52 



RELATIONS PERTAINING SIMPLY 



[BOOK I. 



either neglected, or, if the means are at hand, being estimated ; our table will 

 then furnish the approximate value of B, with which the work will be repeated ; 

 the new value of B resulting in this manner will scarcely ever suffer sensible cor 

 rection, and thus a second repetition of the calculation will not be necessary. C 

 will be taken from the table with the corrected value of A, which being done we 

 shall have, 



From this it is evident, that no difference can be perceived between the formulas 

 for elliptic and hyperbolic motions, provided that we consider /3, A, and T, in the 

 hyperbolic motion as negative quantities. 



46. 



It will not be unprofitable to elucidate the hyperbolic motion also by some 

 examples, for which purpose we will resume the numbers in articles 23, 26. 



I. The data are e = 1.2618820, log q = 0.0201657, v = 18 51 0&quot; : t is 

 required. We have 



13.91445 = *. 



II. e and q remaining as before, there is given t = 65.41236 ; v and r are 

 required. We find the logarithms of the constants, 



