40 CENTRE OF GRAVITY OF MIXED SPACE 



zbi* fii'(3i r) 



3(2ft/-00 



Again, if we suppose the side BC to be horizontal, the area of the 

 triangle remains the same, and the pressure which it sustains in a 

 direction perpendicular to its surface, becomes 

 p = tfll's(3b 0). 



But the pressure on the whole parallelogram A BCD, on the suppo- 

 sition that the side BC is horizontal, according to what has been 

 proved in Problem 3, is 



consequently, the pressure on the irregular figure ABCFE, becomes 



Now, the area of the figure corresponding to the above pressure, is 

 obviously the same as we have previously determined it to be ; that is, 

 the difference between the areas of the triangle and the entire paral- 

 lelogram ; consequently, by division, we shall obtain 

 _ 



The equations (20) and (21) are manifestly symmetrical ; if there- 

 fore, we carefully attend to the conditions of the problem, from which 

 they are respectively derived, the position of the centre of gravity of 

 the figure ABCFE can easily be ascertained byresolvng the equations. 



55. The practical rules for determining the co-ordinates which fix 

 the position of the centre of gravity, may be expressed in the follow- 

 ing manner : 



1. When the side AE is horizontal, as indicated by equation (20). 



RULE. From three times the vertical length of the given 

 rectangular parallelogram, subtract the perpendicular of the 

 triangle, and multiply the remainder by twice its area ; then^ 

 subtract the product from three times the square of the length 

 of the parallelogram drawn into its breadth, and the remain- 

 der will be the dividend. 



Divide the dividend above determined, by three times the 

 difference between twice the area of the parallelogram^ and 

 twice that of the triangle, and the quotient will give the 

 co-ordinate of the line A B. 



2. When the side BC is horizontal, as indicated by equation (21). 



RULE. From three times the vertical breadth of the paral- 

 lelogram, subtract the base of the triangle, and multiply the 



