oclxvi 



FUNDAMENTAL EQUATIONS. 



We have here five systems of equations, if we choose to count the groups furnished by two 

 observations at Altona, which are given for the sake of completeness and which appear to be of 

 high excellence, although the details of the reduction are wanting. The number of unknown 

 quantities is brought down from ten to eight by rejection of the terms containing u. The 

 solution of the additional equations for semidiameters, (those from direct and those from 

 indirect measurements being combined,) gives for the Santiago Equatorial t = + 0&quot;.6214, if 

 we assume u t = 0. Under the same circumstances the meridian-circle at Santiago gives 

 tj = 0&quot;. 51*79. This last value, being negative, was so unexpected that it seemed desirable 

 to incorporate with it the corresponding value deduced from observations at the other conjunction. 

 By the Venus II series of measurements t = 0&quot;.2868 when u = ; and the combination of 

 the results according to the weights, gave t = 0&quot;.3879, which value was introduced into the 

 system of equations. Our unknown quantities are thus reduced to six, and for the experimental 

 combination and solution, which gave 



V = + 0&quot;.595, 



the t of the Greenwich group was disregarded. 



We have then the annexed fundamental equations, which contain only four unknown 

 quantities besides the Santiago and Greenwich t. 



Fundamental Equations for Venus /. 



Santiago Equatorial .... 247.710 x 74. 402 y + 380.398 z +243. 687 v +272. 519 w 101.43 =0 



Santiago Meridian 70.000 x 9.090y + 89.606 z + 33.092 w +216.648 =0 



Washington Equatorial . . . 51. 700 x 57. 540 y + 84.506 z 94.753 w 73-58 =0 



Greenwich Meridian .... 17. 000 x + 8.781 y + 32.410 z + 9.000t - 38.509 \v + 39.92 =0 



Altona Meridian 2.000x + 4.564y + 4.174z - 3.974 w 2.500 =0 



Santiago Equatorial .... 74. 402 x + 950.347 y -140. 582 z 123.942 v 51. 518 w 1246.99 = 



Santiago Meridian 9.090x +224. 002 y 22.218 z + 17. 679 w 297.917 =0 



Washington Equatorial . . . 57.540 x +211. 264 y 135.610 z + 94.506 w 117.64 =0 



Greenwich Meridian .... 8.781 x + 81. 024 y + 18.684 z + 5.797 t - 16. 205 w 101.30 =0 



Altona Meridian 4.664x + 10. 434 y + 9.561 z 9.058 w -- 5.935 =0 



Santiago Equatorial .... 380.398 x 140. 582 y + 788.860 z +267. 689 v +361. 892 w 109.41 =0 



Santiago Meridian 89.606 x 22. 218 y +179. 593 z + 34.705 w +324.320 = 



Washington Equatorial . . . 84.506 x 135. 640 y +173. 963 z 142. 839 w 77.93 



Greenwich Meridian .... 32.410 x + 18.864 y + 91.178z + 8.0021 59. 68-2 iv + 23.00 =0 



Altona Meridian 4.174x + 9.561 y + 8.777 z 8.273w 5.637 



Greenwich Meridian .... 9.000 x + 5 797 y + 8.002 z + 15.000 1 - 23. 624 w + 32.48 



Santiago Equatorial .... 243. 687 x 123. 942 y + 267.689.Z +1155.576 v +295. 185 w +476.53 =0 



Santiago Equatorial .... 272.519x 51.518y +361. 89-2 z +295.185V +320. 140 w 137.90 =0 



Santiago Meridian 33. 092 x + 17.679 y + 34.705 z + 19. 258 w + 77.885 =0 



Washington Equatorial . . . 94.753 x + 94. 506 y 142.839 z +177. 887 w +145.10 =0 



Greenwich Meridian .... - 38. 509 x 16. 205 y 59. 682 z 23. 624 t + 94.306 w 122.40 =0 



Altona Meridian 3.974x 9.058y 8.273 z + 7.905W + 4.833 =0 



Santiago Equatorial . 

 Santiago Meridian 

 Washington Equatorial 

 Greenwich Meridian. 

 Altona Meridian . 



[nn] = 2763.22 

 [nn] = 1304.06 

 [nn] = 829.18 

 [nn] = 435.60 

 [nn] = 5.77 



