114 REPOKT— 1886. 



reference to both the above questions, if a negative answer is given, it is 

 important to have a quantitative determination in order that we may 

 know whether the dififerences in each case are of an order to be detected 

 by experiment, and whether they are definite. Professor James Thomson' 

 published an important paper in which, by the appHcation to Regnault's 

 very extensive and minutely investigated results for water of a thermo- 

 dynamical foi^mula of Sir W. Thomson - he deduced the result that the 



ratio of the value of -^ for water vapour to the value for ice vapour at 



the same temi^erature is 1'13 to 1. The argument of Professor James 

 Thomson is briefly as follows. Take a body which can exist in three states, 

 solid, liquid, and vapour, and which can be examined in respect to each 

 pair, viz., liquid- vapour, vapour-solid, solid-liquid ; on a plane surface 

 mark off on an axis of abscissae the temperature, and perpendicular to 

 the abscissae ordinates representing the pressures ; we can then determine 

 by experiment and draw a diagram of the relation between each of the 

 pairs in i^espect of pressure and temperature ; we shall thus have three 

 lines for this relation, one representing these I'elations for liquid-vapour, 

 one for solid-vapour, and one for solid-liquid. The two vapour-curves 

 are nearly continuous, but they have a slight angle at the point at which 

 they meet, an angle which would be evident if one of the two were pro- 

 longed ; at the point of junction of these two curves there are then two 



values of -t-; the third line, for solid-liquid, passes through this same 

 at 



point, which is therefore called the triple point. 



The line for liquid-vapour if extended with increasing temperature will 

 abruptly tei'miuate at the critical point. 



The thermo-dynamic relation supplied by Sir W. Thomson was 



-±. = CM ; in which m is the pressure, and -4- its rate of increase with 

 dt at 



temperature, the volume being constant ; C is Carnot's function (=:1/T 



where T is the absolute temperature), and M is the rate of absorption at 



which heat must be supplied to the substance 'per imit augvientation of 



volume to let it expand without varying in temperature. 



Apply this formula first to steam with water, and second to steam witlu 



ice, at the triple point, which is almost exactly at 0° C. In either case since 



the vapour-pressure is for any given temperature independent of the volume, 



dp 



-Tf is the same in this case whether there is change of volume or not. 



Hence -j- j i"^^^^ P' i^ pressure for solid with vapour) =:M/M'. 



at I at 



Now, as determined by Regnault, the heat of evapoi'ation of a gram 

 of water at 0° into steam at 0°=606'5 ; and the latent heat of fusion of 

 ice is 79; thus M/M'=606/606 + 7y approximately=l/l-13. 



Professor J. Thomson took Regnault's figures for vapour-pressures 

 from ice and water as they stand, together with the various formulje- 

 which Regnault employed for representing different parts of the curve, 

 and showed, by an exhaustive examination of the whole, that Regnault's 

 actual determinations were so accurate as in fact to be available for con- 



' Phil. Mag. iv. xlvii. p. 447, 1S74. 



* Trans. Roy. Soc. Edinhurglt, March 17, 1851. 



