AND MODERN PHYSICS. 113 



results only, however, were stated in that year. A 

 paper which attempted to establish them was pre- 

 sented to the Royal Society in 1820. It gave rise to 

 very considerable correspondence, and was withdrawn 

 l>y the author before being read It is printed in full 

 in Thomson's " Annals of Philosophy" for 1821, vol. i., 

 pp. 273, 340, 401. The arguments of the author are 

 no doubt open to criticism, and are in many points 

 far from sound. Still, by considering the problem of 

 the impact of a large number of hard bodies, ho 

 arrived at a formula connecting the pressure and 

 volume of a given mass of giis equivalent to that 

 just givea These results are contained in Proposi- 

 tions viii. and ix. of Herapath's paper. 



In his next step, however, Herapath, as we know 

 now, was wrong. One of his fundamental assumptions 

 is that the temperature of a gas is measured by the 

 momentum of each of its particles. Hence, assuming 

 this, we have T = ut r, if T represents the tempera- 

 ture; and 



= N in r = J (in 



Or, again 





These results are practically given in Proposition viii., 

 Corr. (1) and (2), and Proposition ix.* The tempcra- 



I u hi* ** Hydrodynamics,*' puMUhed in 173S, Dutiiel IkTnouilli 

 hud discuaftcd thu constitution of a git*, and had proved from general 

 considerations that the pressure, if it arose from the- impact of a 

 number of moving particle*, must be proportional to the square 

 df th-ir velocity. (&* " Togg. Ann.,'* Bd. 107, 1859, p. 490.) 

 I 



