166 ANNUA!. REPORT SMITHSONIAN INSTITUTION, 1919. 
PLATE X. 
(1) GoTTiparison with Oxford plate G^. — The differential refrac- 
tion for all the eclipse plates is 
a=: — 46.5, h,d — -\- 8.2, e = — 27.0, 
the differential aberration being zero. 
For the comparison plate G^ 
a = —19.1, h,d = +0.7, e= — 28.3. 
Hence for X — G^ 
a=z- 27.4, hyd= + 7.5, e — -\- 1.3. 
To these must be added the terms representing change of scale, 
determined from the check plates (Table XIII.), viz. 
« = + 31.2, h,d=z- 0.6, e = -\- 37.3. 
Hence the whole difference X — G^ is given by 
a=-{- 3.8, h,d=-\- 6.9, e = + 38.6. 
The first step is to take the measured differences Aa^, Ay, and take 
out the parts ax -f- hy, dx -\- ey, due to these terms, leaving the cor- 
rected differences A^a?, A^?/. 
Aj^a? and A^y contain (1) the Einstein displacement, if any and 
(2) the unknown relative orientation of the plates giving rise to 
terms of the form, Ax = -{- 6y, Ay = — Qx. These two parts could 
be separated by a least-squares solution, but in view of the poor 
quality of the material it seems better to adopt a method which 
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 from the 
a?-measures. However, it is clear from preliminary trials that a 
displacement exists — whether the half or the full Einstein dis- 
placement. Hence if we take out three-quarters of the full Einstein 
displacement (l^x) we divide the already slight effect by 4, and at 
the same time deal fairly between the two hypotheses.^ ^ The residuals 
A2a5 result. 
From the equations AoX = c -{-^y we determine by least squares 
the orientation 6, which is found to be +163. Kemoving the term 
163y we obtain the residuals A^x. 
Turning to A^y, we correct for the orientation by taking out the 
term — 163a7, leaving A^y. These values should agree for all the 
stars, except for the displacement and the accidental error. 
"The smaller the displacement provisionally assumed for x, the larger is the displace- 
ment ultimately found from y (see p. 171). 
