CHAPTER III. 



t)N THE PRESSURE EXERTED BY NON-ELASTIC FLUIDS 



PARABOLIC PLANES IMMERSED IN THOSE FLUIDS, WITH THE 

 METHOD OF FINDING THE CENTRE OF GRAVITY OF THE SPACE 

 INCLUDED BETWEEN ANY RECTANGULAR PARALLELOGRAM AND 

 ITS INSCRIBED PARABOLIC PLANE. 



1. WHEN THE AXIS OF THE PARABOLIC PLANE IS PERPENDICULAR TO 

 THE HORIZON, AND ITS VERTEX COINCIDENT WITH THE SURFACE 

 OF THE FLUID. 



PROBLEM XL 



77. If a parabolic plane be just perpendicularly immersed 

 beneath the surface of an incompressible fluid : 



It is required to compare the pressure upon it, with that 

 upon its circumscribing rectangular parallelogram, and to 

 determine the intensity of pressure, according as the vertex 

 or the base of the parabola is in contact with the surface 

 of the fluid. 



First, when the vertex of the parabola is uppermost, and just in 

 contact with the surface of the fluid ; let AC B 

 be the parabolic plane, of which AB is the 

 base or double ordiriate parallel to the hori- 

 zon, and CD the vertical axis just covered by 

 the fluid whose surface is EF, and let ABFE 

 be a rectangular parallelogram circumscribing 

 the parabola. 



Now, it is demonstrated by the writers on 

 mechanics, that the centre of gravity of a parabolic plane is situated 

 in the vertical axis, and the point where it occurs, is at the distance 

 of three fifths of that axis from the summit of the figure. 



Therefore, if the axis CD be divided at m, into two parts such, that 

 cm is to Dm as 3 is to 2,* then is m the centre of gravity of the 



VOL. I. F 



