170 Mr. N. Campbell on the 



as to give a numerical result for one of them, numerical 

 values must be substituted for the other five. But it appears 

 immediately that from the physical, though not from the 

 mathematical standpoint, there is a great difference between 

 the nature of these quantities. Three kinds of physical 

 measurements are connected with the equation — measure- 

 ments of pressure, volume, and temperature, and the 

 measurement of these three properties for any mass of gas 

 can be effected independently of each other, and of any 

 knowledge of Van der Waals's equations. Correlated with 

 these measurements are the three quantities p, v, T, so that 

 when the results of the measurements are known the values 

 of these quantities which are to be substituted in the equation 

 are also known. But the other quantities a, h, B are not so 

 Correlated with any physical measurement ; no amount of 

 physical measurement alone can decide what values are to be 

 attached to these quantities ; their values can only be found 

 by making three independent series of measurements of 

 pressure, volume, and temperature, and forming and solving 

 three resultant equations in a, 6, and B. 



§ 5. It will be noted that I have been careful to speak of 

 the quantity "p" (e. g.) being correlated with the pressure 

 measured experimentally. I want to insist very strongly 

 that the relation is not one of identity, that "p" is not the same 

 thing as the measure of the pressure. This statement should 

 be sufficiently obvious, and yet it contains, I believe, the 

 solution of the difficulties of dynamics. Two concepts are 

 identical only if they are defined in the same way, or if their 

 definitions can be shown to be logically equivalent. Now I 

 do not propose to define either the quantity "p" or the measure 

 of the pressure, but nobody can reasonably doubt that any 

 satisfactory definitions would not be the same or logically 

 equivalent ; they Avould contain totally different conceptions. 

 The definition of "p 9 " at least if defined by Mr. Bussell, would 

 probably contain something about " well-ordered continua," 

 and continuity is, as M. Boincare has often pointed out, 

 foreign to experiment ; the definition of " pressure " would 

 contain much about sense-impressions, and sense-impressions, 

 since the exposure of Mill at least, have been held universally 

 to be foreign to mathematics. But if anyone doubts the 

 diversity of the two classes of concepts, let him consider the 

 quantity " w." Yan der Waals's equation, when numerical 

 values are inserted for the other quantities, is a cubic in v ; 

 for each set of values of p, T, a, b, B we deduce three values 

 for v. But experiment shows that, for any values of the 

 pressure and temperature of a given mass of gas, there are 



