PROFESSOR KELLAND, ON MOLECULAR EQUILIBRIUM. 31 



diminish x; for a like reason, that of the matter on the same particle 

 is jP.-t— tending to increase x; consequently the whole force with which 



the particle is urged in the direction of the axis of x is P i—j j— ]. 



7. By the substitution of integrals in the place of sums, the ex- 

 pression V, as before noticed, is no longer the total action of the caloric 

 on the particle, subject as it is to the powerful variations of action of 

 these particles by which it is immediately surrounded ; it is in fact, 

 the total action, omitting these and corresponding variations for the 

 other particles. In order to obtain the conditions of equilibrium of 

 the particle, we must apply another force, viz. the variation of action 

 due to the place of the particle. 



Without entering into calculation respecting this force, it is evident 

 at once, that its value is increased in the same ratio as the increment 



of the density at that point, and must consequently vary as —*— ; but 



whether it might not also vary as D, does not appear so obvious. The 

 following investigation is perhaps more satisfactory. 



8. Conceive a portion of the mass to form a prism* of which the 

 axis is parallel to x. Let its section be unity, and its length Sx, and 

 suppose the caloric within it to have the uniform density D, then the 

 action on it, due to the above forces, is 



pm*^-^): 



\dx ax ) 



let p be the pressure on the end next the origin, p + -^- Ix + &c. that 

 on the further end, then we must have 



dp - PD (— - — ) • 



dx \dx dx J ' 



here, then, by taking the aggregate of a large nnmber of particles, 

 we eliminate the effect of the molecular variations which retain any 

 individual one in its place, and may consider p as the actual pressure 

 exerted, by whatever means it matters not, to retain the particles 



