Capillary Attraction 339 



But they depend, like the preceding, upon the attraction exerted 

 by the tube upon the liquid and by the liquid upon itself; so 

 that when the thickness of the tube is made to vary, the bore 

 remaining unchanged, the elevations and depressions of the li- 

 quid remain the same, which proves that beyond a certain 

 thickness, probably too small for us to attain, any additional 

 matter that may be accumulated will have no appreciable effect. 

 It follows from this law, that when tubes of the same diameter 

 are completely moistened throughout by the liquid, the ele- 

 vation or depression will be the same in all, whatever the 

 substance of the tube, which shows that the thin film attach- 

 ed to the interior surface, removes by its interposition the rest 

 of the liquid mass so as to render the attraction of the tube 

 insensible ; consequently the elevation is the same in all tubes 

 of the same bore, because it is equal to that which would proceed 

 from a tube of the same diameter formed of the liquid itself.t 



456. Setting out from the results furnished by the calculus, 

 we are able to give a satisfactory explanation of the phenomena 

 of capillary tubes. Beginning with the case in which the fluid is 

 elevated above the' natural level, and which requires the upper 

 extremity of the fluid column to be concave, we suppose an 

 infinitely small filament of fluid extending from the lowest point Fig.222. 

 of the meniscus along the axis of the tube, and then returning 

 in any manner through the mass of the liquid to the free surface. 

 The fluid being in a state of equilibrium, this filament will be in 



t The diameter of the bore of a tube is found by first weighing 

 the tube empty, and then after having introduced a certain quantity 

 of mercury, weighing it again. The excess of the latter weight above 

 the former will be the weight of the column of mercury. By calling 

 this weights, the length of the column Z, and the radius of the bore 

 R, 7i being the ratio of the circumference of a circle to its diameter, Geom. 

 we shall have for the bulk of mercury contained in the tube 7iR 2 l. 291. 

 If w' be the weight of a cubic inch of mercury at the temperature 

 assumed in the experiment, and R and / be also expressed in inches, 

 or parts of an inch, w' n R 2 I will be the weight of the column in 

 question ; whence 



7i R 2 I = w, and R 



= rz: 



<\w'7rr 



