148 ANNUAL REPORT SMITHSONIAN INSTITUTION, 1919. 
19. The values of Dx and Dy were equated to expressions of the 
form 
az + by +¢+ aH, (= Dz) 
da + ey + f+ ak, (= Dy), 
and 
where a, y are the coordinates of the stars given in Table I, and 
E,, Ey are coefficients of the gravitational displacement. 
The quantities ¢ and f 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 6 and d depend mainly on the orientation 
of the two plates. The quantity a denotes the deflection at unit dis- 
tance (7. ¢., 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. Right ascension. Declination. 
11..| c—0.1606—1.261a—0.587a. ..| f—1.261d—0.160e+0.036a. 
5...] €—1.1076— .160a— .557a...| f— .160d—1.107e— .789e. 
4...) c+ .472b+ .334a— .186a...| f+ .334d+ .472e+-1.3360. 
3...| c+ .36004+ .348a— .222a...| f+ .348d+ .360e+1.574a. 
6...| C+1.0996+ .587a+ .080a...| f+ .587d+-1.099¢4- .726a. 
10. .| €+1.321b+ .860a-+- .158a...| f+ .860d-+-1.321e+ .589a. 
2...| c— .328b+-1.0790-+1.540a...| f-+1.079d— .328e— .156a. 
20. Normal equations formed from these equations of condition 
are as follows: 
TaBLE III.—Lclipse plates, right ascension. 
+7. 000c-+-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 42,534 =|] +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. 2710-+-1. 666¢+0. 28la=| —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. 988¢-+-2..366ae=| +-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. 2420=| +0.121 | +0.156 | +0.133 | +0.183 | +0.173 | +0.090 | +0. 180 
o=| +0.098 | +0.126 | +0.107 |. +0.148 | +0.140 | +0.073 | +0.145 
a=] +0.158 | +0.174 | +0.189 |'+0.127 | +0.128 | +0. 233 | +0. 169 
b=] —0.203 | —0.011 | +0. 048 | +0.007 | +0.042 | +0.066 | +0.042 
