A problem proposed to me lately by my friend T. Stevenson, C.E., for constructing what he calls a Differential Mirror, when attacked directly led to the equation

where a is a unit-vector, perpendicular to β.

By another mode of solution it was easy to see that the integral must be of the form

It may be instructive to consider this question somewhat closely, as the form of the unintegrated expression is certainly (to say the least) at first sight unpromising.