2 Mr. Ivory on the Theoiy of Capillary Action, and 



The second principle is the equation of the curve surface of 

 the liquid under the influence of the capillary force. When 

 a liquid is elevated above the general level by capillary action, 

 the surface is always concave upward ; on the contrary, it is 

 always convex upward, when the liquid is depressed below 

 the level. In either case, the distance of any point in the curve 

 surface from the level, is proportional to the sum of the cur- 

 vatures estimated in any two directions at right angles to 

 one another. To speak more precisely, let a normal be drawn 

 to the curve surface at any point; make two planes per- 

 pendicular to one another, pass by the normal and inter- 

 sect the curve surface ; put R and R/ for the radii of curva- 

 ture of the two sections, and y for the distance of the point 

 from the general level ; the equation of the surface in the ca- 

 pillary space is, 



/3 being a quantity to be determined by experiment. It is a 

 property well known to mathematicians, that the sum of the 

 curvatures is always the same, provided the two sections be at 

 right angles to one another. 



A little reflection will show that the two principles we have 

 mentioned fully ascertain every circumstance relating to the 

 capillary phaenomena. The equation determines the position 

 of every point in the curve surface above or below the general 

 level ; and the other principle limits the extent of the same 

 surface in the capillary space, by making known the inclina- 

 tion of its extreme boundary to the surface of the immersed 

 solid. 



It is evident that the equation cannot be verified by direct 

 observation. It was first suggested by the resemblance of the 

 surface of liquids under capillary action to the class of elastic 

 curves treated of in geometry. In reality, there seems to be 

 no circumstance accompanying the greater or less elevation 

 or depression, except a variation of curvature ; so that the at- 

 tention of the inquirer is naturally directed to examine the re- 

 lation of these two things. There is no other way of proving 

 that the equation accords with nature, but by comparing the 

 mathematical deductions from it with the results obtained by 

 careful and accurate experiments. The most general classi- 

 fication of the capillary phaenomena we owe to Dr. Jurin, who 

 makes the quantity of the displaced fluid, which is the proper 

 measure of the capillary force, proportional in all cases to the 

 length of the line of common section of the surfaces of the 

 fluid and solid immersed in it. I do not here allude to the 

 physical cause assigned by Dr. Jurin, which will not bear ex- 

 amination ; 



