SECT. 1.] 



TO POSITION IN THE ORBIT. 



35 



The true anomaly therefore computed from the mean may be incorrect in 

 two ways, if we consider the mean as given accurately; first, on account of the 

 error committed in the computation of v from E, which, as we have seen, is of 

 slight importance ; second, because the value of the eccentric anomaly itself may 

 be erroneous. The effect of the latter cause will be expressed by the product of 





the error committed in E into ^, which product becomes 



206265&quot; = 



^r. 206265&quot; = 



lr 



if seven places of decimals are used. This error, always small for small values of 

 e, may become very large when e differs but little from unity, as is shown by the 

 following table, which exhibits the maximum value of the preceding expression 

 for certain values of e. 



V. In the hyperbolic motion, if v is determined by means of formula III., 

 article 21, from F and ift accurately known, the error may amount to 



p. 206265&quot;; 

 but if it is computed by means of the formula 



u and y being known precisely, the limit of the error will be one third greater, 



that is, 



4 to sin v 



for seven places. 



VI. If the quantity 



206265&quot; = 0&quot;.09 sin v 



nt 



$ 



is computed by means of formula XL, article 22, with the aid of Briggs s logo- 



