FUNDAMENTAL EQUATIONS. 



ll.-ITODAMENTAL EdUATIONS. 



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. 



245.9801+ 50.301 y + 66. 012 z 65.862 v -f 322.302 w + 195.44 =0 



50.301 x + 165.077 y + 39.811 z + 16.342V + 39.760 Mr 470.31 =0 



66.012X + 39.811 y + 32.841Z 17.828 v+ 80.599 w 48.93 =0 



65.862*+ 16.342 y 17. 828 I + 448. 187 v 90.420 w 350.49 =0 



322.302X + 39.760 y + 80.599 z 90.420 v+ 427.058 w + 344.76 =0 



[tin] = 2126. 19 / 

 211. 4601 + 324. 36411 469.397 =0 

 324. 364 t + 503. 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 = 



36.2921+ 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+ 189. 217 n 388.831 =0 



[nn] = 976.024 



3. Cape of Good Hope Equatorial. 



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



114.938 X + 187.576 y 103.827 z 121.703 V 169.220 w 561.35 =0 



75.039 X 103.827 y + 69.424 z + 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 



[Tin] =2136. 65 



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

 170.780 t + 283.620 u + 31. 715 =0 



[>m] = 47. 116 



4. Cape of Good Hope Meridian. 



46. (00 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 = 



21. 694 x 30. 617 y + 21. 778 z + 30. 783 w+ 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 5.291 y + 4.297 z 16.548 w 1.00 =0 



- 5.291 X + 10.749 y 5.903 z + 5.911 w 16.64 =0 



4.297 X 5. 903 y + 3.290 z 4.382W+ 5.02 =0 



16.548X+ 5.911 y 4.382 z 14. 102 W 1.72 =0 



[nl=51.77 



