In entropy calculations in connection with the kinetic theory of gases or the quantum theory the changes in functions depending on factorials have hitherto been calculated by a method depending on the replacement of factorials by continuous functions and differentiation. This method is neither simple nor logically satisfying. A new method of calculation is shown which depends on the direct evaluation, by simple well known processes, of $\Delta F=F(x+\Delta x, y+\Delta y, \cdots )-F(x, y, \cdots )$ where $F$ is a function involving the factorials of $x, y, \cdots$, and where $x, y, \cdots$ and $x+\Delta x, y+\Delta y, \cdots$ are taken as integers. The details of this method are illustrated by the treatment of two examples.

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