322 
SIK F. W. DYSON, PROF. A. S. EDDINGTON AND MR. C. DAVIDSON ON A 
To these must be added the terms representing change of scale, determined from 
the check plates (Table XIII.), viz., 
d = 31 ‘2, h, d — 0 • 6, 6 = “h 37 ■ 3. 
Hence the whole difference X — Cb is given by 
(I = “h 3*8, h, d = d“ 6*9, 6 = -F 38*6. 
The first step is to take tlie measured differences Ax, \y, and take out the parts 
ax b tbie to these terms, leaving the corrected differences A^x, Ayj. 
AiX and Ayj contain (1) the Einstein displacement, if any, and (2) the unknown 
relative orientation of the plates giving rise to terms of tlie form, Ax = ^ 6y, Ay = — 6x. 
These two parts could be separated by a least-scpiares solution, but in view of the poor 
quality of the material it seems better to adopt a method wliich keeps a better check 
on possible discordances and shows more clearly what is happening. The Einstein 
displacement in x is small, and we might perhaps neglect it altogether in determining 6 
from the a;-measures. However, it is clear from preliminary trials that a displacement 
exists—whethei' the half or the full Einstein displacement. Hence if we take out three- 
quarters of the full Einstein displacement (|E^) we divide the already slight effect by-4, 
and at the same time deal fairly between the two hypotheses.* The residuals dgcr result. 
From the equations A 2 X = c -f- % we determine by least squares the orientation 0, 
which is found to be + 163. Ilemoving the term 163^ we obtain the residuals Ayr. 
Turning 00 A^y, we correct for the orientation by taking out the term —163a;, leaving 
A .y. These values should agree for all the stars, except for the displacement and the 
accidental error. 
Denoting the value of the disj^lacenient at 50' (or 10 reseau-intervals) from the centre 
of the sun by k, the ^-displacements of the various stars will be where has the 
values tabulated below. We can therefore obtain k by solving by least-squares the 
ecpiations 
=/”l- '<«//• 
The radius of the sun during the eclipse was 15' • 78. Hence the full Einstein displace¬ 
ment of l"-75 corresponds to 0"-55 at 50' distance, or, in our units of 0"-003, /c = 184. 
It is easily seen that the value is somewhere near this, and it is therefore easier and 
more instructive to take out E,^ = 184a^, and determine the correction to k from the 
residuals A^y. We also remove the mean of A.{y olRaining the final residuals. 
The normal equations corresponding to equations of condition 
residual = 8/ -j' S/c 
* The smaller the displacement provisionally assumed for x, the larger is the displacement ultimately 
found from y (see p. 327). 
