6 



Prof. J. Thomson on the 



[Nov. 16, 



places. The model admits of easily exhibiting in due relation to one 

 another a second set of curves, in which each would be for a constant 

 pressure, and in each of which the coordinates would represent tempera- 

 tures and corresponding volumes. It may be used in various ways for 

 affording quantitative relations interpolated among those more immediately 

 given by the experiments. 



We may now, aided by the conception of this model, return to the con- 

 sideration of continuity or discontinuity in the curves in crossing the boil- 

 ing stage. Let us suppose an indefinite number of curves, each for one 

 constant temperature, to be drawn on the model, the several temperatures 

 differing in succession by very small intervals, and the curves consequently 

 being sections of the curved surface by numerous planes closely spaced 

 parallel to one another and to the plane containing the pair of coordinate 

 axes for pressure and volume. Now we can see that, as we pass from curve 

 to curve in approaching towards the critical point from the higher tempe- 

 ratures, the tangent to the curve at the steepest point or point of inflec- 

 tion is rotating, so that its inclination to the plane of the coordinate axes 

 for pressure and temperature, which we may regard as horizontal, increases 

 till, at the critical point, it becomes a right angle. Then it appears very 

 natural to suppose that, in proceeding onwards past the critical point to 

 curves successively for lower and lower temperatures, the tangent at the 

 point of inflection would continue its rotation, and the angle of its inclina- 

 tion, which before was acute, would now become obtuse. It seems much 

 more natural to make such a supposition as this than to suppose that in 

 passing the critical point from higher into lower temperatures the curved 

 line, or the curved surface to which it belongs, should break itself asunder, 

 and should come to have a part of its conceivable continuous course abso- 

 lutely deficient. It thus seems natural to suppose that in some sense 

 there is continuity in each of the successive curves by courses such as 

 those drawn in the accompanying diagram as dotted curves uniting conti- 

 nuously the curves for the ordinary gaseous state with those for the ordi- 

 nary liquid state. 



The physical conditions corresponding to the extension of the curve 

 from a to some point b we have seen are perfectly attainable in practice. 

 Some extension of the gaseous curve into points of temperature and pres- 

 sure below what I have called the boiling- or condensing-line (as, for in- 

 stance, some extension such as from c to d in the figure) I think we need 

 not despair of practically realizing in physical operations. As a likely 

 mode in which to bring steam continuing gaseous to points of pressure 

 and temperature at which it would collapse to liquid water if it had any 

 particle of liquid water present along with it, or if other circumstances 

 were present capable of affording some apparently requisite conditions for 

 enabling it to make a beginning of the change of state *, I would suggest the 



* The principle that " the particles of a substance when existing all in one state only, 

 and in continuous contact with one another, or in contact only under special circum- 



