DEFLECTION OF LIGHT—DYSON AND OTHERS. 167 
Denoting the value of the displacement at 50’ (or 10 réseau-in- 
tervals) from the center of the sun by x, the y-displacements of 
the various stars will be xa, where «, has the values tabulated below. 
We can therefore obtain x, by solving by least-squares the equations 
Ay = f+ ey. 
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 EK, = 184¢,, and determine the correction to « 
from the residuals A,y. We also remove the mean of A,y obtaining 
the final residuals. 
The normal equations corresponding to equations of condition 
residual = df + ay ox 
are found to be 
5df-+2.838% —— 1 
2.8387/-+4.833% — +64 
whence 
3.236% = +64, 
ox = +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 4E,, obtaining A,z, and then tabulate 
the residuals from the mean values—5942. 
The successive steps are shown below: 
Resid. 
Star. oS YIN 3-82, 6-9y. At. Ez. Ast. | +163y.] “at. Aat.. | Canit= 
; 0-003’) 
PPh yy ree 228 1.39 |—3, 916 5 86 |—4, 007 —76 |—3,931 | 2,021 |—5, 952 |—5, 927 + 15 
EF eos ace, aS 12.40 |—5, 518 47 20 |—5, 585 —79 |—5, 506 478 |—5, 984 |—5, 958 — 16 
val Bel eine 17. 34 |—2, 869 66 129 |—3, 064 —54 |—3,010 | 3,051 |—6, 061 |—5, 043 —101 
Bia eles wa aes 17. 48 |—2, 924 66 121 |—3, 111 —69 |—3,042 | 2,869 |—5,911 |—5, 888 + 54 
Spey 4442 19. 87 |—1, 568 75 172 |—1,815 |, + 3. |+1,818'|. 4,075 |—5,893 |—5, 894 | . + 48 
Star y Ay 6-92 38-6y Ai. | —163z Assy Ey Ay. ay Resid 
i ease Wes 12.40 | 6,398 10 479 | 5,909 |— 227) 6,136] + 6] 6,130] +0.03 + 5 
by cxpcas lps ae SA 2.93 | 4,121 86 113 | 3,922 |—2,021 | 5,943 | —127] 6,070 | —0.69 — 55 
Aerie ciee ee 18.72 | 4,512 120 722 | 3,670 |—2,826 | 6,496 | +234] 6,262 | +1.27 +137 
Ba...) Oe 97.60 4,236 121 679 | 3,436 |—2,849 | 6,285 | +272] 6,013] +1.48}] —112 
a 24.99 | 4,148 137 965 | 3,046 |—3,239 | 6,285] +136| 6,149] +0.74] + 24 
