14 FREE SURFACE OF A LIQUID AT REST. 



the vertical line PO, be drawn to represent the weight of 

 tin' particle of liquid at P, and resolve this weight into two 

 components PR and PQ, the former perpendicular, and the 

 latter parallel to the surface. The first of these is opposed 

 by the reaction of the surface ; the second, being unopposed, 

 causes the particle to move downwards to a lower level. It 

 is evident, therefore, that if the free surface be one of equi- 

 librium, it must at each point be perpendicular to the direc- 

 tion of gravity, i. e. y it must be horizontal. 



COR. 1. Since the directions of gravity, acting on parti- 

 cles remote from each other, are convergent to the earth's 

 centre, nearly, large surfaces of liquids are not plane, but 

 curved, and conform to the general figure of the earth. 

 But, for small areas of surface the curvature cannot be de- 

 tected, because the deviation from a plane is infinitesimal. 



COR. 2. The pressure of the atmosphere is found to be 

 about 14.73 Ibs. to a square inch, or very nearly 15 Ibs. 

 The pressure, therefore, on any given area can be calculated, 

 and if TT be the atmospheric pressure on the unit of area, 

 the pressure at a depth z of a liquid, the surface of which 

 is exposed to the pressure of the atmosphere, will be, from 

 (7) of Art. 10, 



P = Sfpz + w. (1) 



COR. 3. Since the pressures are equal when the depths 

 are equal (Art. 10), it follows that the areas of equal press- 

 ure are also areas of equal depth ; therefore, since the 

 surface of a liquid is a horizontal plane, an area of equal 

 pressure is everywhere at the same depth below a horizontal 

 plane, i. e., an area of equal pressure is a horizontal 

 plane ; and, conversely, the pressure of a liquid at 

 rest at all points of a horizontal plane is the same. 



Hence it appears that when the pressure on the surface 

 of a liquid is either zero or is equal to the constant atmos- 

 pheric pressure, all points on its surface must be in the 



