146 THEORY OF CONSTRUCTION AND SCIENTIFIC DESCRIPTION 



RULE. Divide 35.2024 times the load to be sustained upon 

 the moveable board, by the square of the diameter of the 

 bellows, and the quotient will be the altitude of the equi- 

 librating column. 



We shall determine the perpendicular altitude by this rule, on the 

 supposition that the diameter of the bellows and the weight upon the 

 moving plane, are the same as in the foregoing example ; therefore 

 we have 



. 35.2024X5760 _, Q10 . , 

 ^ nz 625.8 19 inches. 



The equation (114) for the weight of the equilibrating column, was 

 deduced from the equation (113), by simple division only, without the 

 enunciation of any problem ; but in order to render the subject a 

 little more systematic, we shall determine the other elements of the 

 general equation, severally from the resolution of their respective and 

 appropriate problems. 



PROBLEM XXII. 



155. In a hydro-statical bellows of a cylindrical form, there 

 are given, the diameters of the bellows and of the equilibrating 

 tube, together with the weight of the fluid by which the equili- 

 brium is maintained : 



It is required to determine the weight upon the moveable 

 plane, at the instant when the equilibrium obtains. 



Let both sides of the general equation (113), be divided by d* the 

 square of the diameter of the balancing tube, and we shall obtain 



_pV 



~-~d^' (117). 



And this equation affords the following practical rule. 



RULE. Multiply the weight of the equilibrating fluid, by 

 the square of the diameter of the bellows, and divide the 

 product by the square of the diameter of the tube, for the 

 weight upon the moveable plane. 



EXAMPLE. The diameter of a cylindrical bellows is 24 inches, the 

 diameter of the balancing tube is one fourth of an inch, and the 

 weight of the fluid in the tube is 2 J Ibs. ; what weight will this coun- 

 terpoise on the moving board of the bellows ? 



