OF THE CENTRE OF PRESSURE. 



409 



which are employed to determine the centre of percussion, may also, 

 and with equal propriety, be employed to determine the centre of 

 pressure. 



Now, the writers on the general principles of mechanical science 

 have demonstrated, that if . 



xmed, the side of the plane extending downwards, and 

 ?/:zicc?, the horizontal side parallel tofe; 



t\\Gnfm and pm, the respective distances of the point P, fromfe and 

 fc the sides of the plane, are generally represented by the following 

 fluxional equations, viz. 



/ 



y* 



fm - - , andpwzn 



Jxyx ZJyxx 



(302). 



From these two equations, therefore, the centre of pressure cor- 

 responding to any particular case, can easily be found, as will become 

 manifest, by carefully tracing the several steps in the resolution of the 

 following problems. 



PROBLEM LXIV. 



508. A physical line of a given length, is vertically immersed 

 in a fluid : 



It is required to ascertain at what distance below the 

 surface of the fluid the centre of pressure occurs. 



Let be be a physical line, perpendicularly 

 immersed in a fluid of which the surface is 

 AB, and produce cb to f, so that the point 

 f may be considered as the centre of suspen- 

 sion, and let m be the centre of pressure, or 

 the centre of percussion ; then 



by equation (302), we shall obtain 



* 



-^ 

 f' 



' 9 



in which equation y is constant ; therefore, 



Put d fc, the distance of the lower extremity below AB, 

 8 /, the distance of the higher extremity, and 

 I ~bc, the whole length of the line. 



