 1.09 1.64
29 .......... .. 4.48 3.86 3.31 2.44 1.64 1.58 1 55 2.03
22 .......... .. 5.11 3.59 2.79 1.13 1.02 2.30 1.02 1.32
25 .......... .. 4.13 3.05 3.04 1.92 0.46 1.91 1.47 1 36
28 .......... .. 4.41 2 86 2.68 2.29 0.63 1.37 1.04 1.37
30 .......... .. 4.98 2.93 2.67 ' 1.20 1.09 1.70 1.14 1.49
Mean ....... ..... .. +4.93" +3.39" +3.09" +2.19" +1.18" +1.93" +1.36" +1.67"









48
MICHIGAN ACADEMY OF SCIENCE.



305° 310° 320° 325° 335° 340° 350° - 355°
December 21..~ ........ .. +0.89" . -0.35" -0.13" _1.24" -0.07" +0 55" —1.67”
1.02 +0.42 +0.03 -0.44 - 0.42 -0.48 +0.41 —1.98
28 .......... .. 0.87 -0.19 -0.39 -0.13 +0.03 -0.01 +0.61 —1.16
29 .......... .. 1.87 -0.04 - 0.43 —0.48 +0.19 -0.13 +0.58 _1.42
22 .......... .. 1.01 - 0.48 0.19 —0.95 _1.38 -0.80 —0.01 -1.29
25 .......... .. 0.45 +0.42 _0.93 +0.31 —1.28 -0.13 —0.13 —1.66
28 .......... .. 0.37 -0.39 _0.53 -1.32 -1.10 —1.07 _0.39 _2.52
30 .......... .. 0.58 -0.44 -1.09 -0.21 —1.10 —0.96 —0.54 —1.62
Mean ............... .. +0.83" -0.04" -4>.44" -0.42" —0,78" -0.49" -0.13" —1.66"









To show more distinctly how these observations compare with each
other,- I have taken the mean of the two observations made in the two
opposite positions of the circle. These mean errors ought to be the same,
if the observations were correct, and if the temperature had no influence
on theni. These means are given in the following table :—
















5° 10° 20° 25° 35° 40° 50° 55°
+1.31" -0.38" +0.7 " +1.86" +2.98" +1.94" +2.89" 4.55"
1.48 0.37 0.42 1.70 3.51 1.48 3.41 4.30
1.99 0.13 0.78 1.43 2.59 1.82 3.17 4.08
. 1.27 0.39 0.74 2.03 2.94 2.20 3.34 4.30
Mean ............... .. +1.51" -0.31" +0.67” +1.7 " +3.00" +1.86” +3.20" +4.31"
85° 70° 80° i 85° 95° 100° 110° 115°
+5.20" +4.05" +4.90" +8.37" +6.78” +5.10" +5.98" +6.68"
5.45 4.32 4.87 8.28 8.79 5 09 5 48 8.47
4.90 4.73 5.49 8.87 8.42 5.32 5.79 6.78
4.88 4.77 5.12 8.43 8.77 5.52 5.87 _ 0.39
Mean .............. .. +5.11" +4.47' +5.10" +8.44" +8.89" +5.28" +5.72" +6.58"
125° 130° 140° 145° 155° 160° 170° 175°
+6.36" +7.69” +7.00" +6.77" +8.41" +7.98" +7.40" +8.35"
8.41 , 7.21 7.38 8.44 8.80 7.37 7.88 8.48
7 15 8.99 8.88 7.20 9.02 7.85 7.75 8.75
7.32 8.81 7.48 8.89 8.83 7.92 7.95 8.84
Mean ....... .._ ...... .. +8.81" +7.18" +7.18 +8.82 +8.66" +7.73" +7.89" +8.58"









HALL, ABERRATION CONSTANT. - 49












185° 190° 200° 205° 215° ~ - 220° 230° 235°
+7.88" +7.85" +7.14" +7.07" +7.21" +5.63" +5.94" +6.92"
7.39 7.82 7.02 7.08 7.94 8.13 5.89 8.93.
7.81 7.99 8.78 8.85 7.03 8.28 5.77 8.89
7.84 8.21 7.32 8.83 7.15 5.98 ~ 5.88 8.88
Mean .......... .. +7.8" +7.97" +7.05" +8.91" +7.33" +6.00" +5.81" +6.91"
245° 250° 280° 265° 275° 280° 290° 295°
+5.32" +3.78" +3.00" +1.90" +1.14" +2.49" +1.34" +1.74"
4.89 3.43 3.24 2.41 1.25 1.88 1.88 1.66
4.78 2.93 3.12 2.82 0 98 1.72 1.05 1.50
4.73 3.40 2.99 1.82 1.38 1.84 1 35 1.76
Mean ............... .. +4.93" +3.39" +3.09" +2.19" +1.18" +1.93" +1.38" +1.67"
305° 310° 320° 325° { 335° 340° 350° ' 355°
+0.95" .05" —0.08" -0.54"' -1.30" _0.43" +0.27" —1.48"
0.73 +0.42 0.45 0.08 | 0.85 0.29 0.14 1.82
0.52 -0 29 I 0.48 0.72 0.54 0.54 0.11 1.84
1.11 -0 24 0.78 0.35 ' 0.45 0.70 0.01 1.52
Mean ............... .. +0.83" -0.04" _0.44" +0.42"! —0.78" -0.49" +0.13" —1.66"








lows :—

0° . . . . . . .. 0.00" 75° . . . . .. +5.91" 150° . . . . .. +7.46" 2 5°..... +7.65" 300°..... +0.58”
5 . . . . . . .. +1.51 80 . . . . .. 5.10 5 . . . . .. 8.66 30 5.81 305 +0.83
10 . . . . . . .. —0.31 85 . . . . .. 6.44 160 . . . . .. =- 7.73 235 6.91 310 —0.
l5 . . . . . . .. +1.00 90 . . . . .. 5.46 165 . . . . .. 8.07 0 4.46 5 —0.48
20 . . . . . . .. +0.67 95 . . . . .. 6.69 I 170 . . . . .. 7.69 245 4.93 320 —0,43
2- . . . . . . .. +1.46 100 . . . . .. 5.26 175 . . . . .. 8.56 250 3.39 320 ~—0.42
30 . . . . . . .. +1.30 105 . . . . .. 6.78 180 . . . . .. 7.50 255 4.23 330 —0.05
. . . . . . .. +3.00 110 5.72 185 7.67 260 3.09 335 —0 78
. . . . . . .. +1.86 115 6.58 190 7.97 265 2.19 340 —0.49
45 . . . . . . .. +3.36 120 . . . . .. 6.45 195 . . . . .. 6.77 270 2.20 345 —1.31
50 . . . . . . .. +3.20 125 . . . . .. 6.81 200 . . . . .. 7.05 275 1.18 350 +013
55 . . . . . . .. 4.31 130 . . . . .. 7.18 205 . . . . .. 6.91 280 1.93 355 —166
60 . . . . . . .._ +3.73 13") . . . . .. 7.15 210 . . . . .. 6.81 285 . 1.62
65 . . . . . . .. 5.11 140 . . . . .. 7.18 v215 . . . . .. 7.33 290 1.36
70 . . . . . . .. +4.47 145 . . . . .. 6.82 220 . . . . .. 6.00 295 1.67











The errors thus found are not merely those'of the divisions, but include
also the errors owing to the eccentricity of the circle and to the deviation
of-the pivots from a cylindrical form. The eccentricity produces terms of '
the form ' '
. a+bcosx+csinx;_ ‘ -. -
and from the 72 errors given above, I find the error of the eccentricity,
+ 4.”044 — 3.”835 cos x + 1.”561 sin x, :' 1 -
or + 4."044 — 4.141 cos (xi+ 22° 9’) .
I
50 MICHIGAN ACADEMY OF SCIENCE.
If the error of the eccentricity of the circle be calculated for every fifth
degree, and subtracted from the corresponding error in the table, the
errors of the division will be as follows :— '

0° . . . . . . .. —0.21" 75° . . . . .. +1.35" 150° . . . . .. .69' 225° +2.00" 300°..... —0.19"
5 . . . . . . .. +1.15 80 . . . . .. +0.19 155 . . . . .. +0.48 230 +0.50 305 +0.26
‘10 . . . . . . .. —0.85 85 . . . . .. +1.18 160 . . . . .. —0.45 235 +1.95 310 —0.42
‘15 . . . . . . .. +0.26 . . . . .. -—0. 165 . . . . .. -0.08 240 —0.15 315 —0.71
20 . . . . . . .. —0.30 95 . . . . .. +0.76 170 . . . . .. —0.40 2471 +0.68 320 —0.53
‘25 . . . . . . .. +0.53 100 . . . . .. . 175 . . . . .. +0.56 250 —0.50 325 —0.42
30 . . . . . . .. —0.20 105 . . . . .. +024 180 . . . . .. '—0.38 255 +0.70 330 +0.01
35 . . . . . . .. +1.20 110 . . . . .. —1.10 185 . . . . .. —0.06 260 —-0.08 335 —0.69
40 . . . . . . .. —0.L 115 . . . . .. —0.50 190 . . . . .. +0.42 265 —0.63 340 —0.40
45 . . . . . . .. +0.92 120 . . . . .. -0.86 195 . . . . .. -- 0 57 270 . . . . .‘ —0.28 345 —1_.25
5O . . . . . . .. +0.42 125 . . . . .. -—-0.71 200 . . . . .. —0.06 275 —0.97 350 +0.13
55 . 1 +1.19 130 . . . . .. ——0.52 20.5 +0.05 280 +0.09 355 —1.76
60 . . . . . . .. +0.25 135 . . . . .. - 0.71 210 . . . . .. +0.21 285 +0.08
-65 . . . . . . .. +1.27 140 . . . . .. —0.80 7515 +1.04 290 +0 09
170 . . . . . . .. +0.27 115 . . . . .. -—1.26 220 . . . . .. +0.02. 295 +0 66











It is evident that these errors have two regular periods; one depending
'on the double angle, the other having itself a period of ten degrees. From
the 72 errors, I find the following expreSsion for these periodical errors
of the division :— '
'—0.603 cos (2x+74° 20’)—0.”23 cos 36X.
The first term shows that the circle has a small ellipticity; the latter
very probably arises from the manner in which the division was made.
The introduction of these two terms brings the sum of the squares of the
errors from 39.7 doWn to 22.9.
If we subtract these periodical errors from the errors of the preceding
table, we find at last that the errors of the lines with intervals of five
degress, considered as merely accidental, become as shown in the following
table :— - I -














_The probable error of any line is equal to j; 0."38; and therefore the
probable error‘of the mean of four lines which are used in reading the
microscopes, is i 0."19.
With regard tot'he numbering of the degrees as given by Dr. Briinnow,
he refers, I think, to zenith distances when the circle is in a particular
position on theaxis. ' 8% Publications of the Dunsink Observatory, Part
IV, page 12, where the division marks whose errors have been determined
by Dr. Briinnoware taken in this way. See, also, the Abhandlungen of
(“n-4.. . . _ _
q “M 4......»
HALL, ABERRATION CONSTANT. 51
Bessel, edited by Engelmann, Band II, s. 76. I made an examination of
the errors of several of the five degree marks, taken according to my
notation, and found results so difierent from those of Dr. Briinnow that
I think they can only be explained as above. -
Discussions of the Pistor and Martins circles can be found also in the
Annals of the Leiden Observatory, the volumes of the Naval Observatory,
Washington, and in articles by Professor Boss, in Gould’s Astronomical
Journal. As I understand it, the divisions of these circles were probably
made by means of successive applications of difierent standards. Thus
the 100 marks were first cut. Then these intervals were bisected. Then
the singles degrees, were cut by starting from the 5° marks, and applying
successively a standard degree, and so on. Thus, there would be a cumu-
lative error arising from the error of the standard, to be combined with
the probable error of the placing of the standard in position. It would
hardly answer, therefore, in the case of these circles, to determine the
division errors of the 5° lines, and then interpolate between them. For
ordinary work the safest way might be to turn the circle frequently on
the axis, and not apply any division errors at all. Both circles go on
tapering axes, and are pushed up by collars held by screws, so that the
circles can be revolved into any position.
Counting the circle divisions in the manner I have adopted, the follow-
ing lines have been used for Polaris and the nadir in the observations pub-
lished in this paper, the readings being those given under microscope I
when the clamp iseast.
For the Nadir 71° 32'—34'.
For Polaris . \
Above pole . . . . . . . . . . . . .. 205° 04’—06’ Below pole . . . . . . . . . 202° 36'—38’
Reflected . . . . . . . . . . . . . . .. 118 00 —02 Reflected . . . . . . . . . . . . . . .. 122 28 —30
Since the divisions used for the Polaris observations were not changed
during this series, the errors would not enter into the computation of the
aberration constant. But for the purpose of examining the latitude as
found from these observations a determination was made of the special
marks according to the method described by Bessel in the Abhandlungen.
The mean of the divisions 0°, 90°, 180°, 270° is supposed to have no error.
The errors as determined are the means of the errors of the c.our marks
pointed on with the microscopes.
205° 04' 202°

Position 1. Position 2. , Position 1 Position 2.
+0.17" —1.14" —0.81" +0.32"
+0.32 —1.20 —0.96 +0.44
-0.10 —_ __ ~—
+0.59 —1._17 -0.88 +0.38
+0.24 .
—0.46" —0.25”
118° 00' 120° 28’
Position 1. Position 2. Position 1. Position 2.
+0.54" -0.39" —0.38" . +0.60"
+0.30 wt V2 ~0.41 +0.16 +0.64
+0 58 — —;— ——-—
_ —0.40 -0.11 +0.62 ,
+0.51
+0.06" +026"
' 71 32' -
Position 1. Position 2.
+0.20” +0.40"
+0.03. - +0.31
+0.03 —0 39
+0.09 +0 11
+0.10”
52 _ MICHIGAN ACADEMY OF SCIENCE.
In position 2 the microscopes are changed 180° from the first position.
Evidently the effect of gravity on the circle is considerable. The division
errors are to be added to the actual readings to produce the idea].
As to the marks 205° 06’, 202° 38', etc., the errors were found by com-
paring the spaces 205° 04’-06”, etc., with the mean of a good many 2’
spaces on the circle, this mean being regarded as the true value of a 2'
space. For the required 2’ spaces we have then the following values, it
being understood that 71° 32’-34’ for instance, refers to the mean of the
four spaces 71° 32’-34’, 161° 32'-34’, 251° 32’-34’, 341° 32’-34’.
Space 71° 32'-34’. '
Reduction to Space 118° 00'-02'. . Space 120° 28'-30’.
mean 2’ space. Reduction. Reduction.
—0.47" +0.01" +0.37"
—0.50 ' _ +0.16 +0.24
+0.01 —0.18 +0.49
—0.27 —0.24 +0.60
—0.07 - +0.08 +0.15
—0 33 \—-— ——
—0.03 —-0.03 +0.37
-—0.45
—0.51
—0.37
Mean.... —0.30

Space 205° 0406'. Space 202° 36’-38’.
Reduction. Reduction.
+0.26" +0.28"
+0.18 _ +0.24
+0.14 —0.06
-—0.03 —O
—0.20 —0 10
+0.07 —0 05
Finally, for the errors of the divisions employed in this work
Division. Error. Division. Error.
205.6 04' —0.46' , 202° 36’ —0.25"
205 06 —0.53 202 38 —0.20
Mean . . . . . . .. —0.50 ——0.22
Division. Error. Division. Error.
118° 00' +0.06" 120° 28' +0.26"
118 02 - +0.09 120 30 11
+0.08 +0.08
Division. Error.
71° 32' - +0.10"
71 34 +0.40
+0.25
9.—Eocentr7lcity of Fine Circle.
The eccentricity of the fine circle was determined by pointing on the,
10° lines, first with microscopes I and III, and then with II and IV, the
instrument being clamp east. The readings were made so as to eliminate
progressive changes proportional to the time. Thus are obtained the fol-
lowing values- for Q and 5%, 9 being the direction of the line joining
thecenter of the circle to the center of revolution, 8 the distance between
the centers, and 7‘ the radius of the circle:
HALL, ABEBRATION CONSTANT.
53
I
Microscopes III and I.
e_”
r = 4.41"
4.03
o =1so=> 07'
179 37
The above values give for the means
el!
= 4.04"
Microscopes IV and II.
c"
l'
O = 179° 35’.
= 4.13" O = 182° 04'
3.61
176 32
In order to reduce an actual reading on the circle, A", to a reading A,
counted at the center of the circle, we have
A = A'— % sin (A'—
10.—The M icrosoopes.
0).
These are supported on arms which are clamped to the brass discs de-
scribed in article 3. This arrangement seemed to me at first not a good
one, but in fact the arms do not move much, and the nadir determinations
agree as well as those made with other instruments. This plan of mount-
ing the microscopes I have heard criticised, however, by a number of ex-
perienced observers.
To the brass discs which hold the microscope arms I had brackets
attached, and these brackets carry fine screws which butt against the
arms, making it possible to adjust them easily. '
Illumination is obtained by means of little electric lamps attached to
the ends of the microscopes, the light coming in at right angles to the
line of sight, and being reflected against the circle by a plaster of Paris
surface. The lamps are somewhat near the circle, but as they are lighted
only for an instant I think there is no danger of heating it. The light is
furnished from chloride-accumulator cells which are charged from the
University lighting plant. The microscopes are of low magnifying power,
about 16. The power should be considerably greater.
The periodic errors of the screws were found as described by Professor
Newcomb in the Washington Observations for 1865, by measuring the
interval between the parallel wires of each microscope, bringing each
Wire near a circle division and separating it from this division by a dis-
tance equal to its oWn thickness. In this way the periodic errors for the
respective microscopes were found to be
/ - II ~0.186 cos u +0.23l
cos u +0.057
' cos u +0.075
cos u +0..033"
sin u
sin u
sin u
sin n
For clamp east I is lower microscope on north side, II is upper on north
side, III upper on south side, and IV lower on south side.
For clamp west I is lower on south side, II upper on south side, III
upper on north side, and IV lower on north side.
The microscopes
were taken in this way for my own convenience in recording.
On September 19, 1899, I happened to loosen the div
‘scope IV, and turned it on the shank.
The periodic error was then found to be
IV +0.057" cos u 2{—0.039" sin u
On May 10, 1900, the spider lines of two of the microscopes became
loose, owing to the use of too much oil on the screws, the oil working on to
ided head of micro-
54 MICHIGAN ACADEMY or SCIENCE. ,
the slides and touching the threads. New lines were inserted and the
screws were mounted in a small lathe and cleaned. Though I requested
that the positions of the divided heads on the shanks be carefully marked
this was not done, and large periodic errors were found after the return
of the microscopes. I think that when the instrument was made the
‘ microscope heads were placed on the shanks and divided so as to elimi-
nate the periodic errors of'the screws. Therefore I made a number of
attempts to_ find the proper positions of the heads, but was not able to,
do it in the time at my disposal.
For the period, then, 1900, May 10 to June 6 we have the following
values of the periodic errors, these being determined by measuring the
distance between a division and a well defined speck of dirt found on the
circle, rather a better method, I think than the one spoken of above:
I —0.576" cos u —0.288" sin 11
II —0.28O cos u —O.738 sin 11
III —0.147 cos 11 ——0.047 sin 11
[V +0026 cos u +0.04O sin 11
After 1900, June 6, we have for microscopes I, II and IV
1 +0036" cos u —0.502" sin u
I —0.052 cos u +0.014 sin 11
IV +0.014 cosu +0.107 sin u
In the case of III we have after June 6, 1900, and before July 14, 1900
111 +0532" cos u +0352" sin u
- After 1900, July 14
III +0.176” cos u +0.758" sin u.
_ In the summer of 1901 I made another determination of the periodic
errors which agreed with the final values as given above.
It would be better to arrange to eliminate periodic errors, perhaps by
using two pairs of threads, 1.5 revolutions apart.
The progressive errors of the microscope screws are negligible through-
out the interval in- Which they were employed.
It requires about one day to reverse this meridian circle and readjust
the microscopes.
11.—The Oollimating Telescopes.
These are small, having as approximate dimensions: diameter of object
glasses 2.094 inches, focal length 2 feet, power of eye-pieces 38, distance
between wyes 11.2 inches. The three screws which support each telescope-
stand are at the vertices of an equilateral triangle a side of which is 9.1
inches. Each stand is adjustable in level and azimuth. ,'
A number of attempts were made to obtain the flexure of the meridian
circle by means of the collimators, but I was never able to level them
with a delicate level, and finally gave it up. '
12.—Flemure.
The fiexure coefficients were determined from observations of known
stars, it being assumed that the effect can be expressed in the'form
a; sin 2 + bl cos zil— 32 sin 22 + b2 cos 22, etc.
Then“ calling Z the true zenith distance we have for direct and reflected
observations, N being the nadir reading of the circle, '
:HsmL, ABERRATION CONSTANT. 55
Z: zl + a1sinz+b1dosz+a2sin2z+b2cos2z
— (180° + N) + 111 — b2 (1)
180°—Z = 22+ a1 sinz—bl cosz—a2sin2z +b2 cos 2z
- (180°-|-N)’+b1—b2 - (2)
\ After the instrument is reversed the corresponding formulas are
360—Z: z3—a1sinz+b| cosz—agsin 2z+b2 cos2z
- (180° + N) +101 -—b2 (3)
180°+Z = 24—81 sinz—b, cosz+ a2 sin2z+b2 cosZz
- (180° + N) + b1 — b2 (4)
By combining formulas (1) and (3) the cosine coefficients can be ob-
tained. ‘ Accordingly stars were observed north and south of the zenith
in both positions of the instrument for this purpose. 3
From 22 south stars is obtained
- - b1: _1.43", b; = -0.47
and from 26 north stars
bl = -1.50", b2 = -0.49".
The termb2 seems really to exist, though it will require a good many
observations to determine it with accuracy, since the weights of observa-
tions made at large zenith distances are small.» The following table of
approximate weights has been computed with the zenith distance as
argument:


2 Weight. . 2 Weight.
0° . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 4.4 65° . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 2 7
10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 4.4 70 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 2 3
20 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 4.2 75 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 1 5
3O . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 4.0 80 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 0 9
40 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 3.7 81 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 0 8
45 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1. 3.3 82 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 0 7
60 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 2.9 '



' I
By measuring the distance on the circle between north and south stars
of about 60° zenith distance the coefficient a1 of the sine flexure was
obtained,
‘ a1 = +1.20".
Some attempts were made to find the flexure coefficients by treating
the north and south stars separately. But the cosine coefficients enter
with such large relative weights that the process is not accurate. It was
necessary to insert, also, a term to represent any correction of the lati-
tude, and this has a large relative weight. The latitude was assumed to
be +48° 16’ 49.3”. \
Taking then the north and south stars separately, these values were
obtained: A _


31 b1 A 4’
Clamp West— '
North stars ........................................................ .. 1.72" —2.30" +0.40
South stars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .~ . . . . . . . . . . . .. 1.00 —l .50 —-0.36
Clamp East— I '
North stars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. .72 s —1.00 +0.03_
South stars ....................................................... .. 2.59 —1.66 —0,53




A-4—R
56 MICHIGAN ACADEMY OF SCIENCE.
Combining all the stars used for flexure we find:


a-1 I b1 . A¢
Clamp West . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. +1 00" -—2.10" 0.51"
Clamp East . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. +1.37 —1.12 —0.38




The flexure as found represents the combined effect 9n the circle and
'telescope, which as yet has not been separated into the two parts. Such
a term as 01 in the flexure of the telescope proper would be caused, I
suppose, by the axis of symmetry of the telescope not coinciding with
the neutral axis. ,
As has been stated the value of i was assumed +48° 16' 49:3”, and _A4>
is the correction to be added to this. In order to check the value of Ag
I have assumed the values a1 = + 1.20”, bl = —1.46", and have used only
stars near the zenith for computing this" quantity, with the following
results: , -
Clamp East—South stars A ¢ = - 0 53"
N 0 5
orth stars — l8
,Clamp West—South stars — —0.31
North stars —0.66
Mean . . . . . . .. —0.58
\
For the present, the latitude can be assumed
+42° 16' 48.8".
Situated as we are, an elaborate determination of the division errors
cannot be made, so that it will be necessary to secure more values of the
latitude, turning the circle on its axis, and observing direct and reflected,
and clamp east and west. From my experience with large, heavy instru-
ments I do not believe much in the application of such corrections as those
of flexure and division error, but think that observations should be ar-
ranged as far as possible so 'as to eliminate all such quantities.
The flexure seems to be rather constant. _ Before beginning observations
of Polaris, I had the foreman of the University engineering shops ex-
amine the screws which hold the telescope cones to the cube. It was his
opinion that I had driven them up too tight, and, therefore, they were
loosened a trifle. \
13.——Meteor0 logical Instruments.
The standard barometer was examined at Ann Arbor by Professor
Marvin of the \Veather Bureau Office in the summer of 1892. It was
found‘to be badly out of order, and in trying to make repairs the glass
tube was broken. The instrument was then taken to the Weather Bureau
Ofiice in Washington, and a new tube was filled and inserted. Also, a
new attached thermometer was put on, since the old one was found 1°.
in error. .
Our thermometers,_also, have been examined by the Weather Bureau,
and I have to thank the oflicials in IVashington and Lansing for the con-
siderable attention which they have paid to our meteorological instru-
ments.
HALL, AB ERRATION CON STANT.‘ 5 7
For refractions Bessel’s tables were used as prepared by Professor J.
R. Eastman for the Naval Observatory. The thermometer was hung near
the object glass of the telescope. For daytime observations of Polaris
as much as possible of the open slit was covered with canvas, and a large
piece of canvas was pulled up over most of the roof, which is tin, the
canvas being spread some time before observing. However, with any
such observing room as ours there must be some uncertainty regarding the
refraction, but I did not feel like attempting any reduction for the con-
dition of the room. I was careful to air it for several hours before
working. \ ' '
14.—-The Nadir.
This was determined over a shallow basin of iron, the concave part,
which holds the mercury, being plated with copper. The basin was turned
180° in the middle of any series of observations. As stated, all zenith
distance settings were made with the tangent screw, there being no
micrometer for that cordinate. To observe the nadir it was necessary to
runv up two small rods connected with Hooke’s joints, and supported by
large rods held by the microscope arms of the coarse circle.
A complete determination of the nadir includes four settings, two
divisions on the circle being read after each setting. All nadir observa-
tions were made facing north. For observations of Polaris the nadir was
taken immediately before and immediately after the zenith distance point-
ings. If it is assumed that the diflerence between the nadir at the begin-
ning and that at the end of a series is due only to accidental errOrs, we
have for the probable error of a complete nadir determination, four
pointings, ‘ ' ‘
' - i 0.28”,
and for the meanrof two determinations, I
' i 0.20". '
The above results for the probable error of a nadir determination are
a little larger than is the case with some instruments. The values 'as
given include the error from the circle readings. The microscopes are of
low power, about 16. ‘ _
The number of observations examined was 77. The mean of each night’s
nadir was regarded as the true value. Thus two residuals were formed 1
for each observation. Then for the 77* observations [v'v]=133100, the unit
being 0.01”. ,
A smaller probable error for a nadir determination would be found by
comparing among themselves the separate nadir pointings. In this way is
obtained ['vo]=284942, the unit being 0.01”. Then for the probable error
of a single nadir pointingincluding ,the reading of the circle is found the
value i 0.194”, the number of single pointings considered being 646. For
the mean of four settings, then, or a complete determination of one nadir,
is obtained 0.10”. These smaller yalues I think are fictitious.
1.61—Inclination of Horizontal Threads.
The pointings on Polaris were made symmetrically .on each side of the
meridian so as to eliminate the inclination of the horizontal threads.
These are about 5" apart, the object pointed on being placed midway
between them. ‘ . '
8
58 MICHIGAN ACADEMY OF SCIENCE.
I have examined the wire inclination during the periods 1898, May 23.4
to June 14.3 inclusive, and December 10.3 to December 27.8 inclusive,
taking account of the change of refraction during each day’s observation.
Calling the effect of the inclination of the horizontal threads cos 8 sin t. I,
where t is the hour angle and I the inclination, the values of I for the
two periods as determined from Polaris are:
Telescope clamp east, Polaris direct, East zenith distances too great,
or E. ends of threads too high. . ‘
'


1898. 1898.
May 23.4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. December 10.3 . . . . . . . . . . . . . . . . . . . . . . . . .. —90.5"
24.9 . . . . . . . . . . . . . . . . . . . . . . .. .. . .. 1" 8











16.—Probable Error of Single Pointing on Polaris.
If it is assumed that the value of I for the first period referred to in
article 15 is 58.4”, and for the second period 88.1”, it is possible to com-
pute the probable error of a single pointing for each date taken separate-
ly. The nadir used on each date is the mean of the observed nadirs, and
the reading of the circle is included with the pointing. '
Probable error of a single pointing 0n Polaris.




,.
‘9 Number Probable Number Probable
pom tings. p (3:122); g pomtm gs p (3:11;; g_
1898.
7 40.25" December 10.3 . . . . . . . . . . .. 7 40.40"
7 40.36 12 8 . . . . . . . . . . .. 7 40 45
7 40.48 13.3 . . . . . . . . . .. 7 40.43
7 40.2< I 13.8 .......... .. 7 40 29
7 40.33 , 15.3 .......... .. 7 40.08
7 40.41 1 15.8 . . . . . . . . . . .. 5 40.22
7 40 35 17.3 . . . . . . . . . . .. 7 40 27
1 18.3 .......... .. 7 40.33
7 40.25 21.3 . . . . . . . . . . .. 5 40.37
7 40 31 i 27.3 .......... .. 7 40.52
7 40.21 i 27.8 . . . . . . . . . . .. 7 40.35
7 40.42 I
7 40.35 '








The probable error of a single pointing is taken as 4 0.33”.
For the mean of 7 pointings the probable error is 4 0.13”. Compounding
this with :l: 0.20”, the probable error‘of the mean of two nadir determina—
HALL, ABERRATION CONSTANT. 59
tions, we obtain for the probable error of the corresponding zenith dis-
tance 4 0.24”. This quantity is to be combined with the probable error of
the refraction tables, which for Polaris may be taken as 4 0.3". So that
for one observation of 7 pointings the total probable error is 4 0.38".
In ordinary observations the uncertainty of the division marks should
be included as well as that of the flexure.
17.+Obsercati0ns of Polaris. ' ‘
At first the conditions imposed on the observations were too severe. I
attempted to obtain always successive culminations, and at each culmina-
tion both direct and reflected observations. On account of the weather
and duties of instruction it was necessary to give up the idea of observing
only successive culminations, and being for most of the time without a
recorder I could not make observations both direct and reflected without
working rather near to the edge of the field.
Since the direct observations above and below pole extend over about
the same periods of time, the latitude variation will be eliminated from
the determination of the aberration constant, as well as other disturb-
ances of a like nature, including changes in the flexure.
It is planned to take more of these observations and with some assist-
ance the necessary frequent reversals could be made, in order to determine
the latitude variation with accuracy.
The following are the observations of Polaris corrected for refraction
and reduced to the meridian. For each observation seven pointings were
usually taken, though sometimes five or nine. However, each observation
has been given the same weight. .
For reduction to the meridian has been used the expression
sin? l/g (T—m)
sin 2 8. .
sm 1"
(lIn this, 8 is the apparent declination as taken from the ephemeris, and
the single term is sufficient. -
All the declinations of Polaris have been taken from the Berliner
Jahrbuch. An account of the terms included in the computation of ap-
parent places is‘ given in the J ahrbuch for 1884. '
The reduction to 1900.0 is given in order that the observations may be
compared among themselves. '
The nadirs for any observations were interpolated when they differed
more than 0.3”. .
The images and steadiness are marked on the scale 1-5, 1 being perfect.
60
MICHIGAN ACADEMY OF SCIENCE.







OBSERVATIONS OF POLARIS. CLAMP EAST. NADIRS.



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HALL, ABERRATION CONSTANT. 61











OBSERVATIQNS OF POLARIS. CLAMP EAST. NADIRS.
. Sid. T. Sid. T.
Date. Nadirs. Nadirs.
- H. M. H. M. -
_ ' 1899.
May 8.9 .............................. .. 0 37 71° 32' 57.38" 2 05 71° 32' 57.63"
10.9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 0 32 71 _32 58.01 2 15 71 32 57.88
23.8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 0 25 71 32 58.42 2 10 71 32 58.66
24.8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 0 32 71 32 57.75 2 12 71 32 57.92
June 1.8... . . . 0 42 71 32 57.53 2 15 71 32 58.09
3.8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 0 40 71 32 58.0 2 10 71 32 57.80
4.8 . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 0 30 71 32 58. 2 21 71 32 59.14
29.7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 0 06 71 32 57.84 2 00 71 32 58.39
July 8.7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 0 16 71 32 57.02 2 20 71 58.3
10.7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 0 24 71 32 57.45 2 18 71 32 57.82
18.7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 0 17 .71 32 57.98 2 13 71 58.0
22.7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 0 15 71 33 1. 2 12 71 33 1.98
August 10.7 . . . . . . . . . . . . . . . . . . . . . .. . 0 29 71 32 57.94 2 18 71 32 58.36-
12.7... . . . . 0 20 71 32 56.60 2 15 71 32 58.00
_, 13.7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 0 23 71 32 54.87 2 16 71 32 56.42
September 1.6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 0 33 71 32 58.12 2 16 71 32 58.38
11.6 . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 0 21 71 32 57.77 2 18 71 32 57.87
13.5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 0 15 71 32 59.06 2 17 71 32 59.26
26.5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 0 31 71 32 55. 2 21 71 32 55.21
30.5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 0 40 71 32 55.42 2 14 71 32 55.64
October 2.5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 0 10 71 32 55.20 2 25 71 32 54.82
1898. .
April 26.4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 12 29 71° 33' 8.14" 14 71° 33’ 7.14"
27.4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 12 31 71 33 7.76 14 13 71 33 7.72
May 5.4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 12 25 71 33 7.32 14 12 71 33 7.36
7.4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 12 22 71 33 6.39 14 13 71 33 5.98
9.4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 12 20 71 33 6.62 14 10 71 33 5.80
23.4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 12 44 71 33 4.37 14 30 71 33 4.10
25.4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 12 23 71 33 4.50 14 07 71 33 4.21
30.3 . . . . . . . ._ . . . . . . . . . . . . . . . . . . . . . . .. 12 35 71 33 12.20 14 15 71 33 12. 02
June 1.3 . . . . . . . . . . . . . . .1 . . . . . . . . . . . . . . .. 12 40 71 33 6.38 14 05 71 33 6.28
. 12 27 71 33 6.66 14 13 71 33 5.98
12 31 71 33 4.35 14 10 71 33 4.92
12 27 71 33 2.44 14 14 71 33 2.34
12 26 71 33 2.10 14 10 71 33 2.17
12 28 71 33 2.44 14 16 71 33 2.81
12 12 71 3 5.53 14 15 71 3 5.44
12 24 71 3 6.13 14 10 71 3 6.33
12 20 71 3 5.48 14 12 71 3 5.36
12 28 71 3 6.20 14 13 71 3 5.85
12 38 71 3 5.80 14 12 71 3 5.57
12 7 71 13 6.04 _ 14 08 71 3 5.76
12 18 71 3 5.72 14 15 71 3 590
12 13 71 3 4.90 14 12 71 3 5.29
August 2.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 12 19 71. 3 4.63 14 14 71 3 4.63
4.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 12 10 71 3 4.18 14 25 71 3 4.06
10.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 12 06 71 3 8.00 .14 15 71 3 7.72
25.1. 12 09 71 13 1.76 14 20 71 3 1.50
26.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 12 16 71 3 0.62 14 14 71 3 0.86
27.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 12 26 71 3 0.62 14 00 71 3 0.67
September 25.0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 12 15 71 33 2.05 14 14 71 33 1.83
27. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 12 5 71 33 2.94 14 11 71 33 3.52
29.0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 12 20 71 33 6.32 14 19 71 33 6.78
October 9.0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 12 30 71 33 1 .63 14 12 71 33 1.90
' 14.9.. 12 31 71 33 1.82 14 18 71 33 1.42
24 9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 12 42 71 33 0.67 14 14 71 33 0.64
26.9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 10 71 32 59.90 14 18 71 33 0.04
November 2.9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 12 35 71 33 4.64 14 16 71 33 4.77
15.9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 12 23 71 33 3.72 14 20 71 33 4.58
24.8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 12 71 33 1.16 14 18 71 33 1.56





62
MICHIGAN ACADEMY OF SCIENCE.












5 OBSERVATIONS OF POLARIS. CLAMP EAST. NADIRS.
Sid. T. Sid. T.
Date. Nadirs. N adirs.
"H. M. H. M.
December 12.8......... 12 22 '71988' 7.12" 14 10 71°33’ 6.87"-
18.8........ 12 27 7133 6:38 14 22 7188 6.28
12 19 7188 7.79 14 29 7188 8.19
24 71 88 0.17 14 18 71 88 0.20
January 25 71 32 54.62 14 17 71 32 54.81
16 71 33 0.84 14 15 71 82 59.52
45 71 82 59 79 14 00 71 0.02
26 71 82 55.67 14 25 71 82 55.88
20 71 32 55.92 14 82 '71 82 56.20
February 85 71 82 58.46 14 37 71 32 58.55
27 71 82 55.43 14 38 71 32 58.90
39 71 32 56.01 14 22 71 82 56.70
30 71 32 59.16 14 11 71 82 59.72
March 22 71 32 55.08 14 05 71 82 55.64
April 85 71 33 0.46 14 00 71 33 0.69
17 7182 59.85 14 14 71 82 58.48
00 71 82 58.55 14 02 71 32 58.64
16 71 82 57.47 14 11 71 32 56.28
88 71 82 57.21 14 18 71 82 57.80
25 71 82 57.94 14 15 71 32 57.85
May 12 71 82 55.90 14 00 71 82 54.76
22 71 32 56.17 14 07 71 82 55.88
20 71 82 56.78 14 09 71 32 55.98
48 71 82 58.92 14 03 71 82 57.42
24 71 82 57.51 14 21 71 32 56.87
June 26 71 82 57.78 14 06 71 32 56.86
July 18 71 32 51.16 14 15 71 32 57.50
31 71 82 58.25 14 _15 71 82 57.70
40 71.32 58.82 14 09 71 82 57.95
15 71 82 58.65 13 12 71 82 58.84
August; 17 71 82 58.04 14 06 71 32 57.54
16 71 82 57.22 14 02 71 82 57.84
17 71 82 57.22 14 13 71 82 56.52
September 27 71 32 58.12. 14 12 71 32 57.54
24 71 82 57.17 14 14 71 82 57.28
.19 71 82 56.58 14 11- 71 82 56.70
01 71 32 56.66 14 15 71 82 56.86
02 - 71 32 57.24 14 00 71 32 57.26
00 71 82 57.98 14 11 71 82 57.78
August 15 71° 33’ 5.98” 2 18 710 33' 5.04"
12 71 33 6.00 2 18 71 88 5.86
10 71 88 5.90 2 20 71 88 4.88
.October 26 71' 32 59.87 2 26 71 33 0.35
November 26 71 88 4.56 2 21 71 88 4.48
30 71 88 4.52 2 19 71 33 4.54
24, 71 33 5.08 2 17 71 88 4.78
. 18 71 33 0.71 2 27 71 82 59.85
December 8 17 71 33 10.10 2 16 71 88 9.96
24 31 71 82 57.53 2 07 71 82 58.05
27 71 82 59.55 2 16 71 82 58.07
January 1.3 .............................. .. 0 16 71 82 55.86 2 28 71 82 55.22
7.2 .............................. .. 0 84 71 32 57.49 2 87 71 82 57.60
10.2 .............................. .. 0 84' 71 82 59.21 2 18 71 82 59.00
19.2 ........................... 0 18 71 32 59.58 2 20 71 82 59.98
29.2 .............................. .. 0 39 71 82 57.87 2 22 71 82 57.07

HALL, ABERRATION CONSTANT.
63
OBSERVATIONS OF POLARIS. CLAMP EA ST. NADIRS.






Sid. '1‘. Sid. T.
Date. Nadirs. N adirs.
H.' M. H. M.
1899. _
July 17.7 .............................. .. 0 18 71° 32' 58.20" 2 20 71° 32' 58.70"
21.7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 0 09 71 32 8.09 2 12 71 32 58.20
31.7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 0 14 71 32 56.82 2 14 71 32 57.24
August 1.7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 0 28 71 32 7.70 2 16 71 32 57.58
5.7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 0 21 71 32 56.96 2 16 71 32 56.60
6.7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 0 21 71 32 56.84 2 14 71 32 56.87
September 2.6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 0 01 71 32 57.58 2 19 71 32 58.06
12.6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 0 22 71 32 57.17 2 14 71 32 56.76
14.5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 0 36 71 32 56.96 2' 12 71 32 7.78
1898. .
May 13.4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 26 71° 33’ 5.26" 14 12 71° 38’ 4.60"
. 12 15 71 33 6.20 14 16 71 33 5.19
\
12 16 71 32 57.14 14 26 71 32 57.86
12 12 71 32 53.61 14 29 71 32 53.69
12 14 71 32 59.04 14 13 71 32 59.22
12 12 71 32 58.71 14 16 71 32 58.08
12 4O 71 32 57.98 14 17 71 32 56.86
12 71 33 3.41 14 16 71 33 3.06
12 27 71 32 56.96 14 22 71 32 57.12
12 00 71 32 58.78 14 15 71 32 58.58
12 18 71 32 59.92 14 18 71 32 59.22
12 20 71 33 -0.04 14 20 71 33 .09
12 4O 71 33 1.56 14 08 71 33 1.36
12 30 71 33 0.94 14 15 71 33 0.62
12 39 71 32 56.72 14 04 71 32 56.40
12 10 71 32 58.20 14 15 71 32 58.12
12 26 71 32 56.75 14 34 71 32 56.36
12 24 71 32 56.78 14 09 71 32 55.93
12 24 71 32 57.51 14 71 32 56.87
June 26.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 12 38 71 32 58.24 14 09 71 32 58.54
27.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 12 49 71 32 58.58 14 03 71 32 58.54
29.3 . . . . . . . . . . . . . . . . . . . . . . . . 12 36 71 32 58.12 14 16 71 32 58.20
30.3.. . 12 20 ‘71 32 58.74 14 13 71 32 58.54
Ju1y 1.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 12 3O 71 33 0.32 14 14 71 33 0.36





64 MICHIGAN ACADEMY OF SCIENCE.
OBSERVATIONS OF POLARIS. CLAMP WEST. NADIRS.














Sid. T. Sid. T.
Date. Nadirs. N adirs.
H. M. H. M.
1899.
June 10.8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 0 20 71° 33' 2.82" 2 11 71° 33' 3.43"
15.8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 0 13 71 32 57.93 2 04 71 32 58.25
.8 . . . . ..1 . . . . . . . . . . . . . . . . . . . . . . . .. 0 00 71 33 0.10 2 09 71 32 59.92
Ocnober 5 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 0 30 71 32 56.06 2 22 71 32 55.56
9.5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 0 31 71 32 58.80 2 07 71 32 58.64
22.4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 0 16 71 3 2.22 2 15 71 33 3.14
23.4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 0 35 71 32 52.46 2 10 71 32 52.48
November 26.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 0 05 71 33 3.20 2 58 71 33 2.89
December 17.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 0 27 71 32 43.36 2 12 71 32 43.91
35 71 32 40.97 2 04 71 32 40.62
26 71 32 43.16 2 10 71 32 41.55
January 40 71 32 46 .08 2 18 71 32 45.64
37 71 32 46.50 2 08 71 32 46.10
34 71 32 46.26 2 05 71' 32 46.11
26 71 32 47 .48 2 32 71 32 48.10
February .2 35 71 32 51.68 2 30 71 32 51.58
.2 22 71 32 53.70 2 46 71 32 52.74
.2... 42 71 32 53.22 2 33 71 32 54.06
.2.. 20 71 32 55.84 2 00 71 32 55.43
.1 16 71 33 7.49 2 29 71 33 7.72
March 2 .1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0 39 71 32 52.28 2 30 71 32 53.72
3.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 0 51 71 32 53.52 2 07 7'1 32 53.76
" 23.0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 0 00 71 32 54.06 2 05 71 32 54.08
24.0... 0 28 71 32 55.44 2 06 71 32 56.04
31.0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 0 21 71 32 54.44 2 52 71 32 56.23
April 1.0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 0 27 71 32 54.78 2 57 71 32 .03
4.0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 0 26 71 50.06 2 36 71 32 49.85
7.0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 0 29 71 32 52.14 2 15 71 32 51.76
18.9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 0 32 71 32 57.00 2 37 71 32 57.92
25.9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 0 32 71 32 57.08 2 12 71 32 .44
28.9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 0 42 71 32 51.95 2 11 71 32 52.90
30.9... 0 30 71 32 51.84 2 16 71 32 52.18
May 4.9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 0 51 71 32 53.34 2 08 71 32 54.39
20.8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0 34 71 32 45 .34 2 12 71 32 46. 06
June 12.8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 50 71 32 48.87 2 08 71 2 49.44
14.8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 37 71 32 48.02 2 51 71 2 49.53
15.8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 46 71 32 45.90 2 06 71 2 46.80
17.8... 25 71 32 _49.77 2 17 71 2 50.41
19 8 28 71 32 50.97 2 57 71 2 51.19
July 11.7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 19 71 32 50.56 2 60 71 2 50.26
12.7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 33 71 32 51.01 2 37 71 2 50.71
15.7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 41 71 32 53.25 2 16 71 2 53.19
21.7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 38 71 32 51. 2 08 71 - 2 51.89
25.7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 40 71 32 53.23 2 27 71 2 51.27
August 3.7... 71 32 52.08 2 34 71 2 51.57
5.7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 23 71 32 57.29 2 14 71 2 57.10
6.7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 24 71 32 51.48 2 30 71 2 50.64
14.7 . . . . . . . . . ‘ . . . . . . . . . . . . . . . . . . . . . .. 48' 71 32 52.16 2 22 71 2 52.04
15.7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 43 71 32 52.31 2 O8 71 2 51.57
18.6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0 33 71 32 51 . 2 _ 08 71 2 51.67
31.6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 0 31 71 32 52.70 2 10 71 2 51.80
September 21.6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 0 25 71 32 53.3 2 32 71 32 52.92
27.5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 0 29 71 32 53.38 2 30 71 32 52.70
29.5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. O 30 71 32 54.30 2 29 71 32 53.76
October 3. O 20 71 32 54.94 2 13 71 32 54.52
9. 0 24 71 32 52. 2 43 71 32 51.97
12. 0 33 71 32 54.58 2 19 71 32 54.12
19. 0 34 71 32 56.97 2 50 71 32 56.66
November 26.4 . . . . . ..‘ . . . . . . . . . . . . . . . . . . . . . . . .. 0 22 71 32 48.64 2 15 71 32 48.81
December 2.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 0 55 71 32 49. 2 05 71 32 49.10
0 34 71 32 49.60 2 30 71 32 48.50

HALL, ABERRATION CONSTANT. 65
OBSERVATIONS OF POLARIS. CLAMP WEST. NADIRS.





Sid. T. Sid. '1‘.
Date. Nadirs. Nadirs.
H. M. H. M.
1901.
January 20.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 0 31 71° 32 53.44" 2 15 71° 32' 54.46"
30.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 0 27 71 32 51.30 2 40 71 32 51.08
February 7.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 0 23 71 32 57.76 2 25 71 32 57.81
1899.
June. 12.3 . . . . . . . . . . . . . . . .... . . . . . . . . . . . . . .. 12 20 71° 33' 1.84" 14 11 71° 33' 1.54'
16.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 12 71 32 59.88 14 09 71 33 0.14
23.3 . 12 31 71 32 59.86 14 17 71 32 59.64
October 12 20 71 32 58.22 14 14 71 32 58.22
17.9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 15 24 71 33 0.14 14 15 71 33 0.20
20.9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 12 14 71 33 01.03 14 05 71 33 01.80
23.9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 12 31 71 32 52.18 14 09 71 32 52.89
24.9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 12 29 71 3251.56 14 71 32 52.88
November29.8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 12 48 71 32 50.12 14 14 '71 32 50.34
December 12 32 71 32 47.72 14 30 71 32 48.16
7.8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 12 30 71 32 4712 14 11 71 32 47.66
198 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 12 23 71 32 4003 14 10 71 32 40.04
208 12 14 71 32 14 10 71 32 40.32
1900.
January 21.7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 12 22 71 32 45.37 14 11 71 32 45.
12 20 7L 32 45.50 14 11 71 32 45.34
277 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 12 40 71 32 48.46 14 22 71 32 48.11
287 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 12 20 71 32 44.24 14 34 71 32 .05
307 12 24 71 32 49.24 71 32 48.36
February 9.6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 12 21 71 32 51. 14 12 71 32 51.68
10. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 12 26 71 32 52.90 14 14 71 32 53.15
. 13.6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 12 33, 71 32 52.48 14 14 71 ' 52.53
17. 12 16 71 33 06.55 14 39 71 33 06.76
March 1. 12 28 71 32 51.26 14 44 \71 32 50.81
2. 12 32 71 32 52.92 14 29 71 52.18
19. 12 43 71 32 53.56 14 07 71 32 53.22
23. 12 20 71 32 54.48 14 03 71 32 53.48
30. 12 31 71 32 56.20 14 03 71 32 55.41
31. 12 49 71 32 54.46 14 09 71 32 54.31
April 3. 12 24 71 32 49.06 14 14 71 32 49.75
9. 12 19 71 32 50.30 14 15 71 32 .94
10. 12 46 71 32 50.90 14 05 71 32 50.70
_ _25.4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 12 37 71 32 57.34 14 13 71 32 56.50
27.4 12 26 71 32 57. 14 13 71 32 .14
30.4....‘ . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 12 43 71 32 51.74 14 13 71 32 51.40
May 12 ~ 48 71 32 53 14 13 71 32 53 32
263 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 12 45 71 32 5307 14 25 71 32 52.72
June 12.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 12 71 3 .50 14 13 71 32 49.18
18.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 12 47 71 32 52.00 14 15 71 32 51.
28 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 12 40 71 32 50.07 14 _ 06 71 32 49.54
July 4.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 12 10 71 32 51.54 14 54 71 32 50.78
5.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 12 21 71 32 50.13 14 11 71 32 50.18
9.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 12 71 32 50.12 14 51 71 32 50.08
.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 12 38 71 32 51.80 14 60 71 52.16
21‘ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 12 38 71 32 52.68 14 51 71 32 52.39
282 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 12 47 71 32 52.40 14 I3 71 32 52.34
August 7 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 12 55 71 32 .22 14 04 71 32 48.46
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 12 40 71 32 48.76 14 08 71 ‘ 48.88
241 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 12 27 71 32 52.98 14 11 71 32 53.02
291 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 12 42 71 32 53.60 14 17 71 3.90
September 6.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 12 35 71 32 48.74 14 30 71 32 49.00
12.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 12 25 71 32 49.66 14 35 71 32 49.96
14.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 12 48 71 32 53.21 14 11 71 32 53.16
30.0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 12 19 71 32 54.76 14 47 71 32 54.74




















O
66 MICHIGAN ACADEMY OF SCIENCE.
OBSERVATIONS 0F POLARIS. CLAMP WEST. NADIRS.
Sid. T. Sid.T ‘
Date. Nadirs. Nadirs.
H. M. H. M.
1900
October 14.0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 12 26 71° 32' 55.46" 14 18 71° 32' 56.59"
16.9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 12 07 71 32 55.78 14 15 71 32 56.76
27.9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 12 30 71 32 49.90 14 08 71 32 50.34
30.9 . . . . . . . . . . . . . . . . . . . . . . . ..-. . . . . .. 12 34 71 32 49.83 14 25 71 32 50.07
Ncvember 3.9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 12 24 71 32 49.80 14 07 71 32 50.53
December 12 27 71 32 9.12_ 21 71 32 49.07
12 42 71 32 48.82 14 17 71 32 49.30
12 37 71 32 48.11 45 71 32 48.14
February 10.6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 12 30 71 32 59.97 14 32 71 32 .5
14.6... 12 32 71 32 59.86 14 36 71 ' 58.58,
1899
June 18.8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 0 16 71° 33' 1.00" 2 19 71° 33' 0.70"
20.8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 0 20 71 32 59.14 2 12 71 32 59.50
24.8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. O 26 71 32 59.32. 2 16 71 32 59.68
October 12.5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 0 26 71 32 58.37 2 15 71 32 58.25
15.5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 0 14 7133 0.” 2 05 71 33 0.30
31.4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 0 00 71 32 52.15 2 20 71 32 51.73
December 1.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 0 31 71 32 47.29 2 18 71 32 46.38
4. 0 26 71 3;. 45.72 2 00 71 32 45.96
0 40 71 32 46.08 2 18 71 32 45.64
June 0 47 71 2 50.72 2 17 71 32 50.64
0 35 71 32 51.02 2 22 71 32 50.94
0 18 71 2 50.29 2 30 71 32 .72
July 0 28 71 32 53.58 2 17 71 32 53.34
August 0 20 71 32 53.07 2 23 71 32 52.38
0 24 71 32 52.63 2 21 71 32 52.74
0 3) 71. 32 52. 2 23’ 71 32 52.02
September 3.6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 0 34 71 47.74 2 15 71 32 47.78
25.5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 0 18 71 32 53.56 2 22 71 32 53.58
October 5.5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 0 16 71 32 54.38 2 . 18 71 32 54.23
14.5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 0 26 71 32 54.77 2 25 71 32 54.48
17.5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 0 22 71 32 56.36 2 09 71 32 56.40
20.4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 0 25 71 32 50.28 2 09 71 32 0.13
December 10.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 0 '30 71 ‘32 49.64 2 00 71 32 49.89
15.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 0 34 71 32 50.57 2 20 71 32 0.68
1901
January 22.2 . . . . . . . . . . . . . . . . . . . . . . .. 0 33 71 32 51.46 2 07 71 32 51.16
February 10.] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 0 22 71 32 58.08 30 71 32 58.38
I
1899.
June 11.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 12 25 71° 33' 5.52" 14 10 71° 33' 5.49"
13.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 12 26 71 33 1.04 14 08 71 33 0.52
17.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 12 25 71 33 1.01 14 \08 71 33 0.49
December 21.8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 12 16 71 32 40.35 14 16 71 32 40.00
1900.
February 2.6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 12 21 71 32 51.90 14 30 71 32 51.25
15.6.....~ . . . . . . . . . . . . . . . . . . . . . . . . . .. 12 12 71 32 55.80 l4 18 71 32 55.48
25.6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 12 31 71 32 50.06 14 30 71 32 49.66
March 11.6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 12 22 71 32 49.67 14 24 71 32 50.73
. .265 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 12 31 71v 32 55.90 14 08 71 32 55.53
HALL, ABERRATION CONSTANT. 67




’ OBSERVATIONS OF POLARIS. CLAMP WEST. NADIRS.
Sid. rr. sm. T.
Date. Nadirs. - Nadirs.
H. M. H. M. ‘
1900.
April 4.5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 12 20 71° 32' 49.23" 14 14 71° 32' 49.32”
. . 19 71 32 50.30 14 15 71 32 49.94
46 71 56.46 14 13 71 32 57.08
_ 45 71 32 56.46 14 14 71 32 56.38
May 50 71 32 53.88 14 14 71 32 53.
36 71 . 32 53.71 14 26 71 32 53.58
June 30 71 32 53.46 14 40 71 32 53.22
32 71 32 49.50 14 13 71 32 49.18
26 71 32 52.92 14 17 71 32 52.52
47 71 32 52.00 14 15 71 32 .61
36 71 32 51.86 14 11 71 32 52.26
41 71 32 50.83 14 16 71 32 51.3
July 22 71 32 55.70 14 19 71 32 .2
44 7'1 32 52.28 14 11 71 32 52.27
- 31 71 32 54.11 14 21 71 32 53.37
33 71 32 53.72 14 12 71 32 53.75
December 11.8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 12 40 71 32 49.66 14 39 71 32 49.76
‘ 15.8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 12 22 71 32 .24 14 50 71 32 49.00
- " 1901. '
January 30.7 . . . . .., . . . . . . . . . . . . . . . . . . . . . . . .. 12 42 71 32 52.20 14 58 71 32 51.39
February 7.6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 12 27 71 32 56.53 26 71' 32 56.66





68 MICHIGAN ACADEMY OF SCIENCE. _


OBSERVATIONS OF POLARIS. CLAMP EAST.’
Red. 1900.0 Per.
No. Date. I. S. App. Z. 1900'“ Z Run error.
1898. —
1 April 25.9.. 3 3 46° 29' 3.34" +31.03" 34.37' —0.17" .07"
2 26.9 .............. .. 3 3 46 2 3.15 +3129 34.44 —0.14 .04
3 May 5.9 . . . . . . . . . . . . . . .. 3 3 46 29 0.25 +3384 34.09 —0.09 +0.06
4 8.9 . . . . . . . . . . . . . . .. 3-4 3 46 28 59.38 +3454 33.90 —0.13 +0.05
5 16.9 . . . . . . . . . . . . . . .. 3 3 46 28 57.68 +36. 34.03 —0.15 +0.03
6 24.9 . . . . . . . . . . . . . . .. 3 3 46 6.19 +37.87 34.06 +0.04 +0.04
7 25.9 . . . . . . . . . . . . . . .. 2-3 2—3 46 56.10 +38.03 34.13 +0.08 +0.06
8 26.9 . . . . . . . . . . . . . . .. 3 3 46 28 56.11 +3821 34.32 +0.03 +0.10
9 30.8 . . . . . . . . . . . . . . .. 3 3 46 28 54. +38.96 33.67 +0.03 +0.10
10 June 2.8 . . . . . . . . . . . . . . .. 1 3 46 28 55. +39. 34.48 +0.03 +0.03
11 6.8 . . . . . . . . . . . . . . .. 3 46 28 54.88 +39.78 34.66 +0.06 +0.01
12 16.8 . . . . . . . . . . . . . . .. 3-4 46 28, .16 +40.77 34.93 +002 +0.01
13 19.8 . . . . . . . . . . . . . . .. 3 46 28 53.06 +40.86 33.92 +0.03 +0.01
14 20.8 . . . . . . . . . . . . . . .. 3 28 52.52 +40.88 33.40 +0.02 +0.00
15 22.8 . . . . . . . . . . . . . . .. I 3 46 28 53.43 +40.92 34.35 +0.03 —0.01_
16 July 5.8... 1-3 3 46 28 53.89 +40.79 - 14.68 —1.12 + .07
17 7.8 . . . . . . . . . . . . . . .. 3 28 53.38 +40.70 4.08 +113 +0.04
18 10.7 . . . . . . . . . . . . . . .. 1-2 3-2 46 28. 52.47 +40. 3.08 + . 2 +1.02
19 13.7.. 3 46 28 54.23 +40.44 4.67 +1.12 + .00
20 20.7.. 1 3 46 28 55.12 +39.59 14.71 + . 5 + .06
21' 21.7.. 3 46 28 .10 +3948 13.58 + . 2‘ +4.05
22 22.7 . . . . . . . . . . . . . . .. 3 46 28_ 55 03 39. 4.41 + . 3 + .04
23 25.7.. . 1-4 3 46 28 55.12 +39.06 4.18 + . 3 + .05
24 26.7 . . . . . . . . . . . . . . . . . . . . . . . . . . .. 46 28 55.42 +38.92 34.34 + . 2 + .06
25 August 4.7 . . . . . . . . . . . . . . .. 3-4 3 46 28 57.24 +37.18 4.42 +1. 4 + .05
26 9. 4 3 46 28 59.53 +36.24 5.80 + . 4 + .07
27 13. 3 46 58. +3528 13.94 + .10 + .08
28 19. 3-2 46 29 01.44 +33.83 5.27 +1.14 + .06
29 25. 3 46 29 0238 +3221 4.59 +1. 3 —(.03
30 3—2 46 29 02.23 +31.89 14.12 + . 4 + .03
31 2 46 29 12.44 +22.27 34.71 +0.07 —0.07
32 . . . . .. 46 29 14.25 21.51 35.76 +0.05 —0.03
33 2 46 29 14.96 +20.80 35.76 +0.08 —0.06
34 October 8.5 . . . . . . . . . . . . . . .. 3 3 46_ 29 16.78 +17.07 33.85 +0.08 —0.05
35 11.5.. .. 3 3 46 2 19.54 +15.94 35.48 +0.08 —0.10
36 27.4.... . 3 3 46 29 25.01 +09.88 34.89 +0.10 -0.11
37 31.4... 3 3 2 26.01 +08.47 34.48 +0 09 —0.08
38 November 7.4.. 3 3 46 29 29.56 +05.81 35.37 +0.09 —0.10
39 12.4.. 3 3 46 29 .88 +04.l9 35.07 +0.11 —0.11
40 13.4.. 3 3 46 29 31.36 +03.85 35.21 +0.10 —0.11
41 i 26.3.. . . . . . . . . . . . .. 46 29 35.00 —0. 34.59 +0.10 —0.10
42 December 10.3 . . . . . . . . . . . . . . .. 3 3 46 29 39.69 —04.17 35.52 +0.13 ---0.08
43 13.3' . . . . . . . . . . . . . . .. 3 3 46 29 39.62 —04.93_ 34.69 +0.13 —0.03
44 15.3 . . . . . . . . . . . . . . .. 2—3 2—3 46 29 41.11 —05.45 35.66 +0.13 —0.02
45 17.3....‘ . . . . . . . . . . .. 3 2—3 46 29 .19 —05.91 35.28 +0.13 +0.01
46 31.3 . . . . . . . . . . . . . . .. 3-4 4-3 46 29 42.50 —08.15 34.35 +0.11 —0.10
47 January . 2—3 2-3 46 29 3.51 —08.33 35.18 +0.15— —0.06
48 9. 3 2 46 29 43.73 —08.85 34.88 +0.13 —0.04
49 14. 3 2—3 46 29 43.57 —09.21 34.36 +0.12 —0.08
50 21. 2—3 2—3 46 29 44.05 —09.10 34.95 +0.14 —0.03
51 24. 3 3 46 29 3.19 —09.09 34.10 +0.13 —0.06
52 31. 3 3 46 29 42.84 —08.61 34.23 +0.09 —0.10
53 February 8.2 . . . . . . . . . . . . . . .. 3 3 46 29 41.60 —07.83 33.77 +0.14 —0.08
54 13.2' . . . . . . . . . . . . . . .. 3 3 46 29 41.65 —07.08 34.57 +0.12 —0.05
55 16.2 . . . . . . . . . . . . . . . . . . . . . . . . . . .. 46 29 41.73 —06.49 35.24 +0.11 ~—0.09
56 24.1 . . . . . . . . . . . . . . .. 3 3 46 29 39.39 —05.03 34.36 +0.09 —0.01
57 March 1.1... , 4—3 4—3 46 29 38.03 —03.72 34.31 +0.11 —0.04 ,
58 April 4.0.. 3 3 46 29 28 50 +0592 34.42 +0.11 —0.11
59 9.0 . . . . . . . . . . . . . . .. 3 3 29 26.53 +07.52 34.05 +0.10 —0.07
60 18.9 . . . . . . . . . . . . . . .. 3—4 4 46 29 24.08 +10.57 34.65 40.07 —-0.14
61 20.9 . . . . . . . . . . . . . . . . _ . . . . . . . . . .. 46 29 23.31 +11.19 34.50 +0.10 —0.12
62 23.9 . . . . . . . . . . . . . . .. 3 3 46 .29 22.53 +12. 34.71 +0.10 —0.14
63 25.9 .. 3—4 3 46 29 20.70 +12.80 33.50 +0.10 +0.10
64 27.9 . . . . . . . . . . . . . . .. 3 3 46 29 21.9 +1334 35.24 +0.10 —0.15
65 23.9 . . . . . . . . . . . . . . .. 2 3 29 21.21 +13.59 34.80 +0.10 —0.13


















HALL, ABERRATION CONSTANT.
69
OBSERVATIONS OF POLARIS. CLAMP EAST.




No. Date. I.
66 May 3
67 4
68 3
69 3
70 June 1.8 . . . . . . . . . . . . . . .. 2—3
71 3.8 . . . . . . . . . . . . . . .. 3
72 4.8. . .. . . . . . . . . . . .. 3
73 29.7 . . . . . . . . . . . . . . .. 3—4
74 July 8.7 . . . . . . . . . . . . . . .. 4
75' 10.7 . . . . . . . . . . . . . . .. 2
76 18.7 . . . . . . . . . . . . . . .. 3
77 22.7 . . . . . . . . . . . . . . .. 3
78 August 10.7 . . . . . . . . . . . . . . .. 3-4
79 12 . . . . . . . . . . . . . . .. 4—3
80 13.7 . 3—4
81 September 1.6 . . . . . . . . . . . . . . .. 3
82 11.6... 3—4
83 13.5 . . . . . . . . . . . . . . .. 4
84 26.5 . . . . . . . . . . . . . . .. 4
85 30.5 . . . . . . . . . . . . . . .. 4
86 2-3

October 2.5 . . . . . . . . . . . . . . . . . . ..

N OOOJQQOO‘
l
OD
2—3


0309000269 WWW DOWN)“ WWW

Red. 1900.0 Per.
App' Z 1900 0. Z. Run' error.
46° 29' 17.97" +16.2 34.22" +0.07" —0.15"
46 29 17.52 +16.74 34.26 .09 -—0.12
46 29 15.10 +19.60 34.70 0.07 —0.09
46 29 14.73 +19.77 34.50 .07 .l2
46 29 13.60 +2094 34.54 +0.08 +0.04
46 29 13.24 +21.28 34.52 +0.08 .11
46 29 13.73 +21.44 35. +0.08 —0.10
46 29 11.40 +22.94 34.34 +0.05 —0.05
40 29 11.35 +22.62 33.97 _ +0.06 —0.08
46 29 12.12 +225 34.62 +0.08 —0.12
46 29 12.72 +21.95 34.67 +0.06 ——0.08
46 29 13.77 +21. .11 +0.05 —0.05
46 29 16.74 +18. 34 86 +0.08 +0.12
46 29 16.23 +17.73 33.96 +0.09 —0.13
46 29 16.06 +17. 33.57 +0.07 —0.14_
46 29 22.26 +12.21 34.47 +0.09 —0.11
46 29 26.03 +09.18 35.21 +0.11 —0.09
46 29 25.68 +08.43 34.11 +0.10 —0.11
46 29 30.33 +03.84 34.17 +0.11 —0.11
46 29 31.89 +02.30 34.19 +0.11 —0.12
46 .29 33.32 +01.61 34.93 +0.12 -0.10





7O
MICHIGAN ACADEMY OF SCIENCE.
/
OBSERVATIONS OF POLARIS. CLAMP EAST. S. P.















Red Z. Per.
No. Date. I. S. App. Z s. p. 19000. 1900-(L Run error_
1898.
1 Aprll 26.4 . . . . . . . . . . . . . . . . . . . . . . . .. 48° 57' 12.94" —31.16" 56’ 41.78" —0.18" —0.01"
2 - 27.4.. 2-3 3 48 57 .46 —31.42 56 41.04 - 0.08 —0.01
3 May 5.4 . . . . . . . . . . . . .. 3-4 2 48 57 15.46 —33.73 56 41.73 —).12 —(.)0
4 7.4.. 3 3 48 57 16.02 —34.20 56 41.82 — .15 + . 1
5 9.4 . . . . . . . . . . . . .. 2 2 48 57 15.95 —34.62 56 41.33 — .11 -1 .1
6 23.4... 2—3 2—3 48 57 20.25 —37.64 56 42.61 + .01 + .4
7 25.4.. 2—3 2 48 57 19.74 —37.95 56 41.79 + .02 + . 2
8 30.3 . . . . . . . . . . . . .. 3 3 48 57 20.53 —38. 56 41.67 + .01 + .17
9 June 13 . . . . . . . . . . . .. 2-3 2 48 57 20.73 —3.). 56 41.52 +(.01 + . 3
10 3.3 . . . . . . . . . . . . .. 2—3 2 48 57 21.72 —39.47 56 42 25 + .00 + . 3
11 14.3 . . . . . . . . . . . . .. 2—3 3 48 57 21.87 —4 .57 56 41.30 + .05 + . 2
12 17.3 . . . . . . . . . . . . .. 3 2 48 57 22.79 —4 .79 56 42.00 + .01 — . 1
13 21.3.. 3 2-3 48 57 22.74 —4 .89 56 41.85 + .01 — . 2
14 22.3 . . . . . . . . . . . . .. 3 3 48 57 23.51 —4 . 56 42.60 + .01 —0. 1
15 July 6. 3 48 57 22.59 —4 .76 56 41.83 + . 3 + . 5
l6 9. 2—3 48 57 .85 —4 .66 56 41.19 + . 2 + . 4
17 11.'. 2 3 48 57 22.49 —4 .59 56 41.90 + . 1 + .3
18 12. 3-2 48 57 22.76 —4 .55 56 42.21 + . 1 + . 2
19 14. 3 48 57 21.72 —4 .39 56 41.33 + . 1 -|- . 0
20 21. 3 48 57 21.13 —31 54 56 41.59 + . 2 + . 4
21 22.‘ 3 48 57 20.93 —3).43 56 41.50 + . 2 + . 5
22 29. 3 48 57 19.45 —33.47 56 40.98 + . 2 + . 3
23 August 2. 3 48 57 18.85 —37.63 56 41.22 +0.1 _+ 07
24 4.2 3-4 48 57 18.47 —37.26 56 41.21 +0. 1 + .04
25 10. . 3-4 48 57 17.16 —36.16 56 41.00 +0. 2 + .10
26 25. 3 48 57 13.40 -—32 38 56 41.02 +0.10 - .02
27 26.1 2-3 48 57 13.35 —32.05 56 41.30 —0. 1 + .06
28 27.1 . . . . . . . . . . . . .. 3 48 57 13.07 —31.72 56 41.35 +0. 1 + .04
29 September25.0.............. 3 2 48 57 04.10 —22.07 56 42.03 —0.04 —0.06
30 27.0..... . . . . . . . . . . . . .. 48 57 02.7 —21.33 56 41.38 —0.03 —0.05
31 29.0 . . . . . . . . . . . . . . . . . . . . . . . . .. 48 57 02. —20.63 56 41.45 —0.09- -0.02
32 October 9.0 . . . . . . . . . . . . .. 3-4 3 48 56 57.77 —16.88 56 40.89 —0.05 —0.08
33 149 . . . . . . . . . . . . .. 3—4 3 48 56 55.96 —14.72 56 41.24 —0.06 —0.07
34 24.9 . . . . . . . . . . . . .. 3 3 48 56 53.08 —10.75 56 42.33 —0.12 -—0.11
35 26.9... 3 3 48 56 50.52 —10.05 56 40.47 —0.07 —0.10
36 November 2.9 . . . . . . . . . . . . .. 2-3 2—3 48 56 49.62 —07.49 56 42.13 —0.06 —0.05
37 15.9.. 3 3 48 56 44.63 —02.92 56 41.71 —0.11 —0.05
38 24.8 . . . . . . . . . . . . .. 2—3 2-3 48 56 .27 —00.02 56 41.25 —0.11 —0.
39 December 12.8 . . . . . . . . . . . . .. 3—4 3—4 48 '.73 +0480 56 40.53 —0.14 +0.03
40 13. 3 48 56 36.90 +0506 56 41.96 —0.13 +0.02
41 15. 3 48 56 36.78 +0557 56 42.35 —0.12 +0.09
42 28. 3 48 56 34.87 +0781 56 42.68 —0.12 -—0.01
43 January . .. . . . . .. 56 31.83 +0862 56 40.45 —0.13 —0.09
44 9.7 . . . . . . . . . . . .. 34 3 48 56 32.65 +0890 56 41.55 —0.11 —0.02
45 14.7 . . . . . . . . . . . . .. 2 2 48 56 32.86 +0922 56 42.08 -—0.09 —0.11
46 26.7 . . . . . . . . . . . . .. 4 3 48 56 31.99 +0902 56 41.01 —0.03 —0.08
47 . 31.7 . . . . . . . . . . . . .. 4 3 48 56 33.31 +0855 56 41.86 _—0.14 .07
48 February 6.7 . . . . . . . . . . . . .. 4-3 3 48 56 32.78 +0797 56 40.75 —0.13 +0.01
49 13.7.. 3-2 3 48 56 34.83 +0699 56 41.82 —0.13 —0.09
50 24.6 . . . . . . . . . . . . .. 2-3 2—3 48 56 37.11 +0491 56 42.02 —0.13 —-0.08
51 27.6 . . . . . . . . . . . . .. 4 4 48 56 38.30 +04.13 56 42.43 —0.13 —0.01
52 March 23.5 . . . . . . . . . . . . .. 3-4 3—4 48 56 44.09 —02.35 56 41.74 —0.08 —0.19
53 April 8.5 . . . . . . . . . . . . .. 3 3 48 56 49.96 —07.35 56 42.61 .08 -0.05
54 9.5 . . . . . . . . . . . . .. 3 2 48 56 50.19 —07.69 56 42.50 —0.08 —0.13
55 10.5.... . . . . . . . . .. 3 3 48 56 49.97 —08.04 56 41.93 —0.04 —0.16
56 20.4 . . . . . . . . . . . . .. 3-4 3 48 56 53.62 —ll.1'3 56 42.59 —0.07 —0.13
57 22.4 . . . . . . . . . . . . .. 3 48 56 53.25 —11.69 56 .56 —0.09 —0.12
58 25.4 . . . . . . . . . . . . .. 2—3 2 48 56 54.81 —12.66 56 42.15 —0.05 —0.09
59 May 3.4 . . . . . . . . . . . . .. 2-3 2-3 48 56 57.25 —14.70 56 42.55 —0.03 +0.04
60 5.4 ............. .. 3 2 48 56 57.32 —15.26 56 42.06 —0.05 —0.
61 8.4 . . . . . . . . . . . . .. 2-3 2 48 56 57.93 —16.11 56 41.82 —0.08 —0.17
62 » 24.4 . . . . . . . . . . . . . . . . . . . . . . . . .. .48 57 02.07 —19.69 56 42.38 —0.03 —0.11
63 .3 . . . . . . . . . . . . .. 3 3 48 5 02.67 —20.25 56 42.42 —0.06 —0.16








HALL, ABERRATION CONSTANT.
71
OBSERVATIONS OF POLARIS. CLAMP EAST. S. P.













Red. Z. Per.
No. Date. I. S. App. Z. s. p. 19000. 19000. Run. error_
1899. -
64 June 2.3 . . . . . . . . . . . . .. 3 3 48° 57' 04.20" —21.03" 56' 43.17" —0.03" —0.06"
65 July 6.2 . . . . . . . . . . . . .. 2 2-3 48 57 05.12 —22.82 56 42.30 —0.05 —0.16
66 11.2 . . . . . . . . . . . . .. 2 2-3 48 57 05.00 —22.47 56 42.53 —0.03 —0.09
67 12.2 . . . . . . . . . . . . .. 2-3 2—3 48 57‘ 05.05 —22.43 56 42.62 —0.03 -0.08
68 22.2 . . . . . . . . . . . . .. 2 3 48 57 02.83 —21.4 56 41.41 —0.02 —0.06
69 August 2.2. 3-4 3-4 48 57 00.88 —19.79 56 41.09 —0.02 —0.06
70 7.2 . . . . . . . . . y . . .. 2-3 2-3 48 57 00.16 18.75 56 41.41 —0.01 —0.08
71 12.2 . . . . . . . . . . . . .. 3 3 48 56 59.29 —17.84 56 41.45 —0.04 —0.10
72 September 3.1...... 3-4 3 48 56 53.01 —11.74 56 41.27 —0.06 —0.12
73 ~ 4.1 . . . . . . . . . . . . .. 3 3 48 56 52.53 -11.45 56 41.08 —0.06 —0.14
74 9.1 . . . . . . . . . . . . .. 3 ’3 48 56 51.50 —10.03 56 41.47 —0.06 —0.14
75 11.1 . . . . . . . . . . . . .. 3 3 48 56 50.66 —09.36 56 41.30 —0.04 —0.14
76 13.1 . . . . . . . . . . . . .. 3 34 48 56 49.38 ——08.62 56 40.76 -0.04 —0.13
77 _ 16.1 . . . . . . . . . . . . .. 4 3 48 56 49.85 -07.50 56 42.35 —0.07 —0.13
OBSERVATIONS OF POLARIS. CLAMP EAST. R.
Red. Z. Per.
No. Date. I. S App. Z. R. 19000. 19300 Run error
1898.
1 August 1.7 . . . . . . . . . . . . . . .. 3 3 133° 30' 60.53" —37.73" 22.80" -—0.03" —0.04"
2 14.7 . . . . . . . . . . . . . . .. 2—3 3 133 30 57.12 —-35.02 22.10 —0.04 —0.03
3 20.6 . . . . . . . . . . . . . . .. 3 3 133 30 55.67 —33.60 22.07 —0.06 —0.04
4 October 15.5 . . . . . . . . . . . . . . .. 3 I 3 133 30 37.82 —14.54 23.28 —0.09 —0.06
5 November 2.4 . . . . . . . . . . . . . . . . . . . . . . . . . . .. 133 30 30.03 —07.68 22.35 —0.11 +0.02
6 3.4 . . . . . . . . . . . . . . . . . . . . . . . . . .. 133 30 29.59 7.29 22.30 —0.10 +0.01
7 19.4 . . . . . . . . . . . . . . .. 3 3 133 30 24.99 -01.65 23.34 -0.13 +0.02
8 27.3 . . . . . . . . . . . . . . .. 3 3 133 30 21. +00..71 22.26 —0.13 —0.05
9 December 18.3 . . . . . . . . . . . . . . .. 2—3 2—3 133 30 15.48 +06.11 21.59 —0.16 +0.06
10 24.3 . . . . . . . . . . . . . . .. 2—3 2—3 133 30 .11 +07.04 22.15 —0.13 +0.01
11 27.3 . . . . . . . . . . . . . . .. 3—4 3-4 133 30 14.23 +07.55 21.78 —0.15 —0.02
1899.
12 January 13... . . . . . . . . . . . .. 133 30 12.92 +08.25 21.17 —0.13 —0.07
13 7.2 . . . . . . . . . . . . . . .. 3 3 133 30 13.65 +08.66 22.31 —0.14 —0.05
14 10.2 . . . . . . . . . . . . . . .. 3—2 3 133 30 12.92 +08.94 21.76 —0.15 -0.06
15 19 . . . . . . . . . . . . . . .. 3 3 133 30 12.30 +09.14 21.44 —0.15 -—0.03
16 29.2 . . . . . . . . . . . . . . .. 3 3 133 30 13.31 +08.83 22.14 -—0.13 —0.03
17 July 17'.7 . . . . . . . . . . . . . . .. 3 3 133 30 45.14 —22.08 23.06 —0.08 —0.11
18 21.7 . . . . . . . . . . . . . . .. 4 3 133 30 43.80 —21.50 22.30 —0.08 —0.11
19 31.7 . . . . . . . . . . . . . . .. 4 3-4 133 30 43.56 -20.09 23.47 —0.09 . —0.10
20 August 1.7 . . . . . . . . . . . . . . .. 2 133 30 42.22 -—19.90 22.32 —0.08 —0.10
21 - 5.7 . . . . . . . . . . . . . . .. 3—4 3 133 30 41.12 —19.05 22.07 —0.09 —0.12
22 6.7 . . . . . . . . . . . . . . .. 3 133 30 41.64 —18. .80 —0.07 -—0.12
23 September 2.6 . . . . . . . . . . . . . . .. 3 2 133 30 33.55 —11.90 21.65 —0.07 —0.07
24 12.6 . . . . . . . . . . . . . . . . . . . . . . . . . . .. 133 30 32.34 —08.81 23.53 —0.10 —0.12
25 14.5 . . . . . . . . . . . . . . .. 3 3 133 30 30.73 —08.05 22.68 — .09 —0.12









A—6-R
MICHIGAN ACADEMY OF SCIENCE.
OBSERVATIONS OF POLARIS. CLAMP EAST. S. P. R.

I509 M"
an |----n-:_n-n— l—
COCO qam-nwm— ow mQO’iU‘
NNNM
CON—O
w
A


Date. I. S.‘ App. Z. s. p. R. 1%?6 19%0'0'
/ /
1898.
May 13.4 . . . . . . . . . . . . .. 2-3 2-3 131° 02' 38.89" +3546" 03' 14.35" —0.33" —0.01”
174 . . . . . . . . . . . . .. 3 3 131 02 38.37 +3647 03 14.84 -0.01 —0.00
December 27.8 . . . . . . . . . . . . . . . . . . . . . . . . .. 131 03 22.39 —07.64 03 14.75 +0.12 —0.10
.8 . . . . . . . . . . . . .. 3 3-2 131 03 22.74 —08.20 03 14.54 +0.11 -0.10
1899.
January 2.8 . . . . . . . . . . . . .. 3 3 131 03 22.45 —08.36 03 14.09 +0.10 —0.11
.7 . . . . . . . . . . . . .. 3 3 131 03 23.63 —09.22 03 14.41 +0.12 -—0.11
18.7., . . . . . . . . . .. 3 3 131 03 23.87 -—09. 03 14.71 +0.12 —-0.11
21.7 . . . . . . . . . . . . .. 3 3 131 03 23. —09.09 03 14.61 +0.13 —0.06
February 16.7 . . . . . . . . . . . . .. 3 3 131 03 4 03 13.76 +0.11 -—0.14
. 3 3 131 03 18 74 —03 86 03 14.88 +0.12 -0.10
April 3.5 . . . . . . . . . . . . .. 2 2 131 03 08 57 +05.78 03 14.35 +0.08 —0.10
4.5 . . . . . . . . . . . . .. 2 2 131 03 0 39 +06.06 03 14.45 +0.08 —0.08
13.5 . . . . . . . . . . . . .. 3 3 131 03 0574 901 03 14.75 +0.05 —-0.04
14.5 . . . . . . . . . . . . .. 3 3 131 03 09.30 03 15.31 +0.05 -—0.00
17.4.. 3 3 131 03 0493 +1012 03 15.05 +0.04 -—0.01
26.4 . . . . . . . . . . . . . . . . . . . . . . . . .. 131 03 01 89 +1295 03 14.84 +0.08 -—0.02
28.4 . . . . . . . . . . . . .. 3 3 131 03 0108 +1347 03 14.55 +0.05 -—0.09
May 8.4 . . . . . . . . . . . . .. 2-3 2 131 02 58.39 +1611 03 14.50 +0.02 +0.01
28.3 . . . . . . . . . . . . .. 3 3 131 02 55.06 +2025 03 15.31 +0.00 -—0.00
June' 263 . . . . . . . . . . . . .. 2 2 131 0 51.71 +22 87 14.58 +0.02 .03
3 . . . . . . . . . . . . .. 2-3 2 131 02 51.53 + 03 14.41 —0.09 .
293 . . . . . . . . . . . . .. 23 2-3 131 02 52.02 +2“ 92 03 14.94 +0.03
303 . . . . . . . . . . . . . . . . . . . . . . . . .. 131 02 51.49 +2295 03 14.44 0.02
July 1.3 . . . . . . . . . . . . . . . . . . . . . . . . .. 131 02 50.56 +2297 03 13.53 +0.00








HALL, ABERRATION CONSTANT.
OBSERVATIONS OF POLARIS. CLAMP WEST.

P-ll—
How m flaw» ww~
0000' N) N) N N) N; I-lI-‘i-l "Hill-l
~o$§gm wfiwg— oEwqa mwww
‘
0500
MN
34




Red. 1900.0. Per.
Date. I. S. App. Z. 1900_0_ Z_ Run. error
1899.
.Iune 10.8 . . . . . . . . . . . . .. 2-3 2-3 46° 29' 17.89’ —F22_03” 29’ 39-92” —FO-09 —F0-00
15.8 . . . . . . . . . . . . .. 3 3 46 29 16.42 22. 29 .93 +0.06 +0.18
16.8 . . . . . . . . . . . . . . . . . . . . . . . . .. 46 29 16.94 +2262 29 39.56 +0.10 +0.18
October 5.5 . . . . . . . . . . . . .. 4 3 46 29 38.57 +00.61 29 39.18 +0.13 +0.04
95 . . . . . . . . . . . . .. 3 3 46 29 40.30 —00.92 29 39.38 +0.12 —0.02
22.4 . . . . . . . . . . . . .. 3—4 3 46 29 45.58 —05.88 29 39.70 +0.14 —0.02
23.4 . . . . . . . . . . . . .. 3 3 46 29 45.71 —06.28 29 39.43 +0.15 +0.03
November 26.3 . . . . . . . . . . . . .. 3 2 46 29 57.30 —18.14 29 39.16 +0.18 +0.03
December 17.3 . . . . . . . . . . . . .. 2 2 46 30 02.83 —23.47 29 . +0.19 +0.02
193 . . . . . . . . . . . . .. 3 3 46 30 02.39 —23.9 29 38.47 +0.16 ~0.03
26.3 . . . . . . . . . . . . .. 2-3 2-3 46 30 03.39 —24.97 29 38.4 +0.17 +0.02
1900. - -
January 21.3 . . . . . . . . . . . . .. 2-3 2-3 46 30 06.27 —26.79 29 39.48 +0.22 +0.06
22.2 . . . . . . . . . . . .. 2—3 2 46 30 06.04 —26.72 29 39.32 +0.17 +0.06
24.2 . . . . . . . . . . . . .. 3—4 3 46 30 06.02 —26.62 29 39.40 +0.18 +0.04
29.2 . . . . . . . . . . . . .. 2-3 2—3 46 30 06.69 —26.48 29 40.21 +0.16 +0.09
February 1.2 . . . . . . . . . . . . .. 2 2-3 46 30 05.87 —26.29 29 39.58 + .19 +0.10
9.2.. .. 4 4 46 30 04.59 —25.28 29 .31 +1.19 +0.10
10.2 . . . . . . . . . . . . .. 3 3 46 30 05.09 —25.17 29 39.92 + .19 +0.08
11.2.. 2 2 46 30 05.17 —-25.06 29 40.11 + .17 +0.07
19.1 . . . . . . . . . . . . .. 4 3—4 46 30 02.96 —23.56 29 39.40 + .17 +0.00
March 2.1 . . . . . . . . . . . . .. 3 3 46 30 00.99 —21.26 29 39.73 + .15 +0.06
3.1.. 3 3 46 30 00.03 —20.98 29 39.05 + .16 +0.02
23.0... 3-4 3-4 46 29 54.12 —15. 29 38.79 + .15 +0.02
24.0.. 4 4 46 29 54.23 —15.07 29 9.16 + .15 +0.02
310 . . . . . . . . . . . . .. 34 3 46 29 52. —12. 29 39.51 + .14 +0.03
April 1.0... 3 3 46 29 51.97 —12.53 29 39.44 + .14 +0.01
4.0 . . . . . . . . . . . . .. -3-4 3-4 46 29 50.52 —11.58 29 38.94 + .14 +0.03
7.0 . . . . . . . . . . . . .. 3-4 46 50.65 —10.73 29 39.92 + .16 +0.04
18.9.. 4 4 46~29 46.10 —06.88 29 39.24 + .14 +0.01
25.9... 2-4 3 46 29 44.93 —04.89 29 40.04 + .14 +0.02
28.9 . . . . . . . . . . . .. 3-2 3-2 46 29 44.45 —03.94 29 40.51 + .14 +0.02
30.9.. .4. 3 2—3 46 29 42.86 —03.39 29 39.47 + .13 +0.04
May 4.9 . . . . . . . . . . . . .. 2 2 46 29 41.7 —02.43 29 39.34 +0.12 +0.02
20.8 . . . . . . . . . . . . . . . . . . . . . . . . .. 46 29 37.83 +01.36 29 39.19 +0.11 —0.02
June 12.8 . . . . . . . . . . . . .. 3 3 46 29 35.41 +0492 29 40.33 +0.12 —0.04
14.8 . . . . . . . . . . . . .. 3 3 46 29 34.9 +05. 29 39.99 +0.10 —0.08
15.8 . . . . . . . . . . . . .. 2 2—3 46 29 34.59 +05.06 29 39.65 +0.10 —0.03
17.8 . . . . . . . . . . . . .. 2 2-3 46 29 34.48 +05. 29 39.67 +0.11 -— 15
19.8 . . . . . . . . . . . . .. 2—3 2—3 46 29 34.79 +05 35 29 40.14 +0.12 —0.16
July 11.7 . . . . . . . . . . . . .. 3 3 46 29 33.78 +0521 29‘ 38.99 +0.12 —0.21
12.7 . . . . . . . . . . . . .. 3 3 46 29 33.61 +05.“ 2 .7 +0.10 —0.21
15.7 . . . . . . . . . . . . .. 3 3 46 29 4.15 +0485 29 39.00 +0.12 .25
‘21.? . . . . . . . . . . . . .. 3—4 3-4 46 29 34.82 +0434 29 9.16 +0.11 —0.21
25.7 . . . . . . . . . . . . .. 3 46 29 34.56 +0370 29 38.26 +0.12 —0.23
August 3.7 . . . . . . . . . . . . .. 3 3 46 29 37.06 +0240 29 39.46 +0.11 —0.36
.7 . . . . . . . . . . . . .. 3 1-2 46 29 37.83 +0200 29 39.83 +0.14 —0.16
6.7 . . . . . . . . . . . . .. 3 2 46 29 38.07 +01.7 2939.85 +0.12 —0.26
14.7 . . . . . . . . . . . . .. 4 4 46 29 39.08 +00.03 29 9.11 +0.12 —0.29
15.7 - - - - - - . . . . . . .. 4 4 46 29 9.49 —00. 29 39.31 +0.11 —0.30
18.6.. . . . . . . . . . . .. 46 29 40.56 -—00.92 29 39.64 +0.13 —0.24
31.6 . . . . . . . . . . . . .. 34 3 46 29 42.58 —04.42 29 38.16 +0.13 —0.24
September21.6 . . . . . . . . . . . . .. 4 3 46 29 50.43 —11.47 29 38.96 +0.15 —0.16
27. . . . . . . . . . . . . .. 4 3 46 29 52.35 —13.44 29 38.91 +0.16 —0.18
29.5 . . . . . . . . . . . . .. 3 3 46 29 54.28 —14.20 29 40.08 +0.16 —0.16







74
MICHIGAN ACADEMY OF SCIENCE.
- OBSERVATIONS OF POLARIS. CLAMP WEST.

























No. Date I. S. _ App. Z. 19%9'0' Run. 5:5}.
I 00. ’
55 October 3.5. . . . , 2—3 2 46° 29' 55.5 " —15.79" 29' 39.7 " +0.15" —0.17"
56 9.5 . . . . . . . . . . . . . . 3 3 46 29 58.85 -—17.93 29 40.92 +0.17 — 16
57 12.5 . . . . . . . . . . . . .. 2- 3 2~3 46 29 58.75 —19.08 29 .67 +0.16 +0. 16
58 19.4 . . . . . . . . . . . . . 2—3 2—3 46 30 01.69 —21.82 29 39. 87 +0. —0.05
59 November 26.4 . . . . . . . . . . . . . . 2—3 2—3 46 30 14.64 —35.10 29 39.54 +0.19 —-0.04
60 December 2.3 . . . . . . . . . . . . .. 2 2 46 30 16.54 —36.70 29 39. .+0.20 —0:03 \
6] 13.3..... 3 3 46 30 18.93 —39.61 29 39.32 +0.20 +0.00
1901. -
62 January 20.2 . . . . . . . . . . . . . . 3 3 46 30 23.86 —43.8 29 40.03 +0.23 -+ 0.02
63 30 . . . . . . . . . . . . . . . 3 v 3 46 30 22.39 —43.32 29 39.07 +0.22 +0.36
64 February 7.2 . 2—3 2—3 46 30 21 . 96 —42 . 57 29 39. 39 +0.22 -—0. 17
OBSERVATIONS OF POLARIS. CLAMP WEST. S. P.
No. Date I. 8. App. z. s. P. 11;&‘_id__ 19%9-0- Run 813%}
1899. '
1 June 12.3 . . . . . . . . . . . . . . 2 2 48° 57' 09.77” —22. 14” 56' 47.63" -—0.01" ——0.00”
2 16.3 . . . . . . . . . . . . . . 2—3 2—3 48 57 10.06 22.56 56 47 .50 —0.02 $0.02
3 _ 23.3... 2—3 2 48 57 09.70 —22.89 56 46.81 —0.03 0.01
4 October 11.9 . . . . . . . . . . . . . . 3 3 48 56 44.75 +01. 56 46.71 —0.06 -+—0.08
5 17.9 ............ .. 3-4 3-4 48 56 41.68 +0420 55 .88 _0.09 +0.08
6 20.9 . . . . . . . . . . . . . . 2—3 2—3 48 56 40.92 +0528 56 46.20 —0.07 +0.00
7 23.9 . . . . . . . . . . . .. 3 3 48 56 40.59 +06.48 56 47.07 +0.09 +0.16
8 24.9 . . . . . . . . . . . . . . 3 3 48 56 39.93 +06.89 56 46.82 —0.09 +0.16
9 November 3 3 48 56 27.36 +19.05 56 46.41 —0.11 +0.13
10 December 5.8 . . . . . . . . . . . . . . 2 2 48 56 25.17 +2083 56 46.00 —0. 11 0.11
11 7. . . . . . . . . . . .. 48 .82 +2138 56 46.20 .12 +0.05
12 3—2 3—2 48 56 21.82 +24 . 03 56 45 . 85 —0 .12 —0 . 02
13 3 3 48 56 21.64 +2422 56 45.86 ——0. 1‘} +0.00
14 January 3 ' 3 48 56 19.74 +2675 56 46.49 - 0.17 _ +0.03
15 3-4 3 48 56 20.14 +26. 56 46.83 —0.14 +0.03
16 3 3 48 56 19.36 +26.52 56 45.88 — 0.13 +0.03
1? 3—4 3—4 48 56 19.35 +2649 56 45.84 —0. 15 +0.02
18 3—4 3—4 48 56 19.56 +26.40 56 45.96 —0.18 1 +0.06
19 February 9.6 . . . . . . . . . . . . . . . . . . . . . . . . . . 48 56 20.67 +2523 56 45.90 —-0. 16 +0.04
20 10.6 . . . . . . . . . . . . . . 3 3 48 56 22.09 +2512 56 47.21 —0.14 +0.06
21 13.6 . . . . . . . . . . . . . . 4 4 48 56 .79 +2171 56 46.50 — 0.15 +0.04
22 17.6 . . . . . . . . . . . . . . 3—4 3—4 48 56 22.99 +23.89 56 46.88 —0.15 —0.11
.23 March 1.6 . . . . . . . . . . . . . . ~1 _4 48 56 24.94 +21.40 56 46.34 —0.14 +0.06
24 2.6 . . . . . . 48 56 25.66 +21.13 56 46.79 —0.13 +0.06
25 19.6 2—3 48 56 30.39 +16.33 56 46.72 —0.10 +0.13
26 23.5 . . . . . . . . . . . . . . 2—3 48 56 31.74 +1520 56 6.94 —0.10 +0.04
27 30.5 - . . . .. 48 56 33.24 +13.05 56 46.29 —0.11 +0.12
28 31 . 3 48 56 33.76 +12.70 56 46.46 ——0. 10 +0.12
29 April 3. 3 48 56 35.19 +11.74 56 46.93 —0.10 +0.05
30 9. 3—4 48 56 36 .08 +09 . 98 6 47.06 .14 +0. 02
31 ' 10. 4 48 56 36.52 +09.66 6 7.18 —-0.10 +0.04
32 25 . 2—3 48 56 40 . 96 +05 . 05 56 46 . 01 —0 . 10 . 1
33 27. . . . . . . 48 46 42.45 04.41 56 46.86 —0.08 +0.09
34 30. . . . . . . 48 56 42.95 +03.52 56 46.47 -—0. 10 +0.16

HALL, ABERRATION CONSTANT.
75'






OBSERVATIONS OF POLARIS.‘ CLAMP WEST. S. P.
_ - Red. 19000. Per.
No. Date. I. S. App. Z. S. P. 1900_0_ Z_ Run anon
1900.
35 May 6 4 . . . . . . . . . . . . .. 2-3 2-3 48° 56' 44.29" +0204" 56’ 46.33" —0.07" +0.15"
36 26.3 . . . . . . . . . . . . .. 2-3 2 48 56 49.08 —02.54 56 46.54 —0.06 +0.07
37 June 12.3 . . . . . . . . . . . . .. 2—3 2-3 48 56 51.82 —04.89 56 46.93 —0.10 —0.01
38 18 . . . . . . . . . . . . .. 2—3 2-3 48 56 52.52 —05.22 56 47.30 —0.08 —0.09
39 28.3 . . . . . . . . . . . . . . . . . . . . . . . . .. 48 56 52.14 —05.57 56 46.57 —0.06 —0.16‘
40 July 4.2 . . . . . . . . . . . . . .. 2—3 2—3 48 56 52.59 —05.59 56 47.00 —0 05 —0.21
41 . 2-3 2-3v 48 56 53.28 —05.60 56 47.68 —0.03 —0.21
42 2 2 48 56 52.21 —05.45 56 46.76 —0.03 —0.20
43 . . . . . . . . . . . .. 48 56 52.52 —05.06 56 47.46 +0.05 —0.00
44 3 2-3 48 56 51.24 —04.41 56 46.83 —0.06 —0.17
45 2 2 48 56 51.2 —03.30 56 47.96 —0.04 —0.25
46 7.2 . . . . . . . . . . .. 48 56 48.89 —01.66 56 47.23 —0.03 —0.05
47 10.2.. 3 3 48 56 47.98 —00.96 56 47.02 —0.06 —0.04
48 24.1 . . . . . . . . . . . . .. 3 3 48 56 44.89 +0248 56 47.37 —0.05 —0.18
49 29.1 . . . . . . . . . . . . . . . . . . . . . . . . .. 48 56 43.88 +0372 56 47.60 —006 —0.31
50 September 6.1 . . . . . . . . . . . . .. 3 3 48 56 .44 +0626 46 47.70 —0.09 —0.06
51 12.1 . . . . . . . . . . . . .. 3 3 48 56 38.03 +08.09 56 46.12 —0.07 —0.06
52 14.1 . . . . . . . . . . . . .. 2-3 2-3 48 56 38.34 +0875 56 47.09 -0.07 —0.14
53 30.0 . . . . . . . . . . . . .. 3 3 48 56 32.69 +1440 56 47.09 —0.09 —0.15
54 October 14.0 . . . . . . . . . . . . .. 3 3 48 56 27.99 +1969 56 47.68 —0.10 —0.24
55 16.9 . . . . . . . . . . . . .. 3—4 3—4 48 56 25.53 +2090 56 46.43 —0.12 —0.16
56 27.9.1 . . . . . . . . . . .. 2-3 2—3 48 56 21.63 +2492 56 46.55 —0.12 —0.13
57 30.9 . . . . . . . . . . . . .. 2—3 2-3 48 56 21.50 +26.10 56 47.60 —0.13 —0.08
58 November 3.9 . . . . . . . . . . . . .. 2—3 23 48 56 19.25 +2752 56 46.77 —0.14 —0.12
59 December 2-3 2—3 48 56 10.03 +3663 56 . —0.15 —0.23
60 2 2 48 56 .59 +3688 56 47.47 —0.16 -0.23
61 2—3 2—3‘ 48 56 05.82 +4125 56 47.07 —0.18 .17
1901. ‘ '
62 February 10.6. 3 3 48 56 03.89 +4199 56 45.88 —0.20 --0.22
63 146 . . . . . . . . . . . . .. 3—4 2 48 56 05.26 +41.44 56 46.70 — .19 —0.22









76
MICHIGAN ACADEMY OF SCIENCE.


\





OBSERVATIONS OF POLARIS. CLAMP WEST. 1%.



2.5.. 3.8. m. 53.... .8. m
n 0 . 0 0 00.00 0 0
Pe +3 w+w _ _ _ _ _ _ _
m. 8.5. 3...... .33 W... m.
00 00 o 000 O
R A? _ _ l _ 4.. _ _ 4 _
om mam. "mam. ..w. wmww m. m.
W . mmuww wfiw w“ %w.. W M“ %
1 I
www www w wwww % w
mm .53 w. 38. 3 m. w.
2 90 6912 89 2
R 2%% 12% % 1122 33 fl 4
1 _ _ _ +++ ++++ ++ + +.
R. 53 34 4 38.7.. .8 8 w.
. “6% wmm % wwmw QM. % M
Z r
n,. . mmw wwm w wmww ww % w
P a
A 8%% %%% % %%%% wwmw woo %
111 111 l 1111 11 1 1
. 33 3 300 33 3
S 5,_~9_~3 o_~23 3 4.9.5; 339,52. 22 3 2
3 3 33 3 3
w 5.5% . A... 2...... . 3 1H
m mm? 3.55.1.8 3% 5.16% mm m4. w
r H r
r m b r m v. w
e t. m e m M a
e .w e e. m. m .w e u m
H 6 O n y D. t 0 n b
u c e u .m .u e c e a 6
J O D J J A S O D J F

HALL, ABERRATION CONSTANT. -
77
I
OBSERVATIONS OF POLARIS. CLAMP WEST. S. P. R.














App. Z. Red. 1900.0. Per.
N°' Date' I- S- S. .R. 1900.0. 2. Run error.
1899. -‘
1 June 11.8.. 8 3 181° 02' 53.24" +2200" 03' 15.80" +0.03" +0.04"
2 18.8 ........................ .. 131 02 52.04 +2224 08 14.88 +0.05 0.07
8 17.8 ............ .. 2 131 02 52.51 +2207 03 15.18 +0.00 +0.00
4 December 21.8 ............ .. 2-8 2—3 131 08 39.54 _24.40 08 15.14 +0.15 +0.08
I 900.
. 5 February 2.0 ............. .. 2-3 2 131 08 41.20 -20. 08 15.09 +0.18 +0.01
0 15.0 ............ .. 8 8 181 08 89.91 -24.88 08 15.58 +0.14 +0.00
7 25.0 8 3 181 03 88.88 -22.82 03 10.01 +0.14 +0.08
8 March 11.0 ............ .. 2-8 2-8 131 08 84.90 —18.81 08 10.09 +0.13 +0.02
9 2 2 ' 181 08 30.15 —14.80 08 15.79 +5.11 +0.04
10 April .5... 181 08 20.88 _11.44 03 15.89 +0.12 +0.07
11 .5 181 08 25.10 -09.98 08 15.18 +0.09 +0.12
12 .5 131 08 28.10 —08.26 08 14.90 +0.08 +0.00
18 .4 131 03 21.88 _05. 08 15.98 0.08 +0.02
14 May .4 181 08 19.05 -02.55 03 10.50 +0.08 +0.07
15 .3... 181 08 11.48 +0315 08 14.08 +0.07 -0.05
10 June .3 181 03 1199 +08. 08 15.07 +0.08 +0.00
17 .8.. 181 08 10.28 +04.89 08 15.17 +0.05 +0.01
18 .3 181 03 10.37 +05. 08 15.52 +0.07 ~0.15
19 .3... 131 08 10.33 +0522 08 15.55 +0.04 —0.09
20 .3 181 03 09.90 +0581 03 15.27 +0.07 -0.15
21 .8... 131 08 08.80 4415.02 08 14.42 +0.05 -0.14-
22 July_ 18.8 ............ .. 2-8 2-8 181 08 10.27 +04 09 08 14.90 441.00 -0.10
23 25.2 ............ .. 2 23 131 13 11.11 +03 78 03 14.89 +0.00 -0.10
24 20.2... .............. .. 181 03 11.40 +0801 08 15.07 +0.04 +0.04
25 December 11.8 ............ .. 2-3 2-3 131 08 55.09 —39.30 08 10.89 +0.17 —0.03
20 5.8 ............ .. 2—3 2-8 181 8 50.00 -40.1.6 03 15.94 +0.18 +0.08
' 1901. ' ’ Y
27 January 3 3 3 131 08 59.59 —43 31 03 10% +0.19 +0.21
28 February 7.0 ............ ..I 3 ’3 131 08 59.42 -42.48 03 10.94 +0.19 -0.22


For the observations
18. Observation Equations.
as given in the preceding section observation
equations can be wrriten of the form
par—@211.-v
’0
80,- 8' + A3+ A‘k.
bsin(®+B)+1rbcos(®+B).
8’ is the observed declination, computed from the zenith distance with
156—1501111514 + 42° 10' 48.0”.
62 is the declination of the Berliner J ahrbuch.
Ak is the correctiOn
bsinB= sin asin 8
b cos B = — cos-asin 8.
to the aberration constant, 20.445 ", and 1 is the
The auxiliary quantities b and Ii are formed as follows:
cos 2— cos 8_sin 2.
Q
_ With the term A 8 would be included all constant corrections.
78
MICHIGAN ACADEMY OF SCIENCE.
OBSERVATION EQUATIONS. POLARIS, CLAMP EAST.












b. b. ,
A‘s- sin(®+B). cos(®+B) 11' 1"
+1 -—0.306 —-0.939 +0 36" +0.039"
1 —0.3'21 —0.934 +0.29 —0.033
1 -0.459 —0.874 +0.57 +0229
1 -0.502 —0.850 +0.81 +0405
1 _0011 -0.775 +072 +0.369
0 1 -0.710 _0080 +0.49 +0188
7.. 1 -0721 _0074 +0.36 +0 008
8... 1 _07:11 -0002 +018 -0.1
9 1 -0.774 —0.613 +0.83 +0482
10 ......................... .. +1 +0.803 -0.572 +0.09 -0.254
11.. +1 —0.841 _0517 _010 ——0.439
12 ......................... .. 1 -0914 0.372 —0.33 -0.050
13 ........................ .. 1 —0.93'3 _0 . 326 +0 . 07 +0.358
14 ......................... .. 1 -—0.937 —0.310 +1.21 +0901
15 ......................... .. 1 -0.917 —0.278 +020 +0043
10 ......................... .. 1 —0.984 _0009 _0.10 —0.359
17 ......................... .. 1 _0.980 _0.027 +048 +0229
18 ......................... .. 1 —0.987 +0012 +1.51 1.271
19 ......................... .. 1 —0.985 +0001 _0.00 -0.285
20 ......................... .. +1 -0971 +0170 _0.19 —0.383
21 ......................... .. +1 —0.968 +0191 +0.98 +0792
22 1 - 0.905 +0207 +0. 15 —0.034
23 1 - 0.953 +0250 +0.37 +0202
1 -0949 +0271 +0.21 +0040
1 —0.897 +0410 +0.12 +0004
1 —0.860 +0.484 —1.28 —1.368
1 —0.827 +0540 +0.01 +0544
1 —0.768 +0020 _074 -0.771
1 +0702 +0094 +0.04 +0044
......................... .. +1 -0090 +0700 +044 +0449
81 ......................... .. +1 - 0.275 +0.948 —0.08 +0090
32 ......................... .. 1 —0.243 +0950 _1.15 -0.971
33 ......................... .. 1 +0 209 +0 _1.15 -0.901
34 ....................... .. 1 -0.012 +0.986 +075 +0.984
35 ......................... .. 1 +0010 +0.987 —0.83 --0.583
36 ......................... .. 1 +0279 +0947 —0.32 _ .020
37 ......................... .. 1 +0.344 +0920 +014 + .451
38 ......................... .. 1 +0454 +0877 —0.73 _ .405
39 ......................... .. 1 +0529 +0.833 _0.44 -- .110
40 ......................... .. +1 +0.543 +0.824 -057 ~ .288
41 ......................... .. +1 +0710 +0079 +004 + .376
42 1 +0800 +0.484 _094 ~ .020
1 +0.885 +0487 _0.10 + .154
1 +0.900 +0.406 —-1.14 — .831
1 +0911 +0.382 -079 - .484
1 +0977 +0.13? +0.27 + .529
1 +0.981 +0105 _0. - .389
1 +0907 —0.018 -—0.3 - .119
1 +0.981 _0.100 +0.28 + .427
+1 +0900 _0220 -0.4 - .208
+1 +0. -0270 +0.45 +0595
1 +0900 —0.392 +0.41 0.517
1 +0812 _0.514 +0.80 +0800
1 +0798 -0 587 _0.01 +0020
1 0.701 —0.628 -0.08 .019
50 ......................... .. 1 +0000 _0.719 +0.19 +0150
57 ......................... .. 1 +0000 -0.785 +0.25 +0.183
58 ......................... .. 1 +0004 —0.985 +0.21 —0.035
59 ......................... . . 1 +0020 -0.987 +0.55 +0294
00. ........................ .. +1 -—0.187 -0909 +0.0 -0.250
01 ......................... .. +1 -0219 _0902 +0.15 -0150
02 ......................... .. 1 ~0201 _0.949 -004 —0.353
63 ......................... .. 1 —0.300 -0.940 +1.13 +0.810
04 ......................... .. 1 .888 —0.930 _0.50 -0.885
05. ....................... .. 1 -0 348" -11.924 -014 -0407



HALL, ABERRATION CONSTANT.
79
OBSERVATION EQUATIONS. POLARIS, CLAMP EAST.








b. b. ,
As- 8111 (0+3). cos(®+B). ‘1 - v‘
00 ......................... .. +1 -0.497 -0.352 +0.49 +0140"
07 ......................... .. 1 +0520 -—0.835 +0.40 +0053
00 ......................... .. 1 +0094 -0.702 _0.0 .402
09 ......................... .. 1 -0.700 _0090 +0.13 +0. 172
70 ........................ .. +1 _0 .791 +0091 -0.03 _0 . 370
71 ......................... .. +1 _0310 -0.505 +014 —0205
72 ......................... .. 1 _0319 +0551 -05 +0303
73 ......................... .. 1 +0971 -0173 +0.29 +0003
74 ......................... .. 1 _0.907 —0.020 +0.03 +0431
75 ......................... .. 1 +0037 +0007 +0.00 +0190
70.. 1 -0979 +0137 _002 +0225
77 ......................... .. 1 +0900 +0202 -0.40 -0.005
73 ......................... . . 1 _0.305 +0493 _017 +0255
79 ......................... .. 1 -0.830 +0.5 +0.71 +0030
30 ......................... .. +1 -0830 +0530 +1.13 +1002
01 ......................... .. +1 _0020 +0703 +0.13 +0222
32 ......................... .. 1 +0432 +0. A). -0.501
33 ......................... .. 1 -0.453 +0377 +003 +0040
34 ......................... .. 1 _0.249 +0955 +0.40 +0037
35 ......................... .. 1 +0133 0909 +0.45 +0047
30 ......................... .. 1 _0.100 +0975 -0. +0114
n' = n _4 00" [00] 22.521
MICHIGAN ACADEMY OF SCIENCE.
OBSERVATION EQUATIONS. POLARIS S. R, CLAMP EAST.




b. b. ,
A‘s- sin (0+3). cos(®+B). ‘1 - "-
+1 -0.313 -0930 +022" -0.333"
1 -0.330 +0930 -042 _0.974 '
1 .451 _0.377 +024 +0312
1 -0.430 -0.303 +0.31 —0.241
1 _ ' _0.345 -014 +0039
1 _0.092 -0.704 +1.29 +0705
1 -0710 -0.030 +040 -0.001
1 _0.770 +0013 033 _0.127
1 _0.790 -0.592 .19 _0.311
+1 _0. -0.500 +0.91 +0410
+1 +0399 _0. 10.00 _0.
1 _0.913 -0.304 0.03 +0.1
1 -0.940 +0302 +0.47 +0047
1 _0.945 -0.230 +0312
1 _0.935 -0.001 .54 0.193
1 4.327 _0. +0.12 1 _0. 7 +0021 +0.5 . 1
1 _0.930 +0037 +0.37 +0557
1 _0.934 .070 _0.03 _0.332
+1 +0970 .133 +023 +0013
+1 -0907 0.199 0.20 _0.
1 -0937 1034 _0.553
1 _0.914 +0372 _0.07 -0200
1 _0.901 +0.4 +0.11 _0.
1 -0.350 +0491 _0.25 -0.392
1 _0.703 +0. _0.37 _0.425
1 _0.090 +0700 +0.02 .009
1 _0.034 +0 +0.03 .013
1 +0207 +0950 +0.50 +0054
+1 _0.234 +0.9 +0.07 +0031
+1 +0201 +0900 +0.03 .
1 +0034 +0930 _0.01 1 _0.473
1 +0. +0935 +0.20 +0109
1 +0237 +0953 +0.31 +0975
1 +0.2 .949 +1.07 _0.904
1 +0334 +0909 +0.05 0.313
1 .573 +0.7 +013 0337
1 .093 +0093 -024 +0102
1 .331 +0. -094 +0903
+1 +0339 +0429 +0.47 +0543
+1 +0904 - .393 +095 +1014
1 +0970 18.131 +1.13 +1.130
1 +0. +0020 -1.14 _1.191
1 +0937 _0.027 +0.09 +0021
1 +0930 _0.114 +0.51 +0410
1 +0934 -0.319 _0.47 +00 7
1 +0. _0.400 +0.23 +0073
1 +0355 -0.492 -0.74 _0.935
1 +0733 _0.594 +023 _0.059
......................... .. +1 +0001 -0.733 +0.44 +0.
51 ......................... .. +1 +0021 +0703 +0.92 +0550
52 ......................... .. 1 +0257 _0.952 +010 -0332
53 ......................... .. 1 +0012 -0.937 +0.01 +0079
54 ......................... .. 1 _ _0. _0.930 +0.92 +0
55 ......................... .. 1 _0.044 -0.930 +030 +0174
50 ......................... .. 1 +0213 -0.904 +1.02 +0470
57 ......................... .. 1 _0.244 ‘ _0.950 -0.02 +0571
53 ......................... .. 1 -0.292 —0.943 +004 +0037
59 ......................... .. 1 _0.417 _0.394 +1.19 +0037
00 ......................... .. +1 +0447 _0.330 +0.50 +0052
01 ......................... .. +1 _0.490 _0.357 +0.20 +0350
02 ......................... .. 1 _0.700 -0.090 +0.37 +0340
03 ......................... .. 1 -0744 -0.043 +0.33 +0317
04 ......................... .. 1 +0795 -0.534 +1.71 +1211
05 ......................... .. 1 +0935 -0.007 072 +0371









HALL, ABERRATION CONSTANT.
81
OBSERVATION EQUATIONS. POLARIS S. P., CLAMP EAST.









'\
b. 5. ,
As- sin (9+3). cos(®+B) ‘1 ' "-
00 ......................... .. 1 _0.937 0.015 +1.04" +0719"
07.. 1 _0.937 0.031 +1.14 +0325
03 ......................... .. 1 _0.903 +0194 -0.04 _0.293
09 ......................... .. 1 _0.910 +0307 -030 -0.552
70 ......................... .. +1 -0.332 +0442 _0.05 -0212
71 ......................... .. +1 _0.342 +0513 _0.00 +0193
72 ......................... .. 1 -0.000 .733 .23 .233
73 ......................... .. 1 _0.537 0.793 _0.49 -0.492
74.. ...................... .. 1 _0513 +0340 _0.10 -0.077
75 ......................... .. 1 _0.439 +0353 -0.24 _0.207
70 ......................... .. 1 _0.400 +0373 _0.32 -0.773 5
77 ......................... .. +1 _0.414 +0395 +0.73 +0335
11’ = n +4.00" [00] = 21.535.
OBSERVATION'EQUATIONS. POLARIS R... CLAMP EAST.










b. b. ,
As- sin (0+3). cos(®+B). n- ”'
1 ......................... .. +1 -0.917 0.304 +0.30" +0329"
3 ......................... .. 1 _0327 10.540 _0. _0.453
2 ......................... .. 1 -0.757 $0033 -0.40 _0.550
4 ......................... .. 1 +0077 0934 +0.70 +0017
5 ......................... .. 1 +0370 +0913 -011 -0.133
0 ......................... .. 1 +0.3 .900 --0.10 _0.170
7 ......................... .. 1 +0027 0.703 +0.30 +0939
3 ......................... .. 1 +0723 -0.29 -0.077
9 ......................... .. 1 +0924 +0357 -0.33 _0.433
10 ........................ .. +1 +0. +0201 +0.34 +0170
11 ......................... .. +1 0.905 .200 .70 -0.214
12 ......................... .. 1 .979 0.121 _1.40 4.
13 ......................... .. 1 +0937 +0013 _0.25 +0413
14 ......................... .. 1 +0937 +0030 - 0.72 .025
15 ........................ .. 1 +0903 +0192 -1.11 —0.327
10 ......................... .. 1 +0919 -0.359 -0.39 +0479
17 ......................... .. 1 -0979 +0129 +0.50 +0.5
13 ......................... .. 1 -0.909 +0137 _0.20 _0.-
19 ......................... . . 1 -0.925 +0343 +0.91 +0339
20 ......................... .. +1 _0.919 +0359 -023 -0.259
21 ................... .... .. +1 _0.392 +0419 _051 +0507
22 ......................... .. 1 _0.33 +0434 +0.24 +0170
23 ......................... .. 1 _0007 +0774 -030 -1.057
24 ......................... . . 1 -0.403 +0370 +0.94 +0725
25 ......................... .. +1 -0.433 +0335 +0.10 -0.11
n' = n —1.00” [’01)] = 6 701
82
MICHIGAN ACADEMY OF SCIENCE.


OBSERVATION EQUATIONS. POLARIS S. P. R. CLAMP EAST.


b. b. ,
A's- sin (6+8). cos(@+B). 1‘ ' v
1 ........................ .. +1 +0505 -0309 +0.02" +0035"
2 ......................... .. 1 .013 -0.770 _020 +0199
3 ......................... .. 1 +0907 +0197 _0 _0.
4 ......................... .. 1 +0973 +0 123 +0 13 —0 107
5 ......................... .. 1 +0932 +0 095 +0 55 +0 324
0 ......................... .. 1 +0 973 _0.131 +0.21 +0 054
7 ......................... .. 1 +0 973 +0134 _0. _0
3 ......................... .. 1 +0 953 +0235 _0. _0 174
9.. 1 75 _0030 +0.90 +0 394
10 ......................... .. +1 +0 007 -0779 --0 -0 235
11 ......................... .. +1 0.073 _0 934 +0.30 +0 335
12 ......................... .. 1 +0055 _0 930 +0.13 +0 205
13 ........................ .. 1 .090 _0 932 _0.
14 ......................... .. 1 +0112 _0 930 -073 -o 351
15 ......................... .. 1 -0.102 -0 974 _0.45 —0 374
1 _0 303 -0.933 -0.27 _0 209
1 +0 340 _0.927 +0.12 +0 170
1 _0 49 357 +0.10 0 132
1' _0 744 —0 043 _0.03 -0 720
+1 - 0 953 +0 230 +0.00 -0 11
+1 _0 904 _0.293 +0 32 +0 104
1 _0 970 _0131 _0. 01
1 - 0 97 +0105 +0.20 +0 004
+1 -0 970 -0 143 +1.11 +0 909






HALL, ABERRATION CONSTANT.
83
OBSERVATION EQUATIONS. POLARIS, CLAMP WEST.












A8 5111 (6+8) cos(®+B) 1‘ @-
+1 _0371 +0400 _033" -0.524"
1 _0-900 -0392 +0.40 +0300
1 _0.913 _0377 _0. +02
1 -0.099 +0932 +0.23 +0057
1 —0.031 +0937 +0.15 _0.
1 +0. 9 +0909 _0.19 -0.307
1 +0205 0.905 +0. +0154
1 +0712 0 034 +023 +0201
1 +0. 1 $0 379 +0.03 +0072
+1 +0925 0 347 +1.03 +1.049
+1 + . +0229 +1.02 + .030
1 ‘ + .902 _0.220 -0.13 +1 .029
1 + .953 _0.237 +0.03 + .133
1 + .949 _0.271 +0.01 +1110
1 + .921 +0353 —033 _ .717
1 + .901 _0402 —024 .124
1 + .330 _0525 +0.03 +0153
1 + .327 _0.540 -0.50 _0430
1 + .317 _0.555 _0.72 -1.590
+1 + .731 +0302 +0.00 + .135
+1 +0.591 _0.791 _0. +4 .133
1 + .577 _0.300 +0.40 +1.521
1 + .271 _0.949 i007 + .704
1 + .254 _0.953 0.30 + .393
1 +. 7 _0977 +005 .023
1 +0121 +0930 +0.04 +0115
1 0.070 _0934 +0.52 +0539
1 .020 -0.93 —04 _0429
1 -0132 -0909 +0.20 +0233
+1 —0295 +0943 _0. +0503
+1 +0342 _0.920 -1.04 _1.042
1 —0.373 _0.914 .01 _0.019
1 -0.433 _0.337 +0.15 +0129
1 -0053 _0739 +0.35 +0274
1 _0333 +0442 +073 _0.929
1 _0397 _0.413 -0.33 -0.535
1 _0.904 -0.393 —0.09 -0.243
1 _0.917 +0307 0.00 _0.104
1 _0.923 +0337 -0.47 -0041
+1 _0.937 +0017 +0.73 +0503
+1 —0930 +0034 +1.02 +0790
1 —0933 +0033 +0.70 +0.
1 -0.970 +0131 +0.57 +0324
1 _0.950 +0245 +1.43 +1227
1 —0.909 +0. +0.42 +0155
+1 —0.395 +0415 +013 -0.447
—0.33 +0429 -0.0 +0343
1 —0323 +0544 +0.09 +0417
1 —0.314 +0.553 +0.51 +0230
+1 —0730 +0593 +0. 10 .175
+1 —0.037 +0754 +1.53 +1300
1 _0. +0927 +0.03 +0429
1 -0.233 +0957 +0.74 +0500
1 -0204 +0905 .45 ~0030
1 —0140 +0977 +013 -0353
1 —0.03 +0930 +1.30 -1.514
1 +0014 +0937 -0.04 -0.240
1 +0133 +0973 —0.35 -0537
1 +0703 +0333 _000 +0120
+1 +0.7 .009 -033 -0.339
+1 +0379 +0443 +0.11 +0109
+0.90 -0197 —005 .551
1 +0917 _0.304 -002 .093
+1 +0357 +0490 +0.19 +0311

n' = n +1.00" [723‘] = 18.191.
MICHIGAN ACADEMY OF SCIENCE.
OBSERVATION EQUATIONS. POLARIS S. P., CLAMP WEST.








b. b. ,
“3' sin (0+3). cos(®+B). n- 1’
+1 _0.331 +0444 +1.25" +0037"
1 _0.909 _0.334 +1.13 +0543
1 -0947 -0.27 +0.42 _0.
1 +0011 +0937 +0.30 +0012
1 +0113 +0930 _0.50 _0.
1 +0 104 +0973 _0.24 _0 522
1 +0 214 +0903 +0.77 +0 510
1 +0959 +0 +0 209
1 +0 752 0.033 +0.00 +0 003
+1 +0 310 +0555 +0.37 _0 325
+1 +0 330 +0.52» _0.24
1 +0 927 +0339 _0.30 +0 542
1 +0 933 +0322 _005 _0 523
1 9 -0229 _0.02 +0 173
1 +0 950 -0240 +0.35 +0 543
1 +0 930 _0.330 _0.59 +0394
1 + 924 _0.340 _0.00 _0.404
1 0 912 +0373 _053 -033
1 +0 332 -0 532 _0.59 _0.412
+1 +0 322 _0 547 +0.70 +0935
+1 +0792 +0539 02 +0.13
1 +0743 +0044 +0 25 +0405
1 +0597 _0.730 _0.
1 +0534 _0.790 +0 35 +0452
1 +0327 +0931 +0 33 +0339
1 +0203 +0951 +0.51 +0493
1 +0140 _0970 _0.07 _0.
1 +0129 _0.979 +011 +0040
1 +0079 _0 934 +0.51 +0419
+1 +0022 _0 937 _0.43 +0504
+1 +0 039 -0930 +0.25 _ .
1 _0 230 _0945 +0.34 _1.
1 319 +0934 +0.50 + .
1 _0 303 _0.917 +0.10 _ .
1 +0 457 +0375 +0.04 - .
30 ......................... .. 1 _0.713 _0.070 +0.13 _ .
37 ......................... .. 1 -0.37 +0449 +0.45 _ .
33 ......................... .. 1 _0.920 -0300 +0.70 + .
39 ......................... .. 1 --0.900 +0202 -0.02 _+ .
40 ......................... .. +1 +0931 -0.105 +0.37 _ .
41 ......................... .. +1 933 -0.039 +107 + .
42 ......................... .. 1 _0 937 _0024 10 _1.
43 ........................ .. 1 _0 930 +0042 +1 04 + .
44 ......................... .. 1 +0 972 +0173 +0 23 _1.
45 ......................... .. 1 _0 940 +0234 + 30 - + .
40 ......................... .. 1 _ .335 +0437 +0.73 + .
47 ......................... .. 1 _0302 .431 +0.55 _ .
43 ......................... .. 1 + .727 +0003 +0.77 + .
49 ......................... .. 1 _1 .0 +0720 +0 30 + .
50 ......................... .. +1 —( .504 +0309 +1 13 + .
51 ........................ .. +1 +1 .430 +0303 +0.33 _0.
5- ......................... .. 1 _ .450 +0373 +0.51 _0023
53 ......................... .. 1 -( .190 +0 907 +0.4 +0045
54 ......................... .. 1 + .040 +9 930 +097 +0034
55 ......................... .. 1 + .091 +0 932 _0.22 _0.534
50 ......................... .. 1 + .275 +0. _0. +0302
57 ......................... .. 1 + .325 +0933 +1.02 +0312
53 ......................... .. 1 + .333 +0903 +0. _0.
59 ......................... .. 1 + .7 +0. -0.09 _0.
00 ......................... .. +1 +0.732 +0002 +0.71 +0735
01 ......................... .. - +1 +0937 +0 311 +0.35 +0475
02 ......................... .. 1 +0325 _0 542 _093 _0.704
33 ......................... .. +1 +0730 -0 593 _0.10 +0000




n' = n —1.00" [00] = 12.510.
HALL, ABERRATION CONSTANT.
85
OBSERVATION EQUATIONS. POLARIS R. CLAMP WEST.



















5. 5. . l
A‘s' sin (0+B).|eos(0+B). 1‘ ' °’-
1 ......................... .. +1 .925 _1 .340 _0.44" _0.252'
2 ......................... .. 1 _0.930 _1. 5 +0.03 +0200
3 ......................... .. 1 _0.953 _1 .253 +0.35 +0501
4 ......................... .. 1 0.019 + .937 -004 _0007
5 ......................... .. 1 +0070 + .934 +002 .034
0 ......................... .. 1 +0323 +1923 _0.03 +0012
7 ......................... .. 1 +0709 + .013 +0.15 +0430
3 ......................... .. 1 +0301 + .570 -0.23 +0072
~ 9 ......................... .. 1 +0930 + .313 _037 +0053
10 ......................... .. +1 _0.943 -( .239 _0.34 _0. 5
11 ......................... .. +1 _0950 _ .242 _1.04 _0.394
12 ....................... .. 1 -0.904 +1210 -004 -0.507
13 ......................... .. 1 -0.907 +1.190 -0.07 +0074
14 ......................... .. 1 _0.710 + .033 +0.04 +0005
15 ......................... .. 1 _0.030 + .710 +0.33 +0223
10 ......................... .. 1 +0049 + .743 +0.33 +0521
17 ......................... .. 1 _0.593 + .730 +1.19 +1079
13 ........................ .. 1 _0.270 + .949 _0. -0.025
19 ......................... .. 1 -0107 + .932 +0.99 +0934
20 ......................... .. +1 +0043 +).933 0.25 +0231
21 ......................... .. +1 +0100 +0.9 +003 +0024
22 ........................ . . 1 +0150 +0. 973 +0. 22 +0229
23 ......................... . . 1 +0354 +0494 _1. _1 . 147
24 ......................... .. 1 +0395 +0410 +1.05 -0.071
25 ......................... .. 1 .959 -0232 —0.42 +0192
. 20 ........................ .. +1 +0330 _0535 +0.34 +1021
11' = n —1.00” [00] = 8.192.
OBSERVATION EQUATIONS. POLARIS s. P. R. CLAMP WEST
b. b. ,
“5' sin (0+B).|00s(0+B). n- @-
+1 _0.374 _0.453 +0.20" +0145"
1 -0.333 _0423 +0.37 _0.051
1 +0910 _0303 +0.39 _0004
1 +0939 +0305 +0.31 +0713
1 +0339 _0425 +0.40 +0979
1 +0772 -0.017 _0.09 +0475
1 +0050 —0742 +1.05 _0519
1 +0453 +0377 .01 +0154
9 1 +0212 _0.933 -0.31 +0034
10 ......................... .. +1 +0002 _0935 +0.05 +0310
11 ......................... .. +1 -( .022 +0937 +0.24 +0459
12 ......................... .. 1 _ .100 _0.931 +0.59 +0.7
13 ......................... .. 1 _( .239 -0.957 _0.40 _0312
14 ......................... .. 1 -. 0 -0390 +1.12 -1.155
15 ......................... .. 1 _1 .701 - 0.027 +0.93 +0035
10 ......................... .. 1 _1 .3 -0575 . -0.453
17 ......................... .. 1 _( .379 -0.44 +0.40 -0010
13 ......................... .. 1 _ .913 _0374 +0.19 -0.200
19 ......................... .. 1 _1 .920 —0.300 +0.13 -0.323
20 ......................... .. +1 -+ .925 _0344 +0.44 -0.025
21. .............. +1 - .954 -0.250 +1.30 +0793
22 ........................ .. 1 _ .979 +0 +0.77 +0147
23 ......................... .. 1 - .953 +0237 +0.34 +0193
24.. 1 -1. 4 +0.23 +0.43 _0104
25 ......................... .. 1 + .303 +0472 _0.90 -0.573
20 ......................... .. - +0-89 0-409 —0-52 —°-164
27 ......................... .. 1 +0. 4 -0372 +1.00 _0.431
23 ......................... .. +1 +0352 _0497 -1.23 —0.702


n' = n +1.00"
[00] = 0.993.
86 MICHIGAN ACADEMY OF SCIENCE.
Corresponding to the several sets of observations are normal equations
and solutions as follows:
Clamp East, above pole.
+86.000 A8 —23.895 Ak — 2.561 I + 6.980 = 0
—23.895 +46.133 + 3.692 _ —12.073 = 0
— 2.561 + 3.692 +37.616 —10.536 = 0
11.
A8 = —4.008" 10.011" 73.6
' Ak = +0237 10.056 39.3
7r = +0256 10.058 37.3
[nn. 3] = 22.523 [00] = 22.521.
Probable error one equation = r = 10.351".
Clamp East, below pole.
+77.000 08 —23.069 41k — 2.464 7r +18.820 = 0
—23.069 +40.3l7 + 1.281 -—10.318 = 0
— 2.464 + 1.281 +34.670 —12.450 = 0
Wt.
A8 = +3.80?" 10.046" 63.7
Ak = +0.13-5 10.063 33.4
7r = +0340 10.062 34.6
[nn. 3] = 21.558 [011] = 21.565 r = 10.364".
Clamp East). reflected, above pole.
+25.000 A8 +- 0.298 413 +10.549 7r —4.340 =
+ 0.298 +16.658 — 2.144 ’ —5.682 = 0
' +10549 — 2.144 + 7.701 +0.677 =
wt.
08 = —0.580" 10.118" 9.9
Ak = +0257 10.096 15.1
1r = —0.592 10.217 2.9
{1111. 3] = 0.702 [00] = 0.701 r = 10.372".
Clamp East, reflected, below pole.
+24.000 A8 —0 .950 Ak —12.423 7r +1.490 =
_0.950 +13.064 2. I +0255 = 0
—12.423 + 2.587 +10.358 +0.392 =
W1;
08 = —0.222" 10.102" 8.7
4k = 0.026 10.087 11.9
7r = —0.310 10.158 3.6
[nn. 3] = 4.150 [07)] = 4.161 r = 10.300".
Clamp West, above pole.
+64.000 08 — 2.120 Ak — 2.499 7r + 4.790" = 0
— 2.120 +32.741 - 2.349 — 5.456 = 0
— 2.499 — 2.349 +29.602 + 4.179 = 0
wt.
A8 = +0925" 10.046" 63.6
Ak = +0.152 10.065 32.5
7r = —0.135 10.068 29.3
[1111. 3] = 13.135 [00] =13.191 r = 10.303". '
Clamp West. below pole.
+63.000 46 + 1.825 Ak — 0.171 1r +1427 " = 0
+ 1.825 +30.481 —- 0.775 -12.686 = 0
—~ 0.171 — 0 775 +30.891 + 3.879 = 0
wt.
A8 = —1.239” 10.039" 62.9
Ak = +0.427 10.056 30.4
1r = —0.116 10.055 30.9
[nn. 3] = 12.493 ['07)] = 12.510 r = 10.308". '
......
HALL, ABERRATION CONSTANT. 87
Clamp West, reflected, above pole.
+26.000 A6 — 2.905 Ak +10.889 r —3.420" =
— 2.905 +13.54O + 1.125 . —2.071 = O
+10.889 + 1.125 +11.777 +0.410 =
Wt.
A8 1: —0.701" $0.105" 14.8
Ak = +0245 i0 114 12.4
7r = —0.334 i0 154 6.8
[nn. 3] = 8.196 [00] = 8.192 . r = i0.405.
Clamp _West, reflected, below pole.
+28.000A8 — 5.006 Ak —11.727 1r +0.680" = 0
— 5.006 +l6.931 .126 —9.138 = 0
—ll.727 “ +' 2.126 +10.330 +1.178 = Q
, wt.
A8 = +0.962" 10.094” 14.3
Ak = +0.563 :|:0.089 16.0
1r = —0.278 10.153 514
nn. 3] = 6.966 [221)] = 6.993 r = 10.357”.
On looking over the residuals it will be seen that some are large. But
it is doubtful whether any could fairly be omitted. It will be observed,
also, that there are changes in the signs of the residuals .which seem to
. correspond to sudden changes in the structural condition of the instru-
ment. However, the observations above and below pole ought to eliminate
such changes. '
In combining the above results, therefore, probably the reflected obser-
vations should be omitted. If the mean is taken of the values derived
from direct observations we have
A 'k = + 0.238”, or k = 20.683".
As stated before, in handling the meridian circle hereafter, I hope to
be able to make frequent reversals, and improve somewhat the accuracy
of the observations. It requires one day’s work with an assistant to re-
verse the instrument and readjust the microscopes. Microscopes of higher
magnifying power might be employed, also, for reading the circles, and it
is expected to make some improvement in this direction.
19.—Latitude.
To find the latitude from the Polaris observations the mean of the re-
sults reduced to 1900.0 can be taken, so that we have ‘








1900.0.
:5 m . . .
°’> Dmswn Div. Red. . Per.
Clamp Ea'St' o' 33' Z A???“ error. for runs. error.
2 m lcl‘. I. I
Above pole . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 86 46° 29' 34.53" 205° 04—06’ +0.75” +0.064” —0.041”
Below pole . . . . . . . ..' . . . . . . . . . . . . . . . . . . . . . . . 77 48 56 41.71 202 36—38 +0.47 —0.051 —0.041
Above pole, reflected . . . . . . . . . . . . . . . . . . .. 25 133 30 22.35 118 00—02 +0.17 —0.103 —0.053
Below pole, reflected . . . . . . . . . . . . . . . . . . .. 24 131 03 _ 14.58 120 28—30 +0.17 +0.042 —0.054 p
m Clamp West.
Above pole . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 64 46 29 39.46 298 00-02 —0.17 +0.148 —0.048
Below pole . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 63 48 56 46.76 300 28—30 —0.17 —0.101 —0.030
Above pole, reflected . . . . . . . . . . . . . . . . . . .. 26 . 133 30 22.44 25 04—06 —0.75 —0.142 —0.065
Below pole, reflected . . . . . . . . . . . . . . . . . . .. 28 131 03 15.44 22 36-38 —0.47 +0.09} —-0.014
|

A o for position of reflection basin = —0.02".
A-S-R
88 MICHIGAN ACADEMY or SCIENCE.
If now the mean is taken of these corrected zenith distances, each being
weighted unity, we have for the latitude
‘¢=+42° 16’ 48.78".
A few observations of 8 Ursae Min0ris, and 51H Cephei give respec-
tively 48.80" and 48.96”. They were taken like Polaris. above and below
pole, direct and reflected, but no division errors were applied.
I acknowledge gratefully a grant from the Bache Fund of the National
Academy of Sciences for assistance in computing.
.1
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