FUNDAMENTAL EQUATIONS. Cclxiii 



Washington Equatorial. 



12,3?0x 0.063 y -{- 0.243 z 5.226 w -f- 17.20 =0 



- O.( 63x + 0.603 y 0.043 z + 0.099 w 0.39 =0 



0.243X 0.043 y 4. 0. COS z 0.108 w + 0.37 =0 



5.226x 4- O.OS9 y 0.108 z -f 2.215w 7.29 =0 



[nn] =25.51 



17. 220 t + 25.736ii 42.817 =0 



25. 736 t + 38.463 ti 63.981 =0 



[nn] = 107.066 



Cape of Good Hope Meridian. 



46. 000 x 6.618 y 4- 16. 550 z 4- 55. 192 w + 29.180 =0 



- 6.6)8 x + 41. 365 y 9.743z 8.399 w 156.136 =0 



16. 550 x 9. 7-13 y + 12.107 z + 19. 004 w + 27.336 =0 



55. 192 x 8. 399 y 4- 19. 024 z 4-66.398 w 4- 38.773 =0 

 [nn] = 632.G9 



Greemuicli Meridian. 



36. 000 x + 29. 646 y + 37.068 z 21.216 w 83.70 =0 



29. 646 x + 92. 658 y + 55.541 z 13.367 w 309.97 = 



37. 068 x -f 55.541 y -f- 73,226 z 19.344 w 217.38 =0 



21. 216 x 13. 367 y 19.344 z -f 12.809 w+ 32.08 =0 



[nn] = 1221.95 



Kremsmunster Meridian. 



13. 000 x + 14. 104 y 4- 10. 118 z 4. 6.638 w 32.500 =0 



14. 104 x 4- 25. 300 y + 18.096 z + 6.448 w 69.529 =0 



10. 118 x 4- 18. 096 y 4- 13.944 z + 4.635 w 53.038 =0 



C.638Z+ 6. 448 y 4- 4.635 z 4. 3.447 w 14.028 =0 



[nn] = 303.509 



In this series we have seven systems of equations, if we retain the supplementary ones from 

 the Santiago Meridian-circle as a distinct group by themselves, which is for the present the best 

 course. These seven systems contain nine unknown quantities, viz : x, y ? z, w in all the 

 equations ; t, u, V in those from the Equatorial at Santiago ; tg, U 2 in those from the meridian- 

 circle at the same place. 



The quantities depending upon the unknown corrections to the semidiameter are already 

 eliminated from the Washington observations, owing to the uniform observance of the rule 

 always to compare both limbs of the planet with the comparison-star. Had other observers 

 pursued the same course much labor and embarrassment might have been avoided. At the 

 Cape of Good Hope, Greenwich, and Kremsmunster, the center was estimated by the observer. 



In consequence of the considerations intimated when considering the final equations for Mars 

 I, the quantities u n U 2 may be removed from all equations in which they occur, and the number 

 of unknown quantities be thus reduced to seven. In the experimental solution, however, the 

 correction of the semidiameter t -f- 0&quot;. 98960, deduced from the additional equations for the 

 Santiago Equatorial, was substituted, and both the quantities t, and U 2 retained in the equations 

 to be solved ; these latter being formed by simple addition of the correlative equations in each of 

 the groups, excepting the one derived from Kremsmiinster observations. This solution gave 



Y! = + 0&quot;.493 

 t 2 + 4&quot;. 63322 

 u,= 2&quot;. 57824 



or after makiug u, 



t. = -f- 1&quot;. 09704 



