Investigation of the case in which t does not occur explicitly

Abstract

The case where t does not occur explicitly in Ψ., already introdudced above, requires special consideration. In this case the partial differential equation $\frac{{\partial V}} {{\partial t}} + \psi = 0$ can be reduced to another which contains one variable less. This rests on a very remarkable transformation of partial differential equations through which one of the independent variables and the partial differential coefficient belonging to it reverse their roles.