REPORT ON CAPILLARY ATTRACTION. 265 



radii of the two cylinders be supposed infinitely great, we have 

 the case of fluid inclosed between two vertical and parallel planes 

 very near each other. The same result still holds good ; and thus 

 the experimental fact cited by Newton in his 31st query re- 

 ceives a theoretical explanation. 



The case in which the fluid is raised or depressed between 

 vertical parallel planes admits of being treated independently ; 

 and this Laplace has also done. The upper surface of the raised 

 or depressed fluid is that of a common cylinder when the interval 

 between the planes is small, and the elevation or depression is 

 directly proportional to the curvature. 



These propositions being proved with respect to the action of 

 parallel planes, we may apply to the case of a drop inserted be- 

 tween two planes inclined to each other at a very small angle, 

 reasoning analogous to that applied to a drop inserted into a 

 cone of small vertical angle. The force by which the drop is 

 urged, is shown, as before, to be inversely proportional to the 

 square of the distance from the juncture of the planes. We 

 have already mentioned that this law was obtained experimen- 

 tally by Hauksbee for the case in which a drop of water is in- 

 serted between planes. He arrived at it by observing the incli- 

 nation the planes must have to the horizon, that the effect of 

 gravity may just counteract the capillary action by which the 

 drop of water is drawn to the line of their junction. The sine 

 of the inclination, to which the resolved part of gravity is pro- 

 portional, was found to vary for the same drop when in equili- 

 brium, inversely as the square of the distance of its middle point 

 from the line of junction. Laplace's calculation, besides verify- 

 ing this experimental result, further informs us, that if the two 

 planes form with each other an angle equal to half the vertical 

 angle of a cone which incloses a drop of the same fluid, the in- 

 clination to the horizon of the plane which bisects the angle 

 formed by the two planes ought to be the same as that of the 

 axis of the cone, in order that the drop may remain in equili- 

 brium ; and that " the sine of the inclination of the axis of the 

 cone to the horizon, is nearly equal to a fraction whose deno- 

 minator is the distance of the middle of the drop from the vertex 

 of the cone, and numerator is the height to which the fluid is 

 raised in a cylindrical tube, the diameter of which is equal to that 

 of the cone at the middle of the drop." 



If fluid be raised by capillary action between two vertical and 

 parallel planes, they will be drawn towards each other. The 

 same thing will happen if the fluid be depressed between them. 

 These two facts, known by experience, were in a great measure 

 explained, as we have seen, by Monge. The theory of Laplace 



