28 



RELATIONS PERTAINING SIMPLY 



[BoOK I. 



26. 



Example. Retaining for e and I the same values as in the preceding example, 

 let t = 65.41236 : v and r are required. Using Briggs s logarithms we have 



log* 1.8156598 



log 31*$-$ .... 6.9702758 



log N 8.7859356, whence N= 0.06108514. From this it is 



seen that the equation N X e tan F log tan (45 -j- F) is satisfied by 

 F= 2524 27&quot;.66, whence we have, by formula III, 



log tan 4 F . . . . 9.3530120 

 log tan 4 y . . . . 9.5318179 



and thus 4 v = 33 31 29&quot;.S9, and v = 



log tan lv .... 9.8211941, 

 67 2 59&quot;.7S. Hence, there follows, 



**.(. + ,.) 0.2137476 



C. log cos 4 (v w) . 0.0145197 J 



logfi. . ... . . 9.9725868 



log r . 0.2008541. 



***(+**) 



0.1992280 



27. 



If equation IV. is differentiated, considering u, v, y, as variable at the same 

 time, there results, 



d_M _ ^ sin ift d v -|- sin v d y _ r tan \f&amp;gt; , . r sin v , 



U ~ ~ 2 COS |(j) - I/)) COS ^ (v -j- ;) ~ ~^ V T&quot; ) T * 



By differentiating in like manner equation XL, the relation between the 

 differential variations of the quantities u, y, JV, becomes, 



or 



COS 2 1/1 



