The Hon. J. W. Strutt on the Law of Gaseous Pressure. 219 



distances, the sphere appears to me the most improbable of all 

 forms. 



The law of attraction (as ^w) I conceive to exist at all dis- 

 tances (subject to a polar force which becomes insensible at mi- 

 nute distances) ; and with regard to chemical equivalents or atomic 

 weights, whether they are due to an unchangeable difference of 

 MASS (in the sense of gravitation) of the ultimate particles, or 

 are essentially different forces of what chemists have termed 

 ^' affinity," we must not forget that they in truth only repre- 

 sent " the mean force of attraction exerted between our earth 

 (as a whole) and the combining quantities of those different 

 substances.^* 



XXVI. On the Law of Gaseous Pressure. By the Hon. J. W. 

 Strutt, M.A.j late Fellow of Trinity College j Cambridge, 



IN reply to Mr. Moon, I will consider first the objections 

 which he offers to the received theory. In the Philo- 

 sophical Magazine for July 1868, four particular cases of the 

 problem in one dimension are considered, in each of which the 

 law j? a p is supposed to lead to error. The first is reprinted in 

 the August Number. 



A cylinder contains air which is at rest, but whose density 

 varies discontinuously in crossing a certain section. Such diffi- 

 culty as the problem presents appears to me to be purely of a 

 mathematical character, arising out of the discontinuity. In 

 any case of fluid motion the possibility of a difference of pressure 

 at two points, P and Q, finitely distant, depends on the inertia 

 of the intervening air and its consequent resistance to accele- 

 ration. If, as in ordinary cases, the acceleration be finite, the 

 difference of pressure will tend to zero as P and Q approach one 

 another, without limit, because this is true of the inertia. But 

 the conclusion no longer follows if there be an infinite accelera- 

 tion. The reaction of an infinitely small mass to an infinite ac- 

 celeration may be as finite as that of a finite mass to a finite 

 acceleration. Now the layer of air situated at the boundary is 

 subject to an infinite acceleration, and therefore, no matter how 

 thin it may be taken, its resistance to acceleration cannot be 

 left out of account. That the pressures which act on its two 

 faces are unequal is, therefore, not in contradiction to any true 

 principle. 



Mr. Moon^s other arguments depend also, as I believe, on 

 logical fallacies in the treatment of infinitesimals. The second 

 supposes the case of " a vertical cylinder closed at its lower end, 

 * Communicated by the Author. 



