476 LECTURE L. 



perhaps impracticable. A drop descending in a vacuum would be perfectly 

 spherical ; and if its magnitude were inconsiderable, it would be of the 

 same form when descending through the air ; a small bubble rising in a 

 liquid must also be spherical ; but where the drop or the bubble is larger, 

 its curvature will be greatest where the internal pressure is greatest, or 

 where the external pressure is least, and in different cases this pressure 

 may be differently distributed. Where a drop is suspended from a solid, 

 its length may be such that the pressure at its upper part may become 

 negative, and its surface will then be concave instead of convex : and 

 when a bubble rises to the surface of a liquid, it often carries with it a film 

 of the liquid, of which the weight is probably smaller than the contractile 

 force with which the surface resists the escape of the air, so that, from the 

 magnitude of the contractile force, we may determine the greatest possible 

 weight of a bubble of given dimensions. A slight imperfection of fluidity 

 probably favours the formation of detached bubbles, by retarding the ascent 

 of the air, but it has a still greater effect in prolonging their duration when 

 formed. (Plate XXXIX. Fig. 532.) 



In order to determine the forms of the surfaces of liquids in the cases 

 which most commonly occur, it is necessary to examine how they are 

 affected by the action of other liquids, and of solids of different descrip- 

 tions. We may form some idea of the effects of this mutual action, by 

 neglecting the force of repulsion, as Clairaut has done, and attending only 

 to that of cohesion. Supposing the horizontal surface of a liquid to be in 

 contact with a vertical plane surface of a solid of half the attractive power, 

 it will remain at rest in consequence of the equilibrium of attractions ; for 

 the particles situated exactly at the junction of the surfaces may be con- 

 sidered as actuated by three forces ; one deduced from the effect of the 

 liquid, the other two from that of the two equal portions of the solid above 

 and below the surface of the fluid ; and it may be shown that the combi- 

 nation of these three forces will produce a joint result in the direction of 

 gravity ; consequently the direction of the surface must remain the same 

 as when it is subjected to the force of gravity alone, since the surface of 

 every fluid at rest must be perpendicular to the joint direction of all the 

 forces acting on it. But if the attractive power of the solid be more than 

 half as great as that of the liquid, the result of the forces will be inclined 

 towards the solid, and the surface of the liquid, in order to be perpendicular 

 to it, must be more elevated at the side of the vessel than elsewhere, and 

 therefore concave ; consequently the fluid must ascend until it arrives at a 

 position capable of affording an equilibrium in this manner: if, on the 

 contrary, the attractive power of the solid be weaker, the liquid will 

 descend, and its surface will be convex. (Plate XXXIX. Fig. 533.) 



This mode of reasoning is, however, by no means sufficient to explain 

 all the phenomena, for it may be inferred from it, that when the attractive 

 power of the solid is greater or less than half that of the liquid, the surface 

 of the liquid must, at its origin, be in the same direction with that of the 

 solid, instead of forming an angle with it, as it often does in reality. But 

 the difficulty may be removed by reverting to the general principle of 

 superficial cohesion, and by comparing the common surface of the liquid 



