OF THE HYDROSTATIC BELLOWS. 147 



Here, by proceeding as directed in the rule, we obtain 



This is something more than 10 tons and a quarter, which is mani- 

 festly a great load to be suspended by 2 Jibs.; but the altitude of the 

 suspending column must be proportionably great, which circumstance, 

 without the aid of some artificial force, would render the instrument 

 very inconvenient for any practical purpose ; it was, no doubt, by 

 viewing the matter in'this light, that Mr. Bratnah, senior, was led to 

 apply the forcing pump, and thereby to produce that very powerful 

 engine, which formed the subject of our last article. 



PROBLEM XXIII. 



156. In a hydrostatical bellows of a circular form, there are 

 given, the diameter of the bellows, the load suspended, and the 

 weight of the suspending fluid : 



It is required to determine the diameter of the equilibrating 

 tube, so that the instrument may be just in a state of equi- 

 librium. 



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

 weight upon the bellows, and we shall obtain 



D 2 M/ 



w 

 and from this, by extracting the square root, we get 



D 2 ^' 



w ' (118). 



_ 

 And the practical rule which this equation supplies, may be 



expressed in words at length in the following manner. 



RULE. Multiply the square of the diameter of the bellows, 

 by the weight of the fluid which maintains the equilibrium, 

 and divide the product by the weight upon the bellows, then, 

 the square root of the quotient will be the diameter of the 

 equilibrating tube. 



* This equation for the diameter of the tube may be otherwise expressed ; thus * 



i 2 



