152 THEORY OF CONSTRUCTION AND SCIENTIFIC DESCRIPTION 



fitting the vessel be placed with a weight upon it, and the tube 

 graduated : 



Then, any additional weight placed upon the cover, may be 

 determined by knowing the height to which the fluid rises in 

 the tube ; and conversely : 



If the additional weight be known, the height to which the 

 fluid rises in the tube may be found. 



Let ABCD represent a vertical section of a cylindrical vessel, or of 

 any other vessel, whose sides are perpendicular 

 to the horizon ; and let K i c be the corres- 

 ponding section of the equilibrating tube. 



Let both the vessel and the communicating 

 tube be open at the upper parts AB and de, 

 and conceive the vessel to be filled with fluid 

 to the line EF or altitude DE; then, on the 

 surface of the fluid at EF, let there be placed 

 a moveable cover exactly fitting the vessel, so 

 that the whole may be water-tight. 



Produce EF to b, then is the point b at the same level in the tube 

 IK, as the surface of the fluid in the vessel whose level is EF : upon 

 the cover EF let the weight w be placed, and suppose a to be the 

 point in the tube, to which the fluid will rise by the action of the 

 cover, together with the weight w which is placed upon it; in this 

 case, the machine is in a state of equilibrium. 



If some additional weight w' be placed upon the cover, then the 

 original equilibrium will be destroyed, and can only be restored, by 

 the fluid ascending in the tube to a sufficient height to balance the 

 additional weight. 



Put DZZ AB or DC, the diameter of the cylindrical vessel, of which 



ABCD is a section, 



d zz de, the diameter of the communicating tube KIC, 

 h zz ba, the height of the original equilibrating column, 

 wzz the weight supported by the column b a, 

 w/zzthe additional weight, whose quantity is required, 

 A'zzaK, the increased altitude of the supporting column, 

 $ zz Em, the descent of the cover occasioned by the additional 



load w', and 

 $ zz the specific gravity of the fluid, 



