AN!) MODERN PHYSICS. 115 



however, still apply the theory by splitting up the 

 particles into groups, and, supposing that each group 

 has a constant velocity, the particles in this group 

 will contribute to the pressure an amount p l equal 

 to i N, m i',*, where r, is the velocity of the group 

 and NI the number of particles having that velocity. 

 The whole pressure will bo found by adding that due 

 to the various groups, and will be given as before by 

 /> = | N m v 2 , where v is not now the actual velocity 

 of the particles, but a mean velocity given by the 

 equation 



N V* = N, v* + N 3 r s 2 + , 



which will produce the same pressure as arises from 

 the actual impacts. This quantity v 2 is known as the 

 mean *qimre of the molecular velocity, and is so used 

 by Watcrston. 



In a paper in the Pkilotopltieal Magazine for 

 1858 Watcrston gives an account of his own paper 

 of 1840 in the following terms: "Mr. Herapath 

 unfortunately assumed heat or temperature to be 

 represented by the simple ratio of the velocity instead 

 of the square of the velocity, being in this apparently 

 led astray by the definition of motion generally re- 

 ceived, and thus was baffled in his attempts to 

 reconcile his theory with observation. If we make 

 this change in Mr. Herapath's definition of heat or 

 temperature viz., that it is proportional to the vis- 

 viva or square velocity of the moving particle, not to 

 the momentum or simple ratio of the velocity we 

 can without much difficulty deduce not only the 

 primary laws of elastic fluids, but also the other 

 it 2 



