

48 RELATIONS PERTAINING SIMPLY [BOOK 1. 



has less effect in facilitating the calculation, it is not necessary to pay any regard 

 to A, but we have at once 



tan } w tan lv 



and hence the time t, by multiplying the mean motion corresponding to the true 



73 



anomaly, w, in the Barkerian table, by . 



42. 



We have constructed with sufficient fulness a table, such as we have just 

 described, and have added it to this work, (Table I.). Only the first part pertains 

 to the ellipse ; we will explain, further on, the other part, which includes the 

 hyperbolic motion. The argument of the table, which is the quantity A, proceeds 

 by single thousandths from to 0.300 ; the log B and C follow, which quantities 

 it must be understood are given in ten millionths, or to seven places of decimals, 

 the ciphers preceding the significant figures being suppressed ; lastly, the fourth 

 column gives the quantity T computed first to five, then to six figures, which 

 degree of accuracy is quite sufficient, since this column is only needed to get the 

 values of log B and C corresponding to the argument T, whenever t is to be 

 determined from v by the precept of the preceding article. As the inverse prob 

 lem which is much more frequently employed, that is, the determination of v and 

 r from t, is solved altogether without the help of T, we have preferred the quan 

 tity A for the argument of our table rather than T, which would otherwise have 

 been an almost equally suitable argument, and would even have facilitated a little 

 the construction of the table. It will not be unnecessary to mention, that all the 

 numbers of the table have been calculated from the beginning to ten places, and 

 that, therefore, the seven places of figures which we give can be safely relied upon; 

 but we cannot dwell here upon the analytical methods used for this work, by a 

 full explanation of which we should be too much diverted from our plan. 

 Finally, the extent of the table is abundantly sufficient for all cases in which it 

 is advantageous to pursue the method just explained, since beyond the limit 

 A ==0.3, to which answers T= 0.392374, or ^=64 7 , we may, as has been 

 shown before, conveniently dispense with artificial methods. 



