LECTURES. 213 



Various hypotheses have been advanced for the explanation of capil- 

 lary phenomena, the most important of which are those of Jurin, 

 Clairant, Robison, Lesley, La Place, Young and Poisson. Almost 

 every one of these may be considered as an improvement on the pre- 

 ceding, or a closer approximation to truth. 



(102.) According to the improved hypothef?is, or theory as it may 

 now be called, of Poisson and Young, the phenomena are not only 

 due to the attractions of the liquid and solid, but also to the contrac- 

 tile force existing in" the free surface of every liquid, and which is 

 increased or diminished in a given direction by a convexity or con- 

 cavity of this surface. 



To apply these principles to the phenomena of capillarity, let us 

 first suppose two plates plunged perpendicularly into a liquid on which 

 they have no action ; then the liquid will be divided from itself, the 

 contractile force will be developed along the free surface contiguous to 

 each plate, the liquid will be drawn down until the hydrostatic pres- 

 sure balances the contractile force, and we will have the following as 

 the equation of equilibrium : 



2c=ziv. (10.) 



(103.) Next let the plates have an attraction for the liquid, but not 

 as great as that of the liquid for itself, as in the example of glass and 

 mercury. 



The liquid in this case will not be entirely separated from the glass 

 so as to produce a perfectly free surface, but will be pressed against it 

 by the attraction ; the contractile force will, therefore, be partially 

 neutralized, and the depression consequently be less. 



If d be the diminution in the contractile force in consequence of the 

 attraction of the glass, then 



2(c—d) = iv. (11.) 



Since c and d must remain the same with the same liquid and 

 solid, lu will also be constant; and hence the depression will be in- 

 versely as the distance of the plates, or the diameter of the tube. 



Also, with the same liquid and solid, the angle of contact will re- 

 main constant, and the ci^rvature of the upper surface will be inversely 

 as the distance of the plates, and therefore the curvature may be taken, 

 as it has been by La Place, as the measure of the capillary force. 



(104.) If the attraction of the liquid for the solid be greater than 

 for itself, then the film in contact will be drawn up, the surface be- 

 tween the plates will be rendered concave — a superficial tension will 

 be developed along the curved surface and the liquid will rise until 

 the tension due to the curvature balances the weight of the column. 



The curvature in this case will also be inversely as the distance of 

 the plates, since the angle of contact remains the same — hence so long 

 as the exterior surface remains unchanged in form, the elevation will 

 be inversely as the distance of the plates. 



But if the surface without the tube be rendered either concave or 

 convex, a contractile force will be developed which will tend to elevate 

 or depress the column. 



