DEFLECTION OF LIGHT — DYSON AND OTHERS. 
167 
Denoting the value of the displacement at 50' (or 10 reseau-in- 
tervals) from the center of the sun by y«, the y-displacements of 
the various stars will be xa^, where oLy has the values tabulated below. 
We can therefore obtain /,, by solving by least-squares the equations 
The radius of the sun during the eclipse was 15.78'. Hence the 
full Einstein displacement of 1.75" corresponds to 0.55'' at 50' dis- 
tance, or, in our units of 0.003", x = 184. It is easily seen that the 
value is somewhere near this, and it is therefore easier and more 
instructive to take out Ey z= 184a2^, and determine the correction to /. 
from the residuals A42/. We also remove the mean of A^y obtaining 
the final residuals. 
The normal equations corresponding to equations of condition 
residual :=.lf -\- (Xy S/, 
are found to be 
whence 
5S/-|-2.83B)^ m — 1 
2.83a/-f4.83S% = -f-64 
3.23av^ 
+64, 
+20. 
An increase of 20 on 184 corresponds to an increase of 0.19" on 
1.75". Hence the resulting deflection at the limb is 1.94." 
Since the full deflection is indicated we complete the results for x 
by taking out the remaining JE^;, obtaining A^o?, and then tabulate 
the residuals from the mean values — 5942. 
The successive steps are shown below : 
star. 
I. 
Ax. 
3-8l. 
6-9y. 
All. 
JE.. 
A2I. 
+ 163y. 
A3I. 
A4I. 
Resid. 
(unit= 
0-003"). 
11 
1.39 
12.40 
17.34 
17.48 
19.87 
-3,916 
-5,518 
-2, 869 
-2,924 
-1,568 
5 
47 
66 
66 
75 
86 
20 
129 
121 
172 
-4,007 
-5,585 
-3,064 
-3, 111 
-1,815 
-76 
-79 
-54 
-69 
+ 3 
-3,931 
-5, 506 
-3,010 
-3,042 
-1,818 
2,021 
478 
3,051 
2,869 
4,075 
-5,952 
-5,984 
-6, 001 
-5,911 
-5, 893 
-5, 927 
-5,958 
-6,043 
-5, 888 
-5, 894 
+ 15 
5 
- 16 
4 
—101 
3 
6 
+ 54 
+ 48 
Star. 
V- 
Ay. 
6-9x. 
38-6y. 
Aty. 
-163x. 
A3y. 
Ey. 
A^y. 
ay. 
Resid. 
11 
12.40 
2.93 
18.72 
17.60 
24.99 
6,398 
4,121 
4,512 
4,236 
4,148 
10 
86 
120 
121 
137 
479 
113 
722 
679 
965 
5,909 
3,922 
3,670 
3,436 
3,046 
- 227 
-2,021 
-2,826 
-2, 849 
-3,239 
6,136 
5,943 
6,496 
6,285 
6,285 
+ 6 
-127 
+234 
+272 
+ 136 
6,130 
6,070 
6, 262 
6,013 
6,149 
+0.03 
-0.69 
+ 1.27 
+ 1.48 
+0.74 
+ 5 
5 
- 55 
4 
+ 137 
3 
—112 
6 
+ 24 
