﻿HOWARD: ANNUAL PARALLAX 



189 



Assuming jR, = 1 1.5300", ^0=50*^, and substituting the values 

 given above in the equation of condition, we get the following con- 

 ditional equations: 







V . 





vv. 



2Q4r ^11 0 0027 



- 0 



+ 0 01X 



0. 



000324 



28Qr 4- ?y 0 01. '^1 



= 0 



- 0.006 



0. 



000036 





- 0 



0 001 



0. 



000001 



Q1 2r + ?y 0 007fi 



= 0 



0.000 



0. 



000000 



'^OOr -1- ?/ 0 000 1 



- 0 



— VJ 



+ 0 006 



0, 



000036 



. yj yj yj vj > j yj 



4- 1 Qfir 4- 77 0 00^3 



= 0 



- 0.006 



0 



000036 



+ 69x + i!/ + 0.0142 



= 0 



+ 0.014 



0 



.000196 



+ 276x + i/ + 0.0130 



= 0 



+ 0.009 



0 



.000081 



+ 242x + ^/- 0.0071 



= 0 



- 0.010 



0 



.000100 



+ 144x + ?/ + 0.0137 



= 0 



+ 0.012 



0 



.000144 



+ 81x + ?/- 0.0025 



= 0 



- 0.003 



0 



.000009 



+ 127x + y - 0.0038 



= 0 



- 0.005 



0 



.000025 







[vv] 



= 0 



.000988 



The normal equations are: 



668644X - 360?/+ 13.1714 = 0 

 - 360x+ 12?/ - 0.0083 = 0 



from which 



x = - 0.000019 - 0.000006 

 y = + 0.000126 - 0.000018 



since Ro = Ri + y 



Ro = 11.53126 - 0.000018. 



11.5313 = the adopted value; now 



11.53126 



1 + (r - ro)x 



11 .5313 [1 - (t. - t)x] approximately. 

 11.5313 + 0.000219 (50 - r) which is the value used. 



Assume R ] = 

 R = 



R = 



The obtained values of R must now be divided into three groups. 

 The first group containing all values of R obtained at a tempera- 

 ture above 70°; the second all values near 40°; and the third, all 

 those at a lower temperature. Then taking the mean of the temper- 

 atures and the mean of the i^'s in each group and computing the 

 values of R, correcting for temperature, we get the following results: 



