The problem of the pulling into step of a synchronous motor has proved very difficult to solve, since it centres about a non-linear differential equation. One solution of the equation is not enough. All possible solutions with all combinations of the coefficients need to be made and classified into two groups, those that synchronize and those that do not. Until recently this has been practically impossible because of the amount of time required to make the solutions by graphical or point-by-point methods.The development of the integraph by Dr. Bush and his associates at the Massachusetts Institute of Technology has made it possible to solve this problem by machine integration. This integraph, which performs two successive integrations simultaneously, is particularly adapted to the solution of first- and second-order total differential equations. The solutions described in this paper were obtained by using the integraph in this way.This paper presents the complete solution of the problem for the case of a non-salient-pole synchronous motor. The results are put in a simple form convenient for practical use. By means of these results all of the necessary relationships between field current, induction-motor torque and slip, which determine whether or not a given load of a definite flywheel effect can be brought into synchronism, are determined. An example of a practical application is given.