SECT. 1.] TO POSITION IN THE ORBIT. 41) 



43. 



We add, for the better illustration of the preceding investigations, an example 

 of the complete calculation for the true anomaly and radius vector from the time, 

 for which purpose we will resume the numbers in article 38. We put then e = 

 0.9674567, log q= 9.7656500, t = 63.54400, whence, we first derive the constants 

 log a = 0.03052357, log ft = 8.2217364, log y = 0.0028755. 



Hence we have log a t = 2.1083102, to which corresponds in Barker s table 

 the approximate value of w 99 6 whence is obtained A= 0.022926, and from 

 our table log B = 0.0000040. Hence, the correct argument with which Barker s 



table must be entered, becomes log ^5 = 2.1083062, to which answers w = 99 6 

 13&quot;.14 ; after this, the subsequent calculation is as follows : 



log tan 2 km . . . 0.1385934 log tan i w ...... 0.0692967 



log/J ..... 8.2217364 logy ........ 0.0028755 



..... 8.3603298 * Comp. log(l 1 4 + 0) . 0.0040143 



A= ..... 0.02292608 log tan i ...... 0.0761865 



hence log B in the same manner as before ; $ v= ..... 50 0&quot; 



C . 0.0000242 v= ..... 10000 



l A-{-C= . 0.9816833 log q ........ 9.7656500 



4+0= . 1.0046094 2. Comp. log cos *t&amp;gt; . . .- 0.3838650 



log(l 1 4+0). . . . 9.9919714 



C.log(l+|4 + 0). . . 9.9980028 



logr ........ 0.1394892 



If the factor B had been wholly neglected in this calculation, the true anomaly 

 would have come out affected with a very slight error (in excess) of 0&quot;.l only. 



* 



! ... 44. , 



It will be in our power to despatch the hyperbolic motion the more briefly, 

 because it is to be treated in a manner precisely analogous to that which we 

 have thus far expounded for the elliptic motion. 



7 



