Til K o i: i: I T o F r i: A N r s 



37 



To obtain tin- derivative with ropect to y we notice that all the appreciable 

 term- in the different \alues of /<, which depend upon the mutual inclination, are 

 of the form 



where <r = sin $ y. These equations give 



r/i 



Consequently 



- 

 dy 



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

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



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

 gi\ en in cxtenso in the following table. At the top of each individual column is given 

 tin value of /*, or of ju-\-j'uf, corresponding to the values of h below, and imme- 

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

 term-, putting for brevity 



(u) = o u>. 



/'and /''arc therefore regarded as constant angles the numerical values of the 

 sines and coMnes of which may be obtained from the values of o and o' already 

 given. 



The condensed h c and h, are given in the two right hand columns. 



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



