﻿Molecular Motions in Thermodynamics, 65 



retardation. The case considered by me in my previous paper is 



du 

 that in which the external pressure is such that -tt = 0. 



The case in which there is no external pressure is expressed as 

 follows : 



Mudu=Q,udt=2mu(v + u)dt; .... (4 A) 

 or, dividing both sides by udt, 



M^=Q=2w(t; + M ) (4B) 



8. With respect to the definition of " work," I may state that, 

 so far as I know, that word is used by writers on dynamics to 

 comprehend all sorts of effects that are produced by a force 

 acting through a space, whether the overcoming of another force, 

 such as an attraction, repulsion, or pressure, or the acceleration 

 of a moving mass (see, for example, Thomson and Tait's ' Natural 

 Philosophy/ § 241). 



9. In the following investigation, the forces exerted by the con- 

 fined particles on each other are taken into account. Let P be 

 the pressure applied to the outside of the piston; Q the pressure 

 exerted by the confined particles against the inside of the piston ; 

 let 8a? denote a distance through which the piston is or may be 

 shifted, and be positive inwards ; let M be the mass of the piston 

 and u its velocity. Then, by the principle of the conservation of 

 energy, we have 



(P-Q)&f = MmSm; (6) 



and in order that the velocity of the piston may be nothing or 

 uniform (that is, in order that we may have either u—0 or 8w = 0), 

 the condition to be fulfilled is P — Q=0. The energy exerted 

 by the external pressure in driving the piston inwards through 

 the distance So? at a uniform velocity is VBx ; the energy trans- 

 ferred from the piston to the particles on which it acts is 

 Q8#=P&r; so that no energy is gained or lost by the piston. 



10. Consider now the set of confined particles which are so 

 near the piston as to exert upon it appreciable forces. The re- 

 sultant or aggregate pressure exerted by that set of particles 

 against the inner face of the piston is — Q; the resultant pres- 

 sure exerted by the piston against the same set of particles is 

 4- Q. Let R (positive inwards, negative outwards) denote the 

 resultant of all the attractions, repulsions, and pressures exerted 

 on those particles by the other confined particles in directions 

 parallel to x. Then Q-f-R is the resultant of all the pressures, 

 attractions, and repulsions exerted on the set of particles now 

 under consideration, in directions parallel to w, whether by the 

 piston or by the other particles. Let //, be the mass of that set of 

 particles, and let % denote the summation of quantities relating 



Phil. Mag. S. 4. Vol. 41. No. 270. Jan. 1871. F 



