159, 160] The Virial 143 



Hence, at the critical point 



RNTv -Us* 

 pv = 7 - r .e RTv 

 (v b) 



The ratio of the value of pv in the critical state as given by Boyle's Law 

 to its actual value is therefore 



%e\ or 3-6945. 



This agrees almost exactly with Young's value 3'7. We must, however, 

 not lay too much stress on the agreement. When, as in the present 



instance, we are dealing with values for which - = ^, it is obvious that 



/6\ 2 

 the error introduced by the neglect of f - j must be very considerable. 



THE VIRIAL OF CLAUSIUS. 



160. Clausius attempted, in a way entirely different from that which we 

 have followed, to determine the relation between the pressure, volume and 

 temperature of a gas*. 



Let x, y, z, be the coordinates of the centre of gravity of a molecule of 

 mass m, and X, Y, Z, the components of force acting upon it. Then its 

 motion is governed by the equations 



m~ = X, etc ....... ".. ................... (332). 



we obviously have 



d? 



by equation (332). If we sum this equation and the corresponding equations, 

 for the two other axes and for all the molecules of the gas, we obtain 



where 2 denotes summation over all the molecules of the gas. 



* Phil. Mag. August, 1870. 



