138 RELATIONS BETWEEN SEVERAL [BoOK 1. 



or 



whence, in the same manner as in article 90, is deduced 



4.6 . 4.6.8 4.6.8.10 ,, , 4.6.8.10.12 , 



= 3 --O g + 3^77 gg ---3T5T779-^+ 8.5.7.9.11-^ 



It is evident, therefore, that Z depends upon z in axactly the same manner 

 as X does upon x above in the ellipse ; wherefore, if we put 



C also will be determined in the same manner by z as f, above, by a;, so that 

 we have 



[141 t = _ ^ es 



1 -f- etc.. 

 or, 



1 -\- etc. 



In this way the values of are computed for s to single thousandths, from z = 

 up to 2 0.3, which values are given in the third column of table III. 



101. 



By introducing the quantity and putting 



,, rn /(ft \ ^ 



also 



MM 



_____ 



