These conditions take the place of those given above relating to ${\displaystyle n}$. In fact, we might give conditions relating to the differential coefficients of ${\displaystyle V}$, similar to those given relating to the differential coefficients of ${\displaystyle V_{q}}$, instead of the conditions relating to ${\displaystyle n}$, for the validity of equations (360), (363)-(372). This would somewhat extend the application of the equations.