FREE SURFACE OF A LIQUID AT REST. 13 



cone; the pressure is three times the weight of the enclosed 

 water. 



This increased pressure on the base is caused by the re- 

 action of the curved surface of the cone. The pressure on 

 the curved surface consists of an assemblage of forces whose 

 vertical components all point downwards and react upon the 

 base. 



EXAMPLES. 



1. If a surface of one square inch be placed in a vessel 

 completely filled with water, and if the pressure upon it be 

 2 Ibs., what will be the pressure on one square inch placed 

 at a level 75 inches lower ? 



Here A = one square inch, h = 75 inches, and P and 

 P' are the pressures at the upper and lower points; there- 

 fore we have, from (2) and (8), 



P' -P = 252.5* x 75 



= 18937.5 grains 

 = 2.705 Ibs. 



.-. P' = 2.705 + 2 = 4.705 Ibs. 



2. If the pressure on the upper surface, whose area is a 

 circle of half an inch radius, is 1.5 Ibs., find the pressure on 

 another circular area whose radius is one inch, placed at a 

 depth 10 feet lower in the water. Ans. 19.5986 Ibs. 



11. The Free Surface of a Liquid at Rest is a 

 Horizontal Plane. Let ABCD represent the section of a 

 vessel containing a liquid subject to the 

 action of gravity; then will its free 

 surface be horizontal. For, if the free 

 surface is not horizontal, suppose it to 

 be the curved line, APB. Take any 

 point P, of the surface where the tan- . 

 gent to the curve is not horizontal; let 



* The weight of one cubic inch of water at the standard temperature ie 252.5 grains. 



