238 



MATHEMATICAL FORMULA AND ELLIPTIC FUNCTIONS 



after which it is found that gi = -.1486, Aigi = -.1486. Now the first trial y-table 

 can be corrected by using the value of y 2 given in (14). The result is: 



Second Trial y-Table 



In order to correct x z and y 2 by the same method, which is the most convenient 

 one to follow, it is necessary first to obtain approximate values of g s and y*. The 

 trial g-table can be corrected by computing g with the values of x given by (17) 

 and (15). Then the line for g 3 can be extrapolated. The results are: 



Second Trial g-Table 



Then the second equation of 10.7 (4) gives for n = 2, 



18. y 3 = .9705 + ~ I -.4230 + ^ .1334 - ~ 2 -0076 = .9348. 



When this is added to the second trial ^-table, it is found that 



19- ?3 = .9348, A^3 = -.0357, A^ = -.0137, A 3 ;y3 = +.0008. 



Now x 2 and y 2 can be corrected by applying 10.31 to these numbers and those 



in the last line of the second trial g-table. The results are 



^[.9343 



.0997 + 



= -9925 + - 



!*8*5- 



.1334 + . 



9705. 



The preliminary work is finished and x and y have been determined for / = o, 

 .1, and .2 with an error of probably not more than one unit in the last place. As 

 the process is read over it may seem somewhat complicated, but this is largely 

 because on the printed page preliminary values of the unknown quantities can 

 hot be erased and replaced by more nearly correct ones. As a matter of fact, the 



