32 REPORT— 1871. 



and temperature where solidification sets in. Tliis point T is to be noticed as a 

 remarkable point of pressure and temperature, as being the point at which alone 

 the substance, pure from admixture with other substances, can exist in three states, 

 solid, liquid, and gaseous, together in contact with one another. In making this 

 statement, however, the author wishes to submit it subject to some reserve in re- 

 spect to conditions not as yet known with perfect certainty. He observes that we 

 might not be quite safe in assuming that the melting-point of ice solidified from 

 the gaseous state is the same as the melting-point of ice frozen from the liquid 

 state, and in making other suppositions, such as that the same quantity of heat 

 woidd become latent in the melting of equal quantities of ice formed in these two 

 ways. Such considerations as these into which we are forced if we attempt to 

 sketch out the course of the boiling-line, and to examine along with it the corre- 

 sponding boundary-lines between liquid and solid and between gas and solid, may 

 be useful in suggesting questions for experimental and theoretical investigation 

 which may have been generally overlooked before. Proceeding, however, upon 

 assumptions such as usuallj' are tacitly made, of identity in the thermal and dyna- 

 mic conditions of pure ice solidified in ditlerent ways, the author points out that 

 we must suppose the three curves (namely, the line between gas and liquid, the 

 line between liquid and solid, and the line between gas and solid) to meet in 

 one point, shown at T in the figm-e. This point of pressure and temperature for 

 any substance may then be called the triple point for that substance. In the figure 

 the line T M represents the line between liquid and solid. It is drawn showing in an 

 exaggerated degree the lowering of the freezing temperature of water by pressure, the 

 exaggeration being necessary in order to allow small changes of temperature to be per- 

 ceptible in the diagram. The line T N represents the line between the gaseous and 

 the solid states of water substance. The two cui-ves T L and T N, one between gas 

 and liquid and the other between gas and solid, have been constructed for water sub- 

 stance through a great range of temperatures and pressures by Regnault, from his ex- 

 periments on the pressure of saturated aqueous gas at various temperatures above and 

 below 0° Centigrade*. He has represented and discussed his results above and below 

 the temperatm-e at which the water freezes (which in strictness is not 0° C, but is the 

 freezing temperature of water in contact with no atmosphere except its own gas), 

 as if one continuous curve could extend for both. As brought out experimentally, 

 indeed, they present so little appearance of any discontinuity that the distinctness 

 of the two cm'ves from one another might readil}^ escape notice in the considera- 

 tion of the experimental results. Prof. Thomson points out, however, that the 

 range from temperatm-es below to temperatures above freezing comprises what 

 ought to be regarded as two essentially distinct curves meeting one another in the 

 point T ; and he fm-ther suggests that continuations of these curves, sketched in 

 as dotted lines T P and T Q, may have some theoretical or practical significance not 

 yet fully discovered. He thinks it likely that out of the three curves at least the 

 one, M T, between liquid and solid may have a practically attainable extension past T, 

 as shown by the dotted continuation T R. Various known experiments seem to 

 render this supposition tenable, whether the condition supposed may have been 

 actually realized in experiments hitherto or not. He thinks, too, that there is much 

 reason to suppose that the curve L T between gas and liquid has a practically 

 attainable extension past T, as shown by the dotted continuation T P. 



In reference to the continuity of the liquid and gaseous states. Prof Thomson 

 showed a model in which Dr. Andrews's curves for carbonic acid are combined in 

 a curved surface, obtained from them, which is referred to three axes of rectangular 

 coordinates, and is formed so that the three coordinates of each point in the curved 

 surface shall represent, for any given mass of carbonic acid, a pressure, a tempe- 

 rature, and a volume, which can coexist in that mass. This curved surface shows 

 in a clear light the abrupt change or breach of continuity at boiling or condensing, 

 and the gradual transition round the extreme end of the boiling-line. Using this 

 model and a diagram of cui-ves represented here in fig. 2, the author explained a 

 view which had occurred to him, according to which it appears probable that 

 although there be a practical breach of continuity in crossing the line of boiling- 

 points from liquid to gas, or from gas to liquid, there may exist, in the nature of 

 * Memoires de TAcademie des Sciences, 1847, pi. viii. 



