Properties of Matter in the Gaseous State. 107 



that on one drawn in another direction at the same point. It 

 is this difference that Maxwell uses to measure the stress at a 

 point. Prof. Reynolds always measures it by the difference 

 of pressure on two parallel planes drawn at different points. 

 For instance, on p. 830 equation (131) is 



p x —po _ 4 s 2 d?cc 

 2~>i tt a. dx 2 



andjp^— p was got by integrating -f-, and must consequently 



be the difference of pressures on tw T o planes both perpendicular 

 to x at two different points. Notwithstanding this, Prof. 

 Reynolds proceeds to compare his with Maxwell's measure of 

 the stress, and seems to talk of them as the same. That both 

 measures of the stress may exist there is no doubt; but it is 

 equally certain that Maxwell's might exist though Prof. Rey- 

 nolds's vanished. For instance, in the case I have already 

 mentioned at the beginning of this paper, of gas between two 

 parallel plane solids, the pressure would of course be the same 

 on all planes parallel to them, and so Prof. Reynolds's measure 

 of the stress would vanish; w T hile the pressure on a plane per- 

 pendicular to the solids might be different from that on them, 

 and so Maxwell's measure of the stress would not vanish. As 

 they ought to be both equal in the case Prof. Reynolds con- 

 siders, I must suppose that he did not think it worth while 

 noticing the difference, though his way of treating the matter 

 would lead one to suppose, what I can hardly believe, that he 

 never thought of their being any difference. Both measures 

 of the stress must exist when the surfaces of equal pressure 

 are curved. Maxwell's theory requires that this should be the 

 case in order for there to be any stress. Contrary to what he 

 seems to assert, Prof, Reynolds's equations do not give this 

 result. They give, when the heat is passing between two 

 infinite parallel planes, 



4H 2 



where H is the quantity of heat passing; and this, though with 

 an opposite sign, gives exactly the same law for the stress as 

 has long ago been shown to follow from Clausius's hypothesis. 

 I do not attribute much importance to the difference of sign ; 

 for if all the terms in s 2 are included that seem to me ought 

 •to be included, Prof. Reynolds's equations confirm Clausius's. 

 That both measures of the stress exist when the surfaces of 

 equal pressure are curved, is rendered obvious by considering 

 the equilibrium of a shell of gas included between two concen- 



