OF CAPILLARY ATTRACTION AND THE COHESION OF FLUIDS. 427 



force be denoted by /, which obtains equally in both the cases above 

 stated ; therefore, if F denote the intensity of the vertical attractive 

 force, we shall have 



* = 2f. 



536. But there is a negative force acting- in the opposite direction, by 

 which this value of F is influenced, and which arises from the attrac- 

 tion exerted by the fluid surrounding the imaginary tube, on the lower 

 particles in the column BE, and the result of this attraction is a 

 vertical force acting downwards, in opposition to the force 2/"; let 

 this antagonist force be denoted by/', and we shall obtain 



FZZ2/-/'. 



Put m zz the magnitude, or solid contents of the column B F, 

 I zz the density or specific gravity of the fluid, and 

 g zz the power of gravity. 



Then by multiplying these quantities together, the weight of the 

 elevated column is expressed by m%g ; but in the case of an equili- 

 brium between this weight and the attractive forces by which it is 

 elevated, it is manifest that they are equal ; hence we have 



mlglff. (310). 



If the force 2/ be less than /', the value of m or the magnitude 

 of the attracted column will be negative, and the fluid will sink in the 

 tube ; but whenever the force 2/ exceeds /', the value of m will be 

 positive, and the fluid will rise above its natural level. 



537. Since the attractive forces, both of the glass and the fluid, are 

 insensible at sensible distances, the surface of the tube A B will have 

 a sensible effect on the column of fluid immediately in contact with 

 it; this being the case, we may neglect the consideration of curvature, 

 and conceive the inner surface to be developed upon a plane ; the 

 force f will therefore be proportional to the width of this plane, or 

 which is the same thing, to the inner circumference of the tube. 



Put d zz the inner diameter of the tube, 



TT zz the ratio of the circumference to the diameter, 



zz a constant quantity, representing the intensity of the 



attraction of the tube upon the fluid, and 

 9' zz another constant, representing the intensity of attraction 



which the fluid exerts upon itself. 



Then, by the principles of mensuration, we have tin equal to the 

 inner circumference of the tube, and also to the exterior circum- 

 ference of a column of fluid of the same diameter ; therefore, it is 



