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



and having an air-tight piston capable of moving freely in the 

 upper part of it. Below the piston the cylinder is filled with 

 air^ w^hieh is kept in equilibrium by means of a weight, W, rest- 

 ing on the piston, above which there is a vacuum/^ If a second 

 weight, W, be placed on the piston, we know, that the equili- 

 brium will be destroyed ; but, according to Mr. Moon, if the 

 received law of pressure were true, such ought not to be the 

 case. Even Mr. Moon must admit that it is remarkable that so 

 apparently reasonable a law should lead to such an absurd con- 

 clusion. Of course, it is easy enough to deduce the opposite 

 result from the same premises. If the piston do not descend, 

 it must be supported by a pressure which is confessedly in- 

 adequate. 



So far as I understand it, Mr. Moon^s argument may be ex- 

 pressed thus : — The lamina of air beneath the piston will not 

 begin to move until the pressure exercised on it by the piston 

 (equal to its own pressure on the piston) has changed. And the 

 pressure of the lamina (by hypothesis) cannot change until there 

 has been a relative displacement of its parts, which requires that 

 the motion should have already begun. It would appear, there- 

 fore, that the downward motion of the lamina (and piston) can- 

 not begin. Precisely the same argument may be used to prove 

 that a body cannot begin to fall under the influence of gravity ; 

 for a body cannot leave its initial position without acquiring 

 velocity, and (by the law of energy) cannot possess a velocity 

 without having already fallen. An argument of this kind is 

 destitute of validity ; and its conclusion may or may not be true. 

 In the case of gravity, where v^ (xs, we all know that falhng 

 from rest is possible ; bat if the law of motion be that v simply 

 varies as s, it is true, as may easily be shown, that a body once 

 at rest cannot begin to move. In order to arrive at a safe con- 

 clusion by the method followed by Mr. Moon, a much closer 

 consideration of the order of the infinitesimals concerned is in- 

 dispensable. A nearly similar objection would apply to Mr. 

 Moon^s treatment of cases 3 and 4*. 



A remark of a more general character may be made, which in 

 most people^s judgment would be sufficient to dispose of the 

 question. Mr. Moon proves a little too much ; his arguments, 

 if valid at all, would establish that the received view is not merely 

 false, but self-contradictory. Thus in case 2, starting from iden- 

 tically the same premises, we prove by two different lines of rea- 



* Mr. Moon assumes, if I rightly understand kirn, that if a state of 

 things once exist; and it can he shown that, tvhenever it does exist, the 

 rate of departure from it vanishes, then the state is necessarily permanent. 

 On this principle it would follow that a curve once meeting the axis of x, 

 and never meeting without also touching it, necessarily coincides wholly 

 with it. 



