342 Hydrostatics. 



Now the fluid in the lower part of the round tube AB is at- 

 tracted, 1. by itself; but the reciprocal attractions of a body do 

 not communicate to it any motion, if it is solid, and we may, with- 

 out disturbing the equilibrium, conceive the fluid in AB frozen. 

 2. The fluid in the lower part of AB is attracted by the fluid 

 within the tube BE ; but as the fluid of the tube BE is attract- 

 ed upwards by the same force, these two actions may be ne- 

 glected as balancing each other. 3. The fluid in the lower part 

 of AB is attracted by the fluid which surrounds the ideal tube 

 .RE, and the result of this attraction is a vertical force acting 

 downwards, which we may call 9', the contrary sign being 

 applied, as the force is here opposite to the other force q. As 

 it is highly probable that the attractive forces exerted by the 

 glass and the water vary according to the same function of the 

 distance, so as to differ only in their magnitude, we may employ 

 the constant co-efficients />, p', as measures of their intensity, so 

 that the forces 9, q', will be proportional to />, p f ; for the in- 

 terior surface of the fluid which surrounds the tube BE, is the 

 same as the interior surface of the tube AB, Consequently, the 

 two masses, namely, the glass in/?/?,and the fluid around BE, differ 

 only in their thickness ; but as the attraction of both these mas- 

 ses is insensible at sensible distances, the difference of their 

 thicknesses, provided their thicknesses are sensible, will produce 

 no difference in the attractions. 4. The fluid in the tube AB is 

 also acted upon by another force, namely, by the sides of the 

 tube AB in which it is inclosed. If we conceive the column FB 

 divided into an infinite number of elementary vertical columns, 

 and if, at the upper extremity of one of these columns, we draw a 

 horizontal plane, the portion of the tube comprehended between 

 this plane and the level surface BC of the fluid, will not produce 

 any vertical force upon the column ; consequently, the only effec- 

 tive vertical force is that which is produced by the ring of the 

 tube immediately above the horizontal plane. Now the vertical 

 attraction of this part of the tube upon J5E, will be equal to that 

 of the entire tube upon the column BE, which is equal in diam- 

 eter, and similarly placed. This new force will therefore be 

 represented by -j- q In combining these different forces, it is 

 manifest that the fluid column BF is attracted upwards by the 

 two forces -f <7? + 9> and downwards by the force if ; 



