A Comet of the Enlightenment by Johan C.-E. Stén

Author:Johan C.-E. Stén
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

Now, following Lexell, we can in every case put

and therefore

from which one obtains by Leibniz’s chain rule

By comparison with the original expression, the following system of equations results:

where the variables x, y, p, q, …, u are independent of each other, such that the expressions dp∕dx and the like are zero. Thus Lexell contended that, for V dx to be an exact differential,10 the integrability condition will be the equation

Analogously, for V being a function of four variables x, y, z and w,

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