SECT. 1.] TO POSITION IN THE ORBIT. 51 



45. 



The latter part of the table annexed to this work belongs, as we have remarked 

 above, to the hyperbolic motion, and gives for the argument A (common to both 

 parts of the table), the logarithm of B and the quantity to seven places of 

 decimals, (the preceding ciphers being omitted), and the quantity T to five and 

 afterwards to six figures. The latter part is extended in the same manner as 

 the former to ^1=0.300, corresponding to which is T= 0.241207, u= 2.930, 

 or = 0.341, jF + 5219 ; to extend it further would have been superfluous, 

 (article 36). 



The following is the arrangement of the calculation, not only for the determi 

 nation of the time from the true anomaly, but for the determination of the true 

 anomaly from the time. In the former problem, T will be got by means of the 

 formula 



- 



e-\-\ 



with T our table will give log B and 0, whence will follow 



finally t is then found from the formula [2] of the preceding article. In the last 

 problem, will first be computed, the logarithms of the constants 



/5 



- y r_pr e - 



A will then be determined from t exactly in the same manner as in the elliptic 

 motion, so that in fact the true anomaly w may correspond in Barker s table to 

 the mean motion -^,and that we may have 



A = (l tan 2 % w ; 

 the approximate value of A will be of course first obtained, the factor B being 



