322 SIR 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., 



a= + 31-2, b, d= 0-6, e= + 37-3. 

 Hence the whole difference X G! is given by 



a = + 3-8, b, d!= -|-6-9, e= + 38-6. 



The first step is to take the measured differences Ax, Ay, and take out the parts 

 (ix -\- by, dx -f- ey, due to these terms, leaving the corrected differences A&, A-^y. 



A t x and A l 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 + Qy, Ay = 6x. 

 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 displacement. Hence if we take out three- 

 quarters of .the full Einstein displacement (f E 3 ) we divide the already slight effect by 4, 

 and at the same time deal fairly between the two hypotheses.* The residuals A 2 x result. 



From the equations A^x = c -f- Oy we determine by least squares the orientation 6, 

 which is found to be + 163. Removing the term 163y we obtain the residuals A : jc. 



Turning fco AJJ, we correct for the orientation by taking out the term 163x, leaving 

 A..y. These values should agree for all the stars, except for the displacement and the 

 accidental error. 



Denoting the value of the displacement at 50' (or 10 reseau-intervals) from the centre 

 ol! the sun by K, the ^/-displacements of the various stars will be /ca y , where a y has the 

 values tabulated below. We can therefore obtain K by solving by least-squares the 

 equations 



/J :#=/+ KCL ,r 



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, K = 184. 

 It is easily seen that the value is somewhere near this, and it is therefore easier and 

 more instructive to take out E y = 184a y , and determine the correction to K from the 

 residuals A t y. We also remove the mean of A$ obtaining the final residuals. 



The normal equations corresponding to equations of condition 



residual = S/ -f a y S/c 



* The smaller the displacement provisionally assumed for x, the larger is the displacement ultimately 

 found from y (see p. 327). 



