OF THE CENTRE OF PRESSURE. 



413 



Put I ac, the axis of the semi-parabola, 



b zr ad, the extreme ordinate, which is in contact with IK, 

 x =z any abscissa estimated from the vertex at c, and 

 y zz the corresponding ordinate, 



then is I x the distance between the ordinate and the origin of 

 the axes, corresponding to x in the general investigation. Problem 

 LXIII. ; but by the property of the parabola, we have 



l:bl::x:y*; 

 and from this, by reduction, we get 



Therefore, if l x and by |, be respectively substituted for 

 and y in the equations of condition numbered (302), we shall have 



and for the corresponding co-ordinate, it is 



/ 



mn~ 



But by the writers on the fluxional analysis, the complete fluents 

 of these expressions are respectively as follows, viz. 



- , 



bm=: - ^ - ST- - ,and?wn 

 351 



the correction in both cases being equal to nothing; but when arrr/, 

 we get 



imzz|/, and mn T s jb, (305). 



and from these values of the co-ordinates, is the centre of pressure to 

 be found. 



515. EXAMPLE. A plane in the form of a semi-parabola, is immersed 

 perpendicularly in a fluid, in such a manner, that the extreme ordinate 

 coincides with the surface; whereabouts is the centre of pressure 

 situated, the axis being 9 and the ordinate 6 inches ? 



