156 THE QU AQUA VERSUS PRESSURE OF FLUIDS 



in the top and afterwards stopped up, or it may be filled through 

 the tube alone. 



Now, if a load of about seven or eight hundred Ibs., be laid upon 

 the cover of the vessel, it will be depressed into a concavity repre- 

 sented by the dotted line AMD, the displaced water ascending in the 

 tube, in proportion as the cover is bent by the pressure of the super- 

 incumbent load ; but if we pour water into the tube FE, the cover of 

 the vessel, together with its incumbent load, will not only be raised 

 to the original situation, but will even assume a convex form, as 

 represented by the dotted line AND, rising in the middle as much 

 above the point E, as it was formerly depressed below it, the quantity 

 of elevation being measured by the index or ruler IL, which is fixed 

 in an adjoining support in such a manner, as to remain immoveable, 

 the point H which is marked on the tube, ascending or descending 

 with the cover of the vessel. 



If the tube be increased in length and more water added, it will be 

 found that the cover of the vessel, together with its load, will rise 

 higher and higher until a rupture takes place by overstretching the 

 fibres of the material ; this however, is a case not admitted in the 

 experiment, and consequently, we may conclude, that the small 

 column of water in the tube : 



Exerts the same force in raising the cover of the vessel, 

 together with the load upon it, as if the tube and the vessel 

 were of equal diameters, and the incumbent column equal to 

 AGHD, instead of that contained in the tube. 



Now, this is precisely the property of the weighing machine for- 

 merly exemplified ; for the water in the small tube F E, will raise the 

 cover of the vessel, (supposing it to be moveable and water-tight), 

 together with its load, even although it were a thousand times greater: 

 this is manifest, because the velocity with which the water descends 

 in the tube, is to the velocity with which it ascends in the vessel, as 

 the area of a section of the vessel, is to the area of a corresponding 

 section of the tube ; for instance, if the vessel is 30 inches in diameter, 

 while the supplying tube is only one ; then, we know by the prin- 

 ciples of mensuration, that the area of the top of the vessel, is to that 

 of a section of the tube, in the ratio of 900 to unity ; consequently, 

 when the water in the tube has descended one inch, the top of the 

 vessel, and the load upon it, has ascended by a one nine-hundredth 

 part of an inch ; therefore, if the water in the tube weighs one lb., it 

 will be in equilibrio with 900 Ibs. in the vessel, or which is the same 



