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



In the second place, I wish to observe that even if Mr. Moon 

 were right in rejecting Boyle^s law when there is relative mo- 

 tion, it would still be without physical significance to express p 

 as a function of v. That this might be done in any particular 

 case of motion in one dimension is admitted ; but the statement, 

 though true, would express, as it stands, no physical law. What 

 the pressure at any point of a fluid in motion may be under pre- 

 scribed circumstances is (as I said before) a purely physical 

 question ; and we are agreed, I believe, that the magnitude of 

 the actual velocity at the point, whether measured absolutely or 

 relatively to other parts of the fluid at a distance, has nothing to 

 do with it. Under these circumstances the expression of jo as a 

 function of v in a particular case, though it may be correct, is 

 not instructive. Perhaps an illustration will render my meaning 

 clearer. In the actual course of events the length of Mr. Moon's 

 hair and the length of mine are both functions of the time. Eli- 

 minate the time and the length of our hairs are expressed as 

 functions one of another ; but no physical connexion is thereby 

 proved. Again, in the motion of the earth round the sun, the 

 force of attraction exercised upon it is (according to received 

 views) proportional to r~^; but inasmuch as r is a function of 6 

 (the angular coordinate), or of the time t, the force of gravity 

 may without error be expressed in terms of 6 and t — either sepa- 

 rately, or jointly in an indefinite number of ways. Yet no one, 

 I imagine, would say that the law of gravity could properly be 

 so stated. It is therefore desirable that Mr. Moon should state 

 what he conceives to be the real physical law of pressure, true at 

 all times and places. 



It is perhaps abstractedly possible that besides p the differen- 

 tials of p and V with respect to space may be elements on which 

 the pressure depends. (That the velocity itself is not an element 

 in the matter is, I believe, admitted by Mr. Moon, and is at any 

 rate a direct result of experiment.) Indeed any theory of gases 

 which professes to be more than a first approximation, must give 

 an account of the tangential force which acts between two por- 

 tions of the gas separated by an ideal plane, whenever the first 

 differentials taken normally of the tangential velocities of the gas 

 in the neighbourhood of the plane are finite. Of course nothing 

 of this kind can happen when the motion is in one dimension 

 merely. 



I do not know what Mr. Moon may think of the kinetic 

 theory of gases ; but it has certainly great and increasing claims 

 to be considered at least a truthful representation of the facts. 

 The dependence of pressure on the density (and temperature) 

 only, is one of the simplest consequences of its fundamental 

 assumptions. 



