EXPERIMENTAL KNOWLEDGE OF THE PROPERTIES OP MATTER. 511 



and a single equation might give a relation between •p, v, and t, wliich 

 would apply to all pressures and volumes, and to temperatures above tbe 

 critical point. Tet from the discontinuity at lower temperatures this 

 equation would hardly seem applicable throughout. 



In 1371' James Thomson suggested that the isothermal curves are 

 not really but only apparently discontinuous, and that their true form is 

 such that in place of the straight part there is a curved part continuous 

 with the rest, and situated partly on one side and partly on the other of 

 the straight part.- 



The transition from the gaseous to the liquid state, in this view of 

 James Thomson, is gradual, regular, and continuous for each tempe- 

 rature ; and the idea of finding a mathematical relation between p, v, and t 

 for all temperatures may be realised. Such perfectly general equations 

 have been given by Van der Waals, Clausius, and others ; but however 

 approximately these formulte represent certain sets of experiments, none 

 seem to have been proved to have the generality required. 



Less general relations we have, as Boyle's, Gay-Lussac's, and 

 MendelejefiF's laws ; a law stated by Amagat as applicable to fluids under 

 great pressure:^ (z;— a)=const. ['Ann. Chim. Ph.' [5], 22, 1881, p. 

 395] ; and another by Amagat for high temperatures or low pressures • 

 p = c (t-to) ['Ann. Chim. Ph.' [5], 28, 1883, pp. 505, 5061, and 

 [C B. 94, 1882, p. 8-17]. 



General Equations for p, v, and T. 



The general equations of Van der Waals, Clausius, and others, 

 though not yielding results fully in accordance with all the experi- 

 ments for bodies in the state of liquid or of gas or vapour by Amagat 

 and others, give so close an agreement through large ranges in cases to 

 which they have been applied that each of them must be looked upon 

 as a tolerably close approximation ; the most imijortant of these 

 equations are : 



pt'=RT— ^; Rankine.3 

 (_p + r) (v—^)='RT; Hirn." 



pv=UT (l-^); Recknagel.5 



(i> + |)(«-i)=RT; 



or, p=R — — ; Van der Waals.'' 



T c 



^=R = :-— ; Clausius.^ 



v-u T (1? +/3)^ 



p 1 AT"-B 



RT ~ v-a (v + liy 



Clausius.® 



' Froc. Roij. 8oc. 1871, No. 130. 



- 3Iaxweirs Theory of Heat, -ttli ed. p. 125. » Pldl. Trans. 1854, p. 336. 



* Theo. Mic. ChaJeiir, 2nd edit. t. i. p. 195 ; 3rd edit. t. ii. p. 211. 



' Pogg. Ann. Erghd. t. v. p. 563; and t. cxlv. 1872, p. 469. 



« Leipzig edit. ' Die Continuatat,' 1881, p. 125. 



' Wicd. Ann. 9, 1879, p. 127. ' Ihid. 14, 1881, pp. 279, 692. 



