SECT. 2.] TO POSITION IN SPACE. 95 



D \&n(M u) tanfJV i) 



tan P = - . . , or tan = ^_ 



cos to sin i cos w sin t 



from which results 



VT * * ( } __ rsin(M u) coa(N b P) __ r sin (N b) cos (M u Q) 

 VI w/ ^sinP ~dA&~ 



The auxiliary angles M, N, P, Q, are, moreover, not merely fictitious, and it would 

 be easy to designate what may correspond to each one of them in the celestial 

 sphere ; several of the preceding equations might even be exhibited in a more 

 elegant form by means of arcs and angles on the sphere, on which we are less 

 inclined to dwell in this place, because they are not sufficient to render superflu 

 ous, in numerical calculation, the formulas above given. 



77. 



What has been developed in the preceding article, together with what we 

 have given in articles 15, 16, 20, 27, 28, for the several kinds of conic sections, 

 will furnish all which is required for the computation of the differential varia 

 tions in the geocentric place caused by variations in the individual elements. 

 For the better illustration of these precepts, we will resume the example treated 

 above in articles 13, 14, 51, 63, 65. And first we will express dl and db in terms 

 of dr, du, dzj dS2, according to the method of the preceding article; which cal 

 culation is as follows : 



logtanw . 8.40113 logsinw . 8.40099 log tan ( M u) 9.41932w 

 logcosa . 9.98853 log tan z . 9.36723 logcosw sins . 9.35562ra 



log tan M. 8.41260 log tan N . 7.76822 w log tan P . . 0.06370 

 M = l28 / 52 // J\r= 17939 50&quot; P= 4911 / 13 / 



M w=16517 8 N i =186 145 Nl P= 1365032 



