26 



RELATIONS PERTAINING SIMPLY 



[BOOK I. 



Example. Let e = 1.2618820, or V = 37 35 0&quot;, v = 18 51 0&quot;, log r = 

 0.0333585. Then the computation for u, p, I, N, t, is as follows : 



log cos * (v y) . . 9.99417061 



log cos i (t&amp;gt; + y) . 9.9450577) 



logr 0.0333585 



log 2e 0.4020488 



log;? 0.3746356 



log cotan 2 



0.2274244 



log* 0.6020600 



logj 9.4312985 



log sin v 9.5093258 



logX 9.6377843 



Compl. log sin i/&amp;gt; . . 0.2147309 



8.7931395 

 0.0621069 

 0.0491129 



First term of N= 

 log u = 



N = 0.0129940 



logJLA ...... 7.8733658) 



f log b 0.9030900) 



hence, log u 



uu = 



0.0491129 

 1.1197289 



1.2537928 



The other calculation. 



log(Mtt--l) . . . 9.4044793 



Compl. log u . . . 9.9508871 



log I 9.6377843 



logje 9.7999888 



8.7931395 



\N 8.1137429 



Difference .... 6.9702758 



log* 1.1434671 



t= 13.91448 



24. 



If it has been decided to carry out the calculation with hyperbolic logarithms, 

 it is best to employ the auxiliary quantity F, which will be determined by equa 

 tion III., and thence N by XI. ; the semi-parameter will be computed from the 

 radius vector, or inversely the latter from the former by formula VIII. ; the 

 second part of N can, if desired, be obtained in two ways, namely, by means of the 

 formula hyp. log tan (45 -f- J F}, and by this, hyp. log cos $ (v if) hyp. log 

 cos 1 (v -(- if ). Moreover it is apparent that here where X = 1 the quantity N 



