242 MATHEMATICAL FORMULAE AND ELLIPTICAL FUNCTIONS 



As has been remarked, large sheets should be used so that the x, y, and g-tables 

 can be put side by side on one sheet. Then the ^-column need be written but once 

 for these three tables. The g-schedule, which is of a different type, should be on 

 a separate sheet. 



The differential equation (i) has an integral which becomes for K? = - 



2 



j dx 

 and^-y 



21. y* + $x>-lx< = i, 



and which may be used to check the computation because it must be satisfied at 

 every step. It is found on trial that (21) is satisfied to within one unit in the 

 fourth place by the results given in the foregoing tables for every value of t. 



The value of / for which x = i and y = o is given by (6) . When K 2 = J it is 

 found that T = 1.8541. It is found from the final #-table by interpolation based 

 on first and second differences that x rises to its maximum unity for almost exactly 

 this value of /; and, similarly, that y vanishes for this value of /. 



