412 



OF THE CENTRE OF PRESSURE. 



and this pressure being applied at m, operates on the lever me to turn 

 the plane about ef, with a force which is equal to 



Through the point m, draw mn parallel to ef, the base of the 

 immersed plane ; then, the tendency to turn round the vertical side 

 a e, is equal to the whole pressure upon the plane, drawn into the 

 length of the lever mn ; but mn=i \b, and we have seen above, that 

 the pressure is expressed by %bl*s; consequently, the tendency to 

 turn round ae, is 



let these two momenta be compared, and we shall have 



513. This is obvious, for by casting out the common factors, and 

 assimilating the fractions, the ratio becomes 



21 : 3b ; 



and when I and b are equal to one another, or when the immersed 

 plane is a square ; then the ratio is simply as 2:3; that is, the 

 tendency of the plane to turn round the lower horizontal side, is to its 

 tendency to turn round a vertical side, as 1 : 1 J, or as 2 : 3. 



PROBLEM LXV. 



514. A semi-parabolic plane is immersed vertically in a fluid, in 

 such a manner, that the extreme ordinate is just in contact with 

 the surface : 



It is required to determine the position of the centre of 

 pressure, both with respect to the axis and the extreme 

 ordinate , which is coincident with the surface of the fluid. 



Let IK be the surface of the fluid, and acd the semi-parabola 

 vertically immersed in it, in such 

 a manner, that ad the extreme 

 ordinate coincides with i K, while 

 the axis ac is perpendicular to it. 



Let m be the point at which the 

 centre of pressure is supposed to 

 be situated, and through m draw 

 mb and mn, respectively perpen- 

 dicular toad and ac, and suppose 

 the axes of co-ordinates to originate at a ; then, if we 



