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By means of a simple transformation suggested by Bliss, the problem of Lagrange may be reduced to one in which the side conditions are integral equations rather than differential equations, and no derivatives enter explicitly. A multiplier rule for the transformed problem is derived below, in which the multipliers are all constants. When the inverse transformation is applied to this multiplier rule, formulas are obtained for the non-constant multipliers occurring in the ordinary form of the Lagrange multiplier rule, and it is seen that the constant multipliers obtained here may be identified with certain constants appearing in the ordinary form of the rule. In connection with his applications of the calculus of variations to problems in economics, Roost has been led to consider a generalization of the problem of Lagrange in which integro-differential equations occur among the side conditions. The transformation and analysis given below apply with equal facility to Roos' problem. For normal arcs an analogue of the Weierstrass condition is derived for the transformed problem. It is not necessary to assume that the minimizing arc is normal on sub-arcs. For such problems as that of Roos, no generalization of the Jacobi-Mayer condition has to my knowledge yet been obtained, though several attempts have been made. 1. The transformation of the problem. We shall start with the problem suggested by Roos, in the following form: To find necessary conditions on a curve

A transformation of the problem of Lagrange in the calculus of variations