ON CAPILLARY ACTION, 



proportional to f and ?': for the interior surface of the fluid 

 surrounding the second tube is the same as the interior sur- 

 face of the first tube, so that the two masses differ only in 

 their thickness. But as the attraction of masses becomes 

 insensible at sensible distances, the difference in their thick- 

 nesses can produce none in their attractions, provided these 

 thicknesses be sensible. 4thly, and lastly, The fluid of the 

 first tube is attracted vertically upward by this tube. In 

 fact let us conceive this fluid divided into an infinite number 

 of little vertical columns: if we draw a horizontal plane 

 through <he superior extremity of one of these columns, the 

 part of the tube below this plane will produce no vertical 

 force in that column. No vertical force will be produced 

 therefore, but what is owing to the part of the tube above 

 the plane ; and it is evident, that the vertical attraction of 

 this part of the tube for the column will be the same as that 

 of the whole tube on an equal and similar column placed 

 an the second tube. Thus the whole vertical force pro- 

 duced by the attraction of the first tube on the fluid it contains 

 will be equal to that, which the attraction of this tube pro- 

 duces on the fluid contained in the second tube: this force 

 therefore will be equal to Q. 



On combining together all the vertical attractions expe- Vertical force 

 rienced by the fluid contained in the first vertical branch of acting upward. 

 the canal, we shall have a vertical force directed upward, 

 and equal to 2 Q— Q'. This force must balance the excess 

 of the pressure arising from the weight of the fluid raised 

 above the level. Let V be its volume, D its density, and g 

 its specific gravity, gDxV will be its weight. Thus we 

 shall have g Dx ^=2 Q-Q'. 



Now attraction being sensible only at imperceptible dis- The base may 

 tances, the first tube acts sensibly only on columns extrcmdy'* e |^ , e sldered ' as 

 aear to its sides: we may neglect the curvature of these sides 

 therefore, and consider them as developed on a plane sur- 

 face. The force Q will be proportional to the magnitude 

 of this surface; or, which comes to the same thing, to the 

 circumference of the base of the interior surface of the pa- 

 lallelopipedon. Thus, if we call this circumference c, we 

 shall have Q~% xc; ? being a constant proportional to the 

 intensity of tho, attraction of the matter of the first tube for 



the 



