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Let us now consider certain variations of the personal equation in which the condition of the observer is not taken into account. I'. Does a change in the character of the illumination of the

wires affect the personal equation?

Bright wires minus faint wires. Dec. 22= +027s; very faint. 24 +024; faint.

-001 28

+016; moderately faint. Jan. 13

+060; extremely faint. II?. Does the personal equation vary between a natural and an

artificial illumination of the wires.

Natural minus artificial.
May 26=–0028

31 -•011
June 2 -026

2 -011

2 --000 These observations were made during the day time. The artificial illumination was produced in the way already described, the clock-room being darkened. III2. Does the size of the sturs observed affect the personal equa

tion. From Nov. 20, till Nov. 29, only five stars were employed, the first one being larger than the others.

R.-T, from Nov. 20 till Nov, 29.
Large star.

Small stars.
-2338

-1448—•1678—1539--166
Large star minus mean of small stars.

—-2338—(-152°)=--081%.
First wire minus each of the following wires from Nov. 20 till Nov. 29.

R. +0528 + .0498 +.0345 +.053

·0406 — 0228_0498 -- .033s =+0.478

--0368 Difference =R-T=-.083%. I must remark, however, that I did not find a well-defined corresponding difference between bright and faint stars in the observations for relative personal equation with the equatorial. IV2.-Does a variation of the interval between the wires affect

the personal equation? From May 26 till June 27, ten stars were attached to the cylinder, the first three being separated by an interval of from

22

ten to fifteen seconds, and the last seven by an interval varying between two and three seconds.

R-T.
Mean of the first three wires.

Mean of the last seven wires.
May 26 -2018

-'068% June 2 *080

075 4 *086

•088 9 .187

•059 15 •116

052 17 •155

•091 22 •152

.051
26 •122

·064
Differences.
May 26 -1335
June 2 ·005

4 .000
9 •128 Mean --0699
15

*064
17

*064

101

26 *053 While these differences do not agree well with each other they all have the same sign. The disagreement is without doubt partly due to certain local disturbances on some of the wires, which will be noticed under the next head. V.-Does the shape of the stars observed affect the personal equa

tion? By comparing the values R.-T. for each star, I found in several instances that two and sometimes three stars gave results widely differing from the rest, for two or three days at a time, after which the difference would disappear. As these differences did not occur in the values R.-B., it is evident that the variations were mainly due to the observations of T. I can attribute this to no other cause than the influence which the shape of the stars had upon the judgment of the observer in determining the time of transit. In actual observations of bright stars there is no doubt but that projecting wisps of light affect the personal equation. Something analogous to this may have occurred in the present instance. I can assign no reason for the recurrence of the disturbances.

I close this investigation with the following inquiry: Does the relative equation derived from artificial stars agree in

value with that derived from actual observations with the transit instrument?

This inquiry is an important one ; for if this agreement is found to exist, it will then be easy to free longitude from the

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error arising from the variability of personal equation, by determining the value of this function by means of artificial stars, the observations for this purpose being nearly coincident with those of longitude.

The observations of actual stars were made with the equatorial, four, of four wires, constituting a complete set. Thus :

R observed the first four wires.
T
R

T Reducing each observation by the interval from each wire to the mean of the wires, and taking the arithmetical mean of the results, the relative equation was found free from the error of wire intervals. R.-T. from the equatorial.

R.-T. from artificial stars. May 31 =- --08$

-1135 June 2 ·11

·079 4

*087 9 •16

•103 .09

•071
17 06

•110
22
•16

085 Mean from 880 compari

Mean from 1,000 comparisons,

-116.
sons,

--0938 I do not positively assert that this agreement will exist in every case, because

(a.) The result might have been different had the observations been made with the transit instrument.

(6.) The same agreement might not exist with other observers.

I do not consider that the results which I have found, settle definitively any point except the general variability of the personal equation. The conditions of the problem are so complex that it is impossible to assume one condition and reject the consideration of all others. The last inquiry is worthy of further investigation, as affording the means of obtaining the most probable value of the relative equation.

15

ten to fifteen seconds, and the last seven by an interval varying between two and three seconds.

R-T.
Mean of the first three wires.

Mean of the last seven wires.
May 26 -2015

--0689 June 2 *080

075 4 •086

*088 9 •187

·059 15 •116

•052 17 •155

*091 22 •152

.051
26 •122

•064
Differences.
May 26 = -1335
June 2 ·005

4 .000
9 •128 Mean -0695
15 ·064
17 064
22 •101

26 .053 While these differences do not agree well with each other they all have the same sign. The disagreement is without doubt partly due to certain local disturbances on some of the wires, which will be noticed under the next head. V.-Does the shape of the stars observed affect the personal equa

tion? By comparing the values R.-T. for each star, I found in several instances that two and sometimes three stars gave results widely differing from the rest, for two or three days at a time, after which the difference would disappear. As these differences did not occur in the values R.-B., it is evident that the variations were mainly due to the observations of T. I can attribute this to no other cause than the influence which the shape of the stars had upon the judgment of the observer in determining the time of transit. In actual observations of bright stars there is no doubt but that projecting wisps of light affect the personal equation. Something analogous to this may have occurred in the present instance. I can assign no reason for the recurrence of the disturbances.

I close this investigation with the following inquiry: Does the relative equation derived from artificial stars agree in

value with that derived from actual observations with the transit instrument?

This inquiry is an important one ; for if this agreement is found to exist, it will then be easy to free longitude from the

first 6

error arising from the variability of personal equation, by determining the value of this function by means of artificial stars, the observations for this purpose being nearly coincident with those of longitude.

The observations of actual stars were made with the equatorial, four, of four wires, constituting a complete set. Thus :

R observed the first four wires.
T

last
R

T Reducing each observation by the interval from each wire to the mean of the wires, and taking the arithmetical mean of the results, the relative equation was found free from the error of wire intervals. R.-T. from the equatorial.

R.-T. from artificial stars. May 31 =-088

-113s June 2 •11

079 4 •15

*087 9 •16

•103 15 09

071 17 06

•110 22 •16

•085 Mean from 880 compari

Mean from 1,000 comparisons,

-116%.
sons,

--093% I do not positively assert that this agreement will exist in every case, because

(a.) The result might have been different had the observations been made with the transit instrument.

(6.) The same agreement might not exist with other observers.

I do not consider that the results which I have found, settle definitively any point except the general variability of the personal equation. The conditions of the problem are so complex that it is impossible to assume one condition and reject the consideration of all others. The last inquiry is worthy of further investigation, as affording the means of obtaining the most probable value of the relative equation.

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