488 Professor H. L. CalUndar [Feb. 26, 



Table I. — Osmotic Pressures op Cane-sugar Solutions. 

 Osmotic Pressures Calculated by various formulse. 



the state of gas at the same volume and temperature. The vapour- 

 pressure of any substance is a definite physical property of the 

 substance which is always the same under the same conditions of 

 pressure and temperature and state, and is easily measured in most 

 cases for liquids and solutions. Equality of vapour-pressure is one of 

 the most general, as well as the simplest, of all conditions of physical 

 equilibrium. Ice and water can only exist together without change 

 under atmospheric pressure at the freezing-point 0°C., at which their 

 vapour-pressures are the same. Below the freezing-point the vapour- 

 pressure of water is greater than that of ice. Either is capable of 

 stable existence separately within certain limits, but if the two are 

 put in communication, the vapour, being mobile, passes over from 

 the water at higher pressure to the ice at lower pressure until equality 

 of vapour-pressure is restored by change of temperature, or until the 

 whole of the water is converted into ice. 



In the case of ice and water, equality of vapour-pressure can also 

 be restored by a suitable increase of pressure. This is the well-known 

 phenomenon of the lowering of the freezing-point by pressure. By 

 considering the equilibrium of water and vapour in a capillary tube, 

 Lord Kelvin showed that the vapour-pressure of water, or any other 

 liquid, was increased by pressure according to a very simple law, the 

 ratio of the increase of vapour-pressure, dp, to the increase of 

 pressure, d P, on the liquid being simply equal to the ratio of the 

 densities of the vapour and liquid, or inversely as the specific volumes, 

 V and Y. This relation, which may be written Y dV = v dp, is 

 merely a special case of Carnot's principle, and was deduced by 

 assuming the impossibility of perpetual motion. Assuming a similar 

 relation to apply to ice, Poynting showed that when a mixture of ice 

 and water was subjected to pressure, the vapour-pressure of the ice 

 must be increased more than that of the water (since the specific 



