OF THE HYDROSTATIC BELLOWS. 145 



Now, according to the principles of mensuration, the solidity of a 

 cylinder is determined, by multiplying the area of its base into its 

 perpendicular altitude ; consequently, if h denote the perpendicular 

 height of the column, we have 



.0490875 h = 30.72; 

 therefore, by division, we shall obtain 



OA (TO 



153. The solution which we have here given, applies to the parti- 

 cular example preceding, in which the data are assigned ; but in order 

 to accommodate the theory to every case, it becomes necessary to 

 draw up the solution in general terms ; for which purpose, we must 

 recur to equation (114), where the weight of the equilibrating column 

 has already been found ; then, according to the above analogy, we 

 have 



62i : 1728 : : f , ., 



where s denotes the solidity of the column. 



If in the above analogy, we make the product of the jnean terms 

 equal to the product of the extremes, we shall have 



and from this, by division, we get 



tf (115). 



Therefore, if the solidity of the equilibrating column be divided by 

 the area of its base, viz. the quantity .7854d 2 , the quotient will fur- 

 nish the perpendicular altitude ; hence we have 



_ 35.2024 w 



D* (116). 



154. From this it appears, that in order to determine the altitude 

 of the equilibrating column, it is not necessary that its diameter 

 should be known, for the equation is wholly independent of that 

 element, the diameter of the bellows, and the weight upon tne 

 moveable board only, entering into its composition. The following 

 practical rule will therefore determine the altitude of the column by 

 which the equilibrium is maintained. 



VOL. I. L 



