The integration can be effected without much difficulty.
Since the change of energy is independent of the path, the finite change between any two given states may be found by integration along any convenient path.
For a point Q outside the shadow the integration extends over more than half the primary wave.
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.
Here again, on integration over the entire lamina, the aggregate effect of the secondary waves is necessarily the same as that of the primary.