The integration can be effected without much difficulty.
But here he becomes hopelessly inconsistent, because he had already said, in defining it, that " evolution is an integration of matter and concomitant dissipation of motion " (First Principles, § 145).
The volume of the briquette for which u is a function of x and y is found by the operation of double integration, consisting of two successive operations, one being with regard to x, and the other with regard to y; and these operations may (in the cases with which we are concerned) be performed in either order.
He published a memoir on the integration of partial differential equations and a few others, which have not been noticed above, but they relate to subjects with which his name is not especially associated.
Accordingly, the optical distance from AoBo to A is represented by f (A +S/c)ds, the integration being along the original path Ao.