

FUNDAMENTAL EQUATIONS. 



11. MNDAMENTA1 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 + 322.302 w + 195.44 =0 



50.301X + 165. 077 y -j- 39.8111+ 16.342v-j- 39. 7CO w 470.31 =0 



66.01-3x.-j- 39.811y-f-32.841z 17.828v + 80. 599 w 48.93 =0 



65.862X + 16. 342 y 17. 828 z + 448.187V 90.430 w 3:>U. 49 =0 



323.302 x + 39.760 y + 80.599 z 90.420 v + 427.058 w -f 344.76 = 



[nn]=2126.19 



811. 460 t + 321. 364 n 469.397 =U 

 324.364 t -f- 503.332 u 717.614 = 



[rm] = 1095.428 



2. Washington Equatorial. 



93. 950 X 92.428 y -f 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 -f. 498.27 = 



36.2l2x + 39. 342 y 40.298 z + 14.215 w 135.85 =0 



[nnj=2074.59 



76. 990 t + 120. 312 n 248.693 =0 



120.312 t-f- 189.217 u 388.831 =0 



[nil] = 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 



114.932X + 187.576y 103.827Z 121.703 v 169.220 w 561 .X> =0 



75.039X 103.827y+ 69.424 z + 99.935 v -f 106.929 w + 316.13 =0 



' 222. 207 X 121. 703 y-J- 99.935z-f-1509.463v-j-309.533iv-f538.il =0 



221.511 x 169. 220 y + 106. 929 z -f 309.533 v + 314.688 w -f 738.93 =0 



[nn]=2136.65 



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

 170. 780 t + 283. 620 u -f 31. 715 =0 



[nn] = 47.116 



4. Cape of Good Hope Meridian. 







46. tOO x 29. 619 y -f. 21.694 z -f 64.792 w -f. 130.97 =0 



29. 619 x + 54.230 y 30.617 z 43. KM w 170.00 =0 



21. 691 x 30. 617 y + 21.778 z + 30.783 w + 93.80 =0 



64. 792 X 43.931 y -f 30.783 z + 91.590 w-f 191.60 = fl 



[im] =734.81 



5. Greenwich J:'ijn<t/<iriiil. 



20.200 x 5.291y + 4.297 z 16. 548 w 1.00 =0 



- 5.291 X + 10.749y 5.WW7. + 5.911 w 10.111 =0 



4.297 X 5. 903 y+ 3.290 z 4.3b2w+ 5.02 =0 

 lfi.. r >4Sx+ 5.911 y 4.382 z 14. 102 w 1.7-! 



[mil =51. 77 



