Conclusions. It can be seen from the table that the process converges with fair rapidity. Further calculations by the author indicate that the results obtained after three trials contain an error of less than .001 for y(£). If the usual methods of the calculus of variations were employed the resulting non-linear differential equation would presumably have to be solved by finite difference methods anyway and it does not appear that this would be as easy a computation to carry through as the above.In writing (3), first order divided differences have been used, these being the simplest and at the same time adequate. Higher order expressions for the derivatives may be employed but will in general result in more complicated recurrence relations. The iterative procedure for the solution apparently must be devised anew for each different class of problems.