Page:Elementary Principles in Statistical Mechanics (1902).djvu/228

204 which corresponds to the equation  we have  and  This will have a maximum when

Distinguishing values corresponding to this maximum by accents, we have approximately, when $$\nu_1,\ldots\nu_h$$ are of the same order of magnitude as the numbers of molecules in ordinary bodies,  where  and  This is the probability of the system ($$\nu_1\ldots\nu_h$$). The probabilty that the values of $$\nu_1,\ldots\nu_h$$ lie within given limits is given by the multiple integral