The heat per second gained by conduction by an element dx of the bar, of conductivity k and cross section q, at a point where the gradient is dB/dx, may be written **gk**(d 2 6/dx 2)dx.

We thus obtain the differential equation **gk**(d 2 0/dx 2) =cgdo/dt+hpo, which is satisfied by terms of the type =c" sin where a 2 -b 2 = hp/qk, and ab = urnc/k.

The general effect is that the rain falling from between G and K is spread over a greater area of the earth G'K' than that falling from the equal space between B and F, which reaches the ground within the smaller area B'F'.