414 OF THE CENTRE OF PRESSURE. 



Here then we have given I 9 inches, and b zz: 6 inches ; conse- 

 quently, by the equations numbered (305), we have 



bm $ of 9 zn 5j- inches, and mn^n T \ of 6 zz l inches. 



Therefore, with the abscissa ac:=9 inches, and the ordinate 

 ad 6 inches, construct the semi-parabola adc, 

 by means of points or otherwise, as directed by the 

 writers on conic sections ; then, on the axis ac 

 and the ordinate ad, set off an and a b, respectively 

 equal to 5-f and If inches, as obtained by the pre- 

 ceding calculation ; and through the points n and 

 b as thus determined, draw nm and bm, respec- 

 tively parallel to ad and ac, intersecting each other 

 in m; then is m the place where the centre of pressure occurs, as was 

 required by the question. 



516. It would be easy to multiply cases and examples, respecting 

 the parabola and other curves of a kindred nature, considering them 

 either entire or in part, and situated in different positions, as referred 

 to the surface of the fluid ; but since the resolution in every instance, 

 depends upon the integration of the general fluxional equations num- 

 bered (302), when accommodated to the particular figure, we think 

 it quite unnecessary to dwell longer on this part of the inquiry ; we 

 therefore proceed to resolve a problem or two that depend upon 

 similar principles, and consequently, are well adapted for illustrating 

 the manner in which the inquiry is to be extended. 



PROBLEM LXVI. 



517. A vessel in the form of a parallelopipedon with the sides 

 vertical, has one side loose revolving on a hinge at the bottom, 

 and is kept in its position by a certain power applied at a 

 given point: 



It is required to determine how high the vessel must be 

 filled withjtuid, before the revolving side is forced open. 



Let ABC represent the vessel in question, and let avdc be the 

 loose side moveable about the hinges at e andy*; bisect c d in c, and 

 draw cb perpendicular to cd, and let n be the point at which the 

 given power is applied ; then, because the side axdc is just sustained 

 by means of the power acting at n, it follows, that the whole force 

 of the fluid acting at the centre of pressure must produce the equipoise. 



