150 THEORY OF CONSTRUCTION AND SCIENTIFIC DESCRIPTION 



PROBLEM XXV. 



159. If a hydrostatic bellows of a cylindrical form, have a 

 given quantity of fluid poured into the equilibrating or suspend- 

 ing tube : 



It is required to determine through what space the weight 

 on the moving board will ascend in consequence of the supply. 



Before we proceed to the resolution of this problem, it may be 

 proper, as in the foregoing cases, to exhibit an appropriate notation ; 

 for which purpose, 



Put D= AB or DC, the diameter of the cylindrical vessel or bellows, 

 c?zz the diameter of the equilibrating or suspending tube, 

 q HZ the quantity of fluid poured into the tube, and 

 a; Em, the space through which the weight ascends by reason 

 of the supply. 



Then, according to the principles of mensuration, the area of a 

 transverse section of the cylindrical vessel or bellows, is 



and the area of the corresponding section of the tube, is 



where the symbols a and a' denote the respective areas. 

 But by the property demonstrated above, the fluid rises equally in 

 the bellows and in the tube ; therefore, the quantity of fluid which 

 flows into the bellows in consequence of the supply, is 



and the quantity which remains in the tube, is 



where the symbols s and s' denote the solidities of the cylinders, 

 whose diameters are D and d, and their common altitude x. 



Now, the sum of these quantities, is manifestly equal to the quantity 

 of fluid poured into the tube ; hence we have 



and by division, we obtain 



- 9 



(120). 



