SECT. 3.] 



PLACES IN ORBIT. 



113 



87. 



The following examples will illustrate the use of the preceding precepts, while 

 from them the degree of precision can be estimated. 



I. Let log r = 0.3307640, log / = 0.3222239, J=T 34 53&quot;.73 = 27293&quot;.73, 

 t = 21.93391 days. Then is found w 33 47&quot;.90, whence the further compu 

 tation is as follows : 



log A . . 

 logrr . . 

 C. log 3 Jc . 

 C. log t . . . 

 C. log cos 2 co 



4.4360629 

 0.6529879 

 5.9728722 

 8.6588840 

 0.0000840 



J log r r cos 2 o&amp;gt; 

 2 log sin J /t 



C. log a a . 

 C. log cos to . 



0.3264519 

 7.0389972 

 8.8696662 

 0.5582180 

 0.0000210 



log a 



9.7208910 



log/9 ..... 6.7933543 

 = 0.0006213757 



1 + y + 21 /3 = 



3.0074471 



log ...... 0.4781980 



log a ..... 9.7208910 



C. log (1 + 5/3) . 9.9986528 



logy/jo .... 0.1977418 



logjo ..... 0.3954836 



This value of log p differs from the true value by scarcely a single unit in the 

 seventh place: formula VI., in this example, gives log p = 0.3954822; formula 

 VH. gives 0.3954780 ; finally, formula VUL, 0.3954754. 



II. Let log r= 0.4282792, log/ 0.4062033, z/ = 6255 16&quot;.64,* 259.88477 

 days. Hence is derived &amp;lt;a= 127 20&quot;.14, log a = 9.7482348, = 0.04535216, 

 y = 1.681127, log ^p = 0.2198027, log ^ = 0.4396054, which is less than the true 

 value by 183 units in the seventh place. For, the true value in this example is 

 0.4396237; it is found to be, by formula VI., 0.4368730; from formula VII. it 



15 



