OF THE HYDROSTATIC WEIGHING MACHINE. 151 



It therefore appears, that the space through which the weight 

 ascends by reason of the supply : 



Is equal to the quantity of fluid which is poured into the 

 tube, divided by the sum of the areas of a cross section of the 

 tube and the cylindrical vessel or bellows. 



The practical rule, or method of applying the equation, may there- 

 fore be expressed in words at length in the following manner. 



RULE. Divide the quantity of fluid which is poured into 

 the tube, by .7854 times the sum of the squares of the dia- 

 meters, and the quotient will give the quantity of ascent, or 

 the space through which the weight is raised in consequence 

 of the supply. 



EXAMPLE. The diameter of a cylindrical vessel is 20 inches, and 

 that of the suspending tube is one inch ; now, suppose that an incom- 

 pressible fluid is poured into the tube, until its weight sustain in 

 equilibrio, a load of 8760 Ibs. upon the moveable bellows board ; 

 then, how much higher will the load be raised, when 150 cubic inches 

 of the fluid are superadded ? 



Here then, we have given D=r20 inches, d 1 inch, and <? 150 

 cubic inches ; consequently, by the rule, we obtain 



* Hi * = .7854(4 5 00+1) =' 476 f a " inch ' r : ' I' 



From this it appears, that if a machine of the given dimensions be 

 brought into a state of equilibrium, the addition of 150 cubic inches 

 will raise the load .476, or very nearly half an inch higher ; in which 

 case the equilibrium will still obtain, for the altitude of the fluid in 

 the suspending tube, is increased exactly as much as the load has 

 been raised, while the magnitude of the load, and consequently, the 

 height of the equilibrating column, remain the same. 



3. THEORY OF CONSTRUCTION AND SCIENTIFIC DESCRIPTION OF THE 

 HYDROSTATIC WEIGHING MACHINE. 



160. The preceding principles may also be applied to the con- 

 struction of a very simple and convenient weighing machine ; for, if 

 into the side of an open cylindrical or other vessel, a bent tube be 

 inserted, and if on the surface of the fluid, a moveable cover exactly 



