ASTRONOMY: SEARES, VAN MAANEN AND ELLERMAN 
7 
About 50 values of A were available for each line on each day. Means were 
found for groups of 5 or 6 adjoining displacements, thus giving 8 or 10 
observation equations of the form (4) for a least-squares determination of x 
and y. 
The individual values of A for September 2, 1914, a series of average weight, 
are plotted in Fig. 1 against the latitudes as abscissae. The close agreement 
with a sine curve of the type of equation (3) appears at a glance. The calcu- 
lated displacement-curves corresponding to the values of x and y derived from 
these data, are also shown in the figure. Their ordinates for 0 = 0, namely, 
+0.8, +1.0, and +0.5 respectively, are of the order of the small quantities 
S 60° 40° 20° 0° 20° 4JT 60° N 
1914 Sept. 2 
X524 7.737 
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• 
• • 
• • 
.• — — — • 
• 
• 
« 
• 
X5 3 00.9 2 9 
• 9 
1 — 8 * * 
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9— :— — 
J*— • " 
X5329.329 
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-•~S . 
s 
FIG. 1. DISPLACEMENT-CURVES FOR 1914, SEPTEMBER 2 
Abscissae are heliographic latitudes. Ordinates are displacements, the scale being 1 di- 
vision of diagram = 0.005 mm. The curves, which correspond to equation (1), have been 
derived from the observed values of A. Their ordinates for <p = 0 represent the combined 
influence of k, D, i, and X. These data for the three lines give Y = tan i cos X = +0.213 
which is plotted as a single point in Fig. 2, together with similar values of Y for each of the 
other dates. 
which differentiate the displacement-curve (1) from the curve (2) and indicate 
the precision with which the curves must be located in order to determine the 
value of i. 
Having found x and y from each line for each day, the results were combined 
by (6) to form weighted mean values of F, which were then plotted with the 
times as abscissae. These should define a sine curve whose amplitude and 
period are, respectively, tan i and P. The individual points are reproduced 
in Fig. 2, from which approximations for i, P and t 0 were easily derived. The 
final values and their probable errors 
i = 6?2 ± 0?4, P = 31.79 ± 0.31 days 
h = 1914, June 25.31 ±0.42 days, G. M. T. 
