OF FLUID PRESSURE USED AS A MECHANICAL POWER. 113 



2. Upon these principles therefore, and others of a similar nature, 

 which we have mentioned at the outset, is explained the paradoxical 

 property of non-elastic fluids : 



That the pressure on the bottom of a vessel Jilted with 

 fluid, does not depend upon its quantity, but solely upon the 

 perpendicular altitude of its highest particles above the 

 bottom of the vessel or the surface by which the pressure is 

 sustained. 



3. And from the property here propounded, is deduced the remark- 

 able and important principle : 



That any quantity of fluid however small, may be made to 

 balance, or hold in equilibrio, any other quantity, however 

 great. 



Let the upright or vertical section of a vessel containing an incom- 

 pressible and non-elastic fluid, be such as is repre- 

 sented by A BCD in the annexed diagram, and let 

 cdbe the corresponding section of a small pipe or 

 tube inserted into its upper surface at the point d. 



Then, supposing the vessel and the tube to be 

 filled with fluid as far as the point c ; it is manifest 

 from the first case of the preceding problem, that 

 the pressure upon DC the bottom of the vessel, is precisely the same 

 as if it were entirely filled to the height acb\ for the pressure upon 

 the bottom DC, is equal to the weight of a fluid column, the diameter 

 of whose base is DC and its perpendicular altitude an or be; but this 

 is evidently greater than the weight of the fluid in the vessel, and by 

 increasing the height of fluid in the tube, the pressure on the bottom 

 will be increased in the same proportion, while the actual increase 

 of weight is very small, being only in proportion to the increase of 

 pressure, as the area of a section of the tube is to the area of the 

 bo torn. 



PROBLEM XXI. 



118. Having given the diameter and perpendicular height of 

 a cylindrical vessel, together with the diameter of a tube fixed 

 vertically into the top of it : 



VOL. I. I 



