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Date. Equation.

Remarks.
Date. Equation.

Remarks. 1867.

1868. Nov.

April. 8 -.040Abnormal.

27-8–.0338 Time, 9h a. M. 12 ·047 42°=read'g of thermometer. 27-8 *051 Time, 9th A. M. Dec.

27–8 •011 Time, 2h P. M. Slept from 12= 0838-4°. Hands protected with

12h till 2h. cotton gloves.

27–8 851 Time, Th P. u. Engaged in 12 *030-40 Hands unprotected.

severe exercise from 4h till 12 *080—3°. Hands protected. May.

[. 12 •072-3°. After warming; hands 26 --042 Observed by day-light. unprotected.

26 041

• lamp-light. 12 ·061 42o. Regular beat of chro- 26 050 ) Severe physical exercise benograph pendulum.

tween these observations. 16 024 340 "

26 •032 ) Very tired. 16. 040 350. Irregular beat. 31 .051 Day-light. 16 -061 350. Regular beat.

31 ·040 Lamp-light. 16 054 9o Normal.

31 -019 After observation with the 16 039 38°. Normal.

equatorial for relative equa16 .036 380. Abnormal.

tion. Tired. 22 *034 Bright wires.

June. 22 .061 Very faint wires.

2 -- .045 Day-light. 24 *032 Bright wires.

2 ·019 Lamp-light. 24 *053 Moderately faint wires. 2 .034 Day-light. 24 ·023 Bright wires.

2 •045 Lamp-light. 23 ·040 Bright wires.

4 •033) Observed with the equatori28 ·039 Faint wires.

al from 8h P.M. till 11h. Slept 28 ·023 Bright wires.

4 ·040 | from llh P. M. till 1h 30m. A. 1868.

M. Watched with the sick Jan.

5 ·027 1 till 5 A. M. Time of obser. 13 –.057 Bright wires.

vation, 5h 30m A. M. 13 •118 Very faint wires.

9 *033 Normal. 13 061 Bright wires. Abnormal., 15 ·024) Slept very little June 14. 13 ·065

Normal.

Slept from lh P. M. till 3h. 13 078 Dark field.

15 018 Time of observation 3h P. M.

s 13 .087 Normal.

17

-055 After severe exercise. Feb.

22 053 Normal. 10 •075 Thermometer =33°. 26 (45 Normal. 10 -067

26 046 Normal. 22 .069

26 ·019) Assumed that I observed too

22 22 039

late. No knowledge of the 22 035

27 ·008 ) value of my equation. April.

27 028 Normal. 27-8--040 Observed from 8 P. M., Apr. 28 -040) Normal. 27-8 045 27, till 5h A. M. Apr. 28, at 28 •013 | Hungry. 27-8 .077 irregular intervals; the in-28 010 27–8 •069 tervening time being occu- 28 *018 27-8 .049 pied with observations in the 28 007 Ate nothing for 30 hours.

prime vertical for latitude. 28 .007 27-8 .04) Very tired and sleepy. 28 .006 27-8 .029 Time of observation, 8h A.M. 28 .007

Slept from 5h till 8h A. M. 28 - .001) Very hungry.

30 340.

8o. 34o.

TOMLINSON. Nov. 19= +:096% Nov. 24=+:1498 20 116

25 .180 21 116

26 204 22 .139

27 179 23 .167

28 •163 29 *213

June 15 -027

BABcocК. . Nov. 21=+035* 23

+013 24 - 007 25 *000 26

+011 27

+018

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+.047

21

Feb. 10=+.0369 June 15

7:0478 Nov. 29 -030* 10 -.037

17
055

Feb. 10 *035 Apr. 27

22 032

10 •143 May 31 062

26 036

Apr. 27

*071 June 2 •034

27 +:047

27 - 137
4 054
9 +070

Relative Personal Equation.
ROGERS minus TOMLINSONS

ROGERS minus BABCOCK=
R_T.

R-B. Nov. 195-214 Apr. 27-8=–0983 Nov. 22 -112* 20 •209 May 31 •113

23 •101 •163 31 •102

24

-.040 22 •161 31 •081

25

+.025 23 .255 June 2 ·079

26 +.008 24 •196 2 •053

27 016 25 •155 2 .068

29 +047 26 .185

2 079 Feb. 10 -040 27 145 4 •087

10 +076 28 •144

4 094

Apr. 27-8 031 29 .196 4 *081

27-8+026 Feb. 10 •111

9
103

27-8-006 10 .030

15

-061 Apr. 27–8 •087

15

065
27-8 092

17 •110
27-8
•12+

22 •085
27-8 •116

26 •081 27-8 .096

26 082 27-8 .088

26 •055 27-8 076

27-8 .055 27-8 *080

27--8 •075 27-8 098

27-8 -'087 27-8-058 It will be evident from an examination of the values given above, that personal equation is a varying quantity, if it can be shown that the variation exceeds the probable error of obseryation. Without going into details, I give below the value of the probable error from each source, depending upon a sufficiently large number of observations: L Probable error of observation for each starten revolutions,

R=#013
T-Ł017

B=+:016
II. Probable error of each reading on the scale =t:02
III Total error derived from a change in the

common unit of measurement as affected
by a variable beat of the chronograph
pendulum, (estimated),

>Ł:02

IV. Error of centering a single star, ==:02 (estimated).
V. Error arising from the condition that the re-

volving pins may not have been in a verti-
cal plane with the stationary ones at the
instant of conjunction,

=+005 (estimated). VI. Parallactic error, arising from the par-) Inappreciable, the re

allax of the two wires at the instant volving wires almost of observation.

touching the fixed one

at their transit. With regard to these errors it is to be observed :

(a.) Since there were an average of 8 artificial stars attached to the cylinder, and the observations were on the average continued through 10 revolutions, each result depends on about 80 observations. The probable error of observation and reading for the final result must therefore certainly be less than +.01. No allowance has been made for the third source of error. While it was not difficult to detect the error itself by a change in the measured length of the comparison unit, it was so variable in amount between the extreme limits +.02s and — •025, that I did not find it possible to deduce a definitive mean value. I am confident, however, that the final result for any date cannot be affected with so large an error as +005s.

(6.) Errors IV and V affect the absolute equation; but in considering the variability of this function, they are to be disregarded, since the wire frame work, the wires and the stars, remained absolutely in the same position from day to day, unless purposely disturbed. So also, these errors are eliminated, if the observations are for relative personal equation.

It is therefore obvious that the change manifest in the value of the personal equation, whether absolute or relative, cannot be accounted for either as instrumental errors, or as errors of observation, but must be due to the external conditions under which the observations were made. Having determined the fact of the general variability of the personal equation, let us now consider the variations due to certain given physical conditions.

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1. Does the personal equation vary between a normal and an abnormal position of the body during observation ?

Normal position minus Abnormal.
R.-Dec. 6=-031

7 -002 8 -002

16 -003 Jan, 13 --004 13 -026

Mean=-0115

-3°

13

Thus, while the change is not large, every series of observations gives the same sign. It will not answer, however, to assume, either that the mean value remains constant, or that another observer would find the same value, since several conditions contribute to the result found. In reading up the records, the rather curious fact was noticed, that the probable error of observation was less for an abnormal than for a normal position of the body. II. Does a change of temperature affect the personal equation? Absolute.

Relative.
R.
Dec. 12 42° -(-4°)=+.0365

Feb. 10.
12
42°
-4°)=-014

Change.
12 42°—
-3°)=+.019

B.-T.

38=+071
12 42°
- 011

-2° t.105 0348 Jan. 13 35° -9°)=–.007

389

-9°)=+015 Feb. 10 389

-3° -008
22 34°-1-8°)=-'030

T.
Feb. 10 38°—(-3°)=+:073 R.-T.

38°=t:1085

-2°=+.028 *080 B. Feb. 10 38°-(-30)+107

s 38°=+:037*

•114 The observations for ordinary temperature were made in the clock-room. For the low temperature observations, an aperture about 1.5 inch in diameter was made through a pane

of window glass and the theodolite was placed on the outside. The first and third set of observations for Dec. 12 were made with gloved hands, the second and third with hands unprotected. It will be seen that in my own case, the change is slight, while with B. and T. it is large. The values depend upon very careful observations continued through 20 revolutions of the cylinder. The probable error for high and low temperature did not sensibly vary with myself and B., but was about +.005s larger for low temperature in the case of T. III. Does an exhausted state of the system produce a variation of

the personal equation? It will be seen from the observations of Apr. 27–8, May 26– 31 and June 4-5-15-17, that no decisive change resulted from extreme weariness. The mean effect was a slight tendency to diminish the equation by an amount hardly measurable with certainty. This result was contrary to my anticipations, and if confirmed by other observers, establishes a fact of much im

R. – B. { -*

portance, inasmuch as astronomical observations are usually carried far into the night.

In every instance, the equation was quite largely diminished when the observation was made directly after waking from a sleep preceded by extreme exhaustion. Here, as before, I found that an abnormal condition rather improved the probable error of observation. IV. Does hunger affect the value of the personal equation?

Normal state minus a state of hunger.
June 27-8=-027

030
022
032
•034
•034
·034
034

•033

-039 There is thus a decided and quite regular change, the mean being —-032 V. Does the mental state of the observer have any influence on the

personal equation ?
Normal state minus a state in which the observation is assumed too late.

Nov. 20–1=- --036
June 26 --026

27 -038 I have already remarked that I obtained the first knowledge of the value of my personal equation, Nov. 21, 1867, and that after Nov. 29 I had no farther knowledge of its value, till after all the observations were completed, not in fact till I read up the records in July, 1868. As the value for Nov. 29 was positive, I arbitrarily assumed it negative in order to ascertain the effect of this assumption upon it. The result confirms the suspicions which I have for some time entertained, that the simple knowledge of the value of one's personal equation induces a tendency to reduce its value. Since constancy in value is more desirable than this reduction, which is uncertain and variable, it follows that it may not be best for an observer to have a knowledge of his personal equation. I ought to remark, however, that the expectation of having my suspicions on this point confirmed, may have had something to do with the results found, though I endeavored to free my mind from every bias except the single one assumed.

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