δ_r_ = _N_ log _vdt_. (3)
Let _e_ be the quantity of heat employed to maintain the temperature of
the gas constant during its dilatation. According to the reasoning of
page 69, δ_r_ 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
_u_ + _du_ = _F_(_t_ + _dt_).