Page:Reflections on the Motive Power of Heat.djvu/271

Rh dilatation. According to the reasoning of page 69, δr will be the power developed by the fall of the quantity e of heat from the degree t + td to the degree t. If we call u the motive power developed by the fall of unity of heat from the degree t to the degree zero, as, according to the general principle established page 68, this quantity u ought to depend solely on t, it could be represented by the function Ft, whence u = Ft.

When t is increased it becomes t + td, u becomes u + du; whence

Subtracting the preceding equation, we have

This is evidently the quantity of motive power produced by the fall of unity of heat from the temperature t + dt to the temperature t.

If the quantity of heat instead of being a unit had been e, its motive power produced would have had for its value

But edu is the same thing as δr; both are the power developed by the fall of the quantity e of heat from the temperature t + dt to the temperature t; consequently,