FUNDAMENTAL EQUATIONS. 



cclxi 



The Cambridge additional equations for semidiameter gave the values 



t = 8".583, u = + 5".823, 

 or, after putting u = 0, 



t=-f-0".7245, 



which latter value may be substituted in the Cambridge equations. 



Finally, in order to reduce the number of unknown quantities still farther, if possible, and 

 for the sake of a general survey of the character of our materials, all the equations, excepting 

 those derived from the Athens observations, were combined into one set containing seven 

 unknown quantities, by simple addition of the analogous equations in each system. The 

 solution afforded an indication of the admirable precision of Mr. Maclear's measurement of his 

 micrometer-screw, the quantity v 2 (100 times the correction to his adopted value) coming out 

 as zero. The resultant values of x, y, z and w being substituted in the equation containing 

 [ff] in the Cape Equatorial series, this equation becomes 



1509".463 v 2 = + 0".402 



V 2 = + 0".000266 



which authorizes us to dispense with any farther consideration of this term. 



For the Santiago Equatorial this solution gave Vi = + 0".5TO 



for the Greenwich Circle, 1^ = + 0".166 



and for the Athens Circle, ta = + 1".927. 



Considering these last quantities as still undetermined, we hare but seven unknown 

 quantities remaining, and our equations containing w assume the annexed form, which we 

 may consider fundamental. 



FUNDAMENTAL EQUATIONS FOR MARS I. 



Santiago Equatorial . . . 

 Washington Equatorial . . 

 Cape of Good Hope Equatorial 

 Cape of Good Hope Meridian 

 Greenwich Equatorial . . . 

 Greenwich Meridian . . . 

 Cambridge Equatorial . . . 

 Athena Meridian 



245. 980 x+ 50.301 y + 66. 012 z 

 93. 950 X 92. 428y +100.243 z . 



156. 410 X 114. 932 y + 75.039 z 



46.000 x 29.6il)y + 21. 694 z 



20. 200 x 5.391y + 4.297 z 



24. 000 X + 4.677y + 26.950 z + 17.000 t 



60.080 X 59.593 y + 47.431 z 



38.000X 1.865 y + 81.565 x+ O.OOOt 



65.862 V + 322.302 w + 195.44 = 





 

 

 

 

 

 



36. 292 w +329.73 

 + 221. 511 w +510.68 

 + 64.792 w + 130.97 



16. 548 w 1.00 



14. 584 w 11. JO 



37.988 w + 176.26 



11.854 W +257.30 



Santiago Equatorial .... 

 Washington Equatorial . . . 

 Cape of Good Hope Equatorial 

 Cape of Good Hope Meridian 

 Greenwich Equatorial . . . 

 Greenwich Meridian . . . 

 Cambridge Equatorial . . . 

 Athena Meridian 



50.301 X + 165.077 y + 39.811 z 

 92. 428 X +250. 553 y 211. 748 z 

 114.932 X + 187.576 y 103.827 z 

 29. 619 x + 54. 230 y 30. 617 z 



5.291X+ 10. 749 y 5.903 z 

 4.677X+ 67.389y+ 8.152Z+ 2.944 1, 



59. 593 X +118. 579 y 96.401 z 



1.865X+ 53.921 y 0.005 z + 0.097t, 



+ 16.342 V + 39.760 w 470.31 =0 





 

 

 

 

 

 



+ 39.342 w 616.86 

 169.220 w 561.35 

 43.331 w 170.00 

 + 5 911 w 16.64 

 + 0.894 w 139.70 

 + 41.064 w 277.99 

 + 2. 379 w 170.98 



Santiago Equatorial . . . 

 Washington Equatorial . . . 

 Cape of Good Hope Equatorial 

 C ipe of Good Hope Meridian . 

 Greenwich Equatorial . . . 

 Greenwich Meridian . . . . 

 Cambridge Equatorial . .' . 

 Athens Meridian 



66.012X+ 39.811 y+ 32.841 z 



100.243 X 211.748 y + 2S2.347 z 



75. 039 x 103. 827 y + 69.424 z 



21.694 X 30.617 y+ 31. 778 C 



4.297 x 5.903y+ 3.290 z 



26.950X+ 8.152y + 58.878 z + 9.015t, 



47.431 X 96.401 y + 80.976 z 



21.565X 0.005y+ 22.935 z 2.405t 2 



17.828 v + 80. 599 w 48.93 =0 



40. 298 w +498.27 =0 

 + 106. 929 -H- +316.13 =0 

 + 33.783W+ 93.80 =0 



4.382 w + 5.02 =0 



14. 748 w 64.67 =0 



31.783 w +220.35 =0 



6.502 w +131.85 =0 



