FUNDAMENTAL EQUATIONS. 



11. FUNDAMENTA1 EQUATIONS. 



The various products of the coefficients having been duly formed and summed, we obtain the 

 systems of final equations, which constitute the only source for all the deductions possible from 

 the present investigation. They follow in their regular order. 



A. FINAL EQUATIONS FOR MARS I. 



1. Santiago Equatorial. 



245. 980 x + 50. 301 y + 66. 012 z 65.862 v + 323.302 w -f 195.44 =0 



50. 301 x + 165. 077 y + 39.811 z + 16.342v + 39.760 w 470.31 =0 



66.012x.+ 39. 811 y + 32.841 z 17.828v + 80. 599 w 48.93 =0 



65.8621+ 16. 342 y 17. 828 z + 448. 187 v 90.420 \v 350.49 =0 



323. 302 x + 39.760 y + 80.599 z 90.420 v + 427.058 w + 344.76 



[&amp;gt;m]=2126.19 



211. 460 t + 324. 364 u 469.397 =0 

 324. 364 t + 5C3. 332 u 717.614 =0 



[nn] = 1095.428 



2. Washington Equatorial. 



93. 950 x 92. 428 y + 100. 243 z 36. 292 w + 329. 73 =0 



92. 428 x + 250. 553 y 211. 748 z + 39. 342 w 616.86 =0 



100.243 x 211.748 y + 222.347 z 40.298 w + 498.27 = 



~36.292x + 39. 342 y 40.298 z + 14.215 w 135.85 =0 



[nnj=2074.59 



76. 990 t + 120. 312 w 248.693 



120. 312 t+ 189. 217 u 388.831 =0 



[nn] =976. 024 



3. Cape of Good Hope Equatorial. 



156. 410 x 114. 932 y+ 75.039 z + 222.207 v + 221.511 w + 510.68 =0 



114. 932 x + 187. 576 y 103. 827 z 121.703 v 169.220 w 561. 35 =0 



75.039x 103.827y + 69.424z + 99.935 v + 106.929 w + 316.13 =0 



222. 207 x 121. 703 y+ 99.935 z + 1509.463 v + 309.533 w + 538.11 =0 



221.511 x 169.220 y + 106. 929 z + 309.533 v + 314.688 w + 738.93 =0 



[nn]=2136.65 



103. 150 t + 170. 780 11 + 20.102 =0 

 170. 780 t + 283. 620 n + 31. 715 



[nw] = 47.116 



4. Cape of Good Hope Meridian. 



46.000 x 29.619 y + 21.694 z + 64.792 w + 130.97 = 



29. 619 x + 54. 230 y 30. 617 z 43.931 w 170.00 =0 



21. 694 x 30. 617 y + 21. 778 z + 30.783w+ 93.80 =0 



64.792 x 43.931 y + 30.783 z + 91.590 w + 191.60 = 



[nn] =734.81 



5. Greenwich Equatorial. 



20.200 x 5.291y + 4.297 z 16. 548 w 1. 00 =0 



- 5.291 x + 10.749 y 5.903z+ 5. 911 w 16.64 =0 



4.297 x 5. 903 y + 3.290 z 4.382 w + 5.02 =0 



16.548x+ 5.911 y 4.382 z 14.102 w 1.72 =0 



