AN ? D MODEKN PHYSICS. 117 



According to this wo aro thus to put hi the pres- 

 sure equation I ut v- - T, the temperature, and we 

 have at once /> V - N T. 



Now this equation expresses, as we know, the 

 laws of Boyle and Gay Lussac. 



The second section discusses the properties of 

 media, consisting of two or more gases, and arrives at 

 the result that " in mixed media the mean square 

 molecular velocity is inversely proportional to the 

 specific weights of the molecules. 11 This was the 

 great law rediscovered by Maxwell fifteen years later. 

 With modern notation it may be put thus: If 

 mi, mi be the masses of each molecule of two dif- 

 ferent sets of molecules mixed together, then, when 

 a steady state has been reached, since the temperature 

 is the same throughout, w, v* is equal to m 2 * 3 *. The 

 average kinetic energy of each molecule is the same. 



From this Avogadros' law follows at once for if 

 />, p be the pressures, X,, X 2 the numbers of molecules 

 per unit volume 



Hence, if j> { is equal to p, t since tn t i\- is equal to 

 m* i*/, wo must have Xj equal to X 2 , or the number 

 of molecules in equal volumes of two gases at the 

 same pressure and temperature is the same. The 

 proof of this proposition given by Waterston is not 

 satisfactory. On this point, however, we shall have 

 more to say. The third section of the paper deals with 

 udiabaticexpansion.and in it there is an error in calcula- 

 tion which prevented correct results from being attained. 



