LECTURES. 211 



If these effects are due to adhesion and cohesion, it is evident that 

 the first film of water is supported by the attraction of the glass — that 

 the second coheres to the first, and the third to the second, and so on. 

 See model and drawing. 



The quantity of water thus supported hy one side of a plate is equal 

 to about 2^ grains, (or the weight of the hundreth part of a cubic 

 inch of water,) for each linear inch along the glass, parallel to the 

 surface of the liquid in the vessel. 



(94.) When an amalgamated plate of copper is plunged into mer- 

 cury, the quantity of the metal supported above the general level and 

 estimated in the same way is about 17 grains. 



(95.) The following equation expresses the equilibrium of the forces 

 which sustain the first film. In this q represents the attraction of 

 the liquid for the solid, p that of the liquid for itself, and w the weight 

 of the film : 



2q—p = io. (6.) 



Proof of this — according to the method of La Place. We see from 

 this equation that if the attraction of the liquid for the solid is more 

 than half as great as that of the liquid for itself, an elevation will be 

 produced along the surface — hence a film of water will be elevated 

 along a surface of ice, and a second film of water along the surface of 

 the water of the first film, and so on. In this case 



2p — p z=: w, or p = lu. 



If the attraction of the liquid for the solid be less than half of that 

 of the liquid fur itself, then the left hand side of the equation becomes 

 negative, and a depression will be indicated. 



Example — plate of glass plunged into dry mercury. 



(96.) Suppose next that two plates held parallel and opposite each 

 other be placed in the water, the weight of liquid supported will now 

 be double. If the plates be brought nearer, the water will rise between 

 them, so that the weight supported may still be the same ; hence the 

 height of the liquid will be inversely as the distance of the plates. 

 _ Let the interval between the plates be the yi„th of an inch, then, 

 since each linear inch of each plate will support 2^ grains or the hun- 

 dredth part of a cubic inch of water, therefore the liquid will stand at 

 the height of two inches. If tne plates be -^\^ of an inch apart, the 

 elevation will be 6 inches— or, if d be the distance of the plates, and 

 h the height, then 



1 



h = (Y.) 



50c/ 



(97.) Next let four narrow plates be joined at their edges so as to 

 form a prism, of which the transverse section is a square, and let this 

 be placed in water — then the liquid, being supported on four sides 

 instead of two, will rise to tioice the height. Also because the circum- 

 ference of a circle is to its area as the periphery of a circumscribed 

 square is to its area, the liquid will stand at the same altitude in a 



