Page:Elementary Principles in Statistical Mechanics (1902).djvu/37

Rh But since  Therefore,  The equation to be proved is thus reduced to  which is easily proved by the ordinary rule for the multiplication of determinants.

The numerical value of an extension-in-phase will however depend on the units in which we measure energy and time. For a product of the form $$dp\, dq$$ has the dimensions of energy multiplied by time, as appears from equation (2), by which the momenta are defined. Hence an extension-in-phase has the dimensions of the $$n$$th power of the product of energy and time. In other words, it has the dimensions of the $$n$$th power of action, as the term is used in the `principle of Least Action.'

If we distinguish by accents the values of the momenta and coördinates which belong to a time $$t'$$, the unaccented letters relating to the time $$t$$, the principle of the conservation of extension-in-phase may be written or more briefly