49 6 Mr. W. Sutherland on the 



liquids and gases at the same temperature ; for it is involved in 

 the result that the equation for the osmotic pressure of the 

 dissolved sugar molecules comes out as if they were in the 

 gaseous state : many lines of investigation have already made 

 this identity tolerably certain, but none so simply and clearly 

 as van't HofiPs discovery of the identity of the osmotic 

 pressure laws with those of perfect gases. 



Van't HotF has shown how, given semipermeability, it is 

 possible by thermodynamics to deduce the laws of dilute 

 sulitions in a simple manner ; the difficulty has been to get a 

 conception on molecular grounds of the rationale of osmotic 

 pressure and the simple laws of dilute solutions. But with a 

 direct molecular explanation for osmotic pressure we can then 

 adopt van't Hoff's thermodynamical extensions and treat the 

 whole matter as placed on a molecular basis ; but for the sake 

 of the illustration we will essay a direct molecular explanation 

 of another typical simple law of dilute solutions, namely, that 

 of the lowering of vapour-tension. 



In a gas the average velocity and the average distance 

 apart of the molecules are such that, although molecules are 

 continually approaching quite close to one another, they 

 seldom do so under conditions which would cause a pair to 

 remain within finite orbits relatively to one another ; even 

 when two molecules collide, the relative path after the 

 collision is generally part of a curve extending to infinity, 

 just as the paths of comets are sometimes hyperbolas ; the 

 parabola is a possible orbit for a comet, and marks the tran- 

 sition from the infinite hyperbola to the Unite ellipse of 

 certain comets and the planets. So in the case of a gas 

 which has molecular velocity lowered by cooling to the 

 critical temperature, and mean distance apart reduced by 

 compression up to the critical pressure, the relative orbits of 

 colliding molecules become restricted to a finite range, one 

 pair of molecules that have a hold on one another entangles 

 another similar pair, and so on ; the conditions are those of 

 incipient liquefaction. When the temperature is lowered, 

 liquefaction becomes decided, because of the more decided 

 entanglement, and gravitation separates out the entangled 

 portions into a continuous mass with horizontal surface, leaving 

 more space to those which had high enough velocities to 

 escape entanglement, and therefore still further increasing 

 their chances of freedom, which they enjoy as vapour in 

 contact with the liquid. Solidification occurs when each 

 molecule is imprisoned by its neighbours, or if on the surface, 

 is so strongly attracted that it cannot escape. But suppose a 

 liquid surrounding a solid, then if the molecular attraction 

 between solid and liquid is such that the potential energy 



