148 
ANNUAL REPORT SMITHSONIAN INSTITUTION, 1919. 
19. The values of T)x and T)y were equated to expressions of the 
form 
ax -\- hy -\- c -{- <xEx (= Da;) 
and 
dx-^ey + f+a^yi^Dy), 
where x, y a,re the coordinates of the stars given in Table I, and 
Ea,, 'Ey are coefficients of the gravitational displacement. 
The quantities c and / are corrections to zero, depending on the 
setting of the scale plate on the plate measured, a and e are differ- 
ences of scale value, while h and d depend mainly on the orientation 
of the two plates. The quantity a denotes the deflection at unit dis- 
tance (i. e., 50' from the sun's center), so that aE^; and aE^, are the 
deflection in right ascension and declination, respectively, of a star 
whose coordinates are x and y. 
The left-hand sides of the equation for the seven stars shown are : — 
No. 
11.. 
5... 
4... 
3... 
6... 
10.. 
2... 
Right ascension. 
Declination. 
c-0.1606-l.261a-0.587a. . . 
C-1.1076- .160a- .557a... 
c+ .4726+ .334a- .186a... 
c+ .3606+ .348a- .222a... 
C+1.0996+ .587a+ .080a... 
C+1.3216+ .860a+ .158a... 
c- .3286+1.079a+1.540a... 
/-1.261d-0.160e+0.036a. 
/- Ae0d-l.l07e- .789a. 
/+ .334d+ .472p+1.336a. 
/+ .348(f+ .360f+1.574a. 
/+ .587d+1.099f+ .726a. 
/+ .860d+1.321f+ .589a. 
f+1.079d— .328e- .156a. 
20, Normal equations formed from these equations of condition 
a re as follows : 
Table III. — Eclipse plates, right ascension. 
I. 
11. 
III. 
IV. 
V. 
VII. 
VIII. 
+7. OOOc+1. 6576+1. 787a+0. 226a= 
+ 2. 159 
+2. 986 
+3.250 
+2.461 
+2. 185 
+3. 263 
+2.648 
+4.664 +2.089 +0.335 = 
-0.063 
+0. 986 
+ 1.320 
+0. 866 
+ 1.051 
+ 1.464 
+ 1.130 
+4.094 +2.534 = 
+ 1.034 
+ 1.689 
+ 1.866 
+ 1.469 
+ 1.480 
+ 1.972 
+ 1.723 
+3.142 = 
+0. 712 
+0.919 
+0.924 
+0. 860 
+0. 844 
+0.930 
+0. 973 
+4. 2716+1. 666a+0. 281a= 
-0.575 
+0.278 
+0.550 
+0.283 
+0.533 
+0. 691 
+ 0.502 
+3.683 +2.476 = 
+0. 483 
+0. 928 
+ 1.037 
+0. 841 
+0.923 
+ 1.140 
+ 1.048 
+3.135 = 
+0. 643 
+0. 823 
+0. 820 
+0. 781 
+0. 774 
+0. 826 
+0. 888 
+2.988a+2.366a= 
+0. 707 
+0. 820 
+0. 822 
+0. 731 
+0. 715 
+0.871 
+0.852 
+3.116 = 
+0.681 
+0.805 
+0. 784 
+0. 762 
+0. 739 
+0. 780 
+0. 855 
+ 1.242a= 
+0. 121 
+0. 156 
+0. 133 
+0. 183 
+0. 173 
+0.090 
+0. ISO 
a= 
+0.098 
+0. 126 
+0. 107 
+0.148 
+0. 140 
+0.073 
+ 0. 145 
0= 
+0. 158 
+0. 174 
+0. 189 
+0. 127 
+0. 128 
+0. 233 
+0. 169 
6= 
-0.203 
-0.011 
+0. 048 
+0. 007 
+0.042 
+0. 066 
+0. 042 
