458 Mr. A. W. Riicker on the [June 18, 



The form of this curve will therefore be that of an isothermal of the 

 second class ; but for the pressure corresponding to B'C' the water-sub- 

 stance can exist in all three states ; and as the portion of the curve in 

 space corresponding to B'C' is a line perpendicular to the plane of pt, 

 its projection on that plane is the triple point of Professor James 

 Thomson ; and if we assume, with him, that ice, water, and steam can all 

 exist together at the temperature and pressure in question, it follows 

 that this line is both an isothermal and adiabatic ; for if we suppose the 

 water-substance to exist at the same time in all three states in a vessel 

 impermeable to heat, we can evidently by diminishing the volume con- 

 vert some of the steam into water, and employ the heat so set free in 

 melting a portion of the ice, during which operation the state of the 

 mixture will always correspond to a point on B'C'. 



Not only, however, is a single adiabatic coincident with the isothermal, 

 but all the adiabatics within certain limits pass through each point on 

 B'C', and are for a certain distance coincident with it, and therefore 

 with each other ; for as the conversion of ice into water is accompanied 

 by contraction, and that of water into steam by expansion, we can keep 

 the volume and pressure of a mixture of ice, water, and steam constant, 

 while, by supplying or subtracting heat, we alter their relative proportions. 



The mixture can thus be made to go through Carnot's cycle without 

 any change either in the pressure or temperature, the result always 

 being that no useful work is done ; and as in the earlier portion of this 

 paper it has been shown that it is possible for two adiabatics, drawn as 

 plane curves, to intersect, so now we have an instance of the intersection 

 of complete adiabatics, all three variables p, v, and t, to which points on 

 these curves are referred, being insufficient to determine the state of the 

 water-substance along the line B'C'. 



It is easy to determine the points at which the adiabatic corresponding 

 to any given mixture enters and leaves B'C'. 



Let <r, s, and 2 be the specific volumes of the ice, water, and steam, 

 r and p the latent heats of conversion of ice into water and steam respec- 

 tively, and v the volume of a kilogramme of the water-substance, when 

 the proportions by weight of steam, water, and ice are 



t:ce:l-cc-l 

 "We have then, as the temperature is constant, 



and v 



If no heat is supplied or abstracted, 



cZQ=0 and r(o?-.i 



If we consider ,r and to belong to the initial state, two cases arise 

 according as 



is or is not >(1 # ) -, 



