THE r. 15 1 T O P U R ANUS 



37 



To obtain tlie derivative with respect to y we notiee that all the appreciable 

 terms in the ditferent values of h, which depend upon the mutual inclination, are 

 of the form 



7/ = a" ^, 



where a ^=. sin \ y. These equations give 



dli C'h da . , I , . 



Aa cos ^y z^ ^ A sin y. 



Consequently 



dy da dy 

 dR 



dy 



= 1.1 sin J/ cos (.V+P'). 



and the various terms depending on the same argument (/', i) may be condensed 

 into two, exactly as in the case of li itself. 



The diflerent co-efficients h and DJi, computed in the way already described, are 

 given in extenso in the following table. At the top of each individual column is given 

 the value of P, or of jiw +/ij', corresponding to the values of h below, and imme- 

 diately under P is given its modified value, or P', to be used in condensing the 

 terms, putting for brevity 



(l.j) = OJ LJ . 



P and P' are therefore regarded as constant angles the numerical values of the 

 sines and cosines of which may be obtained from the values of u and u' already 

 given. 



The condensed h^. and //,. arc given in the two right hand columns. 



All the numbers are given in units of the third place of decimals. 



