282 APPENDIX. 



a table may be computed from this formula, giving v for values of t as the argu 

 ment, which will readily furnish the true anomaly corresponding to any time 

 from the perihelion passage. Table Ila is such a table. It is taken from the 

 first volume of Annales dc I Observatoire Imperiale de Paris, (Paris, 1855,) and differs 

 from that given in DELAMBRE S Astronomy, (Paris, 1814,) Vol. III., only in the 

 intervals of the argument, the coefficients for interpolation, and the value of k 

 with which it was computed. 



The true anomaly corresponding to any value of the argument is found by 

 the formula 



v = z-o + A! (T TO) + A 2 (* ~ T o) 2 + (T T ) 3 A 3 -f A (t T ) 4 . 



The signs of A 1 , A 2 , A 3 , are placed before the logarithms of these quantities 

 in the table. 



BURCKHARDT S table, BOWDITCH S Appendix to the third volume of the Mecanique 

 Celeslc, is similar, except that log t is the argument instead of T. 



Table ll a contains the true anomaly corresponding to the time from peri 

 helion passage in a parabola, the perihelion distance of which is equal to the 

 earth s mean distance from the sun, and the mass ju, equal to zero. For if we put 

 H = 1 , u = , we have t t . 



By substituting the value of /c in the equation 



T = (3 tan %v -f- tan 3 v) 



it becomes 



T = 27.40389544 (3 tan kv + tan 3 } v) 



= 1.096155816 (75 tan i -f 25 tan 3 irj 

 and therefore, if we put x == 0.9122790G1, 



75 tan i v -4- 25 tan 3 4 v * t 



log x = 9.9601277069 



BARKER S Table, explained in article 19, contains v t for the argument v. 

 The Mean daily motion or the quantity M, therefore, of BARKER S Table may be 

 obtained from table II a , for any value of v, by multiplying the corresponding 

 value of T by x . 



The following examples will serve to illustrate the use of the table. 

 Given, the perihelion distance &amp;lt;? = 0.1; the time after perihelion passage 

 t 0&quot;.590997, to find the true anomaly. 



