The integration can be effected without much difficulty.
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.
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).
Accordingly, the optical distance from AoBo to A is represented by f (A +S/c)ds, the integration being along the original path Ao.
If the grating be composed of alternate transparent and opaque parts, the question may be treated by means of the general integrals (§ 3) by merely limiting the integration to the transparent parts of the aperture.