84 Mr. J. J. Waterston on certain Thermomohcular 



rate at a of the second liquid ; but we have to keep in mind that 

 the unit of volume, as well as the increment of temperature, is 

 — £■£ time the absolute value of the unit and increment of the first. 



159 



Thus the behaviour of the two liquids and their saturated va- 

 pours are precisely the same at absolute temperatures proportional 

 to their liquid molecular volume. 



The evidence is nearly complete that in the same category are 

 to be found hydrochloric ether and chloroform. 



§ 8. M. Regnault's researches on specific heat and latent heat 

 enable us to advance another step. 



The amount of heat-force (denoted by the symbol Co>) required 

 to vaporize a molecule of these ethers also follows the same ratio, 

 h : h 1 . E. g. the amount of heat-force required to raise a liquid 

 molecule of the first body, at B, to become a vapour molecule at 

 the same temperature zT is to the amount required to raise a 

 molecule of the second body, at b, from the liquid to the vapour 

 condition at the temperature zt as 159 : 177. 



§ 9. The full meaning of this relation will be more clearly 

 made out by referring to fig. 2, where the complete range of ex- 

 pansion of two liquids thus related is exhibited, — the ratio, how- 

 ever, being 1 to 2 instead of 159 to 177. 



It is assumed that the law of expansion extends downwards 

 to —274° at A. At this zero we start with the molecular vol- 

 ume of one double that of the other [A B = 2# ft]. In the axis of 

 temperature take AC = 2ac, the corresponding molecular volumes 

 are still in the ratio of 2 to 1 ; and this is the case all the way 

 up to E, e, the points of transition, where the maximum volume, 

 when liquid condition terminates, is nearly three times the initial 

 volume at z computed from theory. From F and / draw 

 F A' A G, fB' Bg parallel to axis. If D A is the value of Ceo of 

 the larger molecule at C, D' A' is the value of the same at C ; ; 

 d B is the value of Ceo of the smaller molecule at c, and d! B' the 

 value of the same at c'. 



The ratio of 2 to 1 is common to all these; D A = 2dB, &c. ; 

 and the thermomolecular lines of these two liquids will be repre- 

 sented on fig. 1 if we suppose n G to be drawn so that /G=^/G'. 



The remarkable point to keep in view is that Ceo and yw, (mo- 

 lecular volume) follow the same ratio. The same absolute incre- 

 ment of /ju is accompanied with the same absolute decrement of 

 Ceo at whatever part of the range it may be measured, either in 

 the liquid with the small molecules, or in that with the large. 



Take, for example, 300 cubic inches of muriatic ether at t 

 temperature, and apply heat so that its volume may increase to 

 301, and let the quantity of. heat absorbed or rendered latent be 

 denoted by k. Take 30 cubic inches of the same liquid at tem- 

 perature t, and apply heat so that its volume may increase to 31. 



