Page:Elementary Principles in Statistical Mechanics (1902).djvu/27



shall use Hamilton's form of the equations of motion for a system of $$n$$ degrees of freedom, writing $$q_1, \ldots q_n$$ for the (generalized) coördinates, $$\dot q_1, \ldots \dot q_n$$ for the (generalized) velocities, and for the moment of the forces. We shall call the quantities $$F_1, \ldots F_n$$, the (generalized) forces, and the quantities $$p_1\ldots p_n$$, defined by the equations where $$\epsilon_p$$ denotes the kinetic energy of the system, the (generalized) momenta. The kinetic energy is here regarded as a function of the velocities and coördinates. We shall usually regard it as a function of the momenta and coördinates, and on this account we denote it by $$\epsilon_p$$. This will not prevent us from occasionally using formulae like (2), where it is sufficiently evident the kinetic energy is regarded as function of the $$\dot q$$'s and $$q$$'s. But in expressions like $$d\epsilon_p/dq_1$$, where the denominator does not determine the question, the kinetic