OF THE CENTRE OF PRESSURE. 419 



Let this value of y be substituted in the first of the equations of 

 condition (302), and we shall have, for the value of the distance en, 

 as follows, viz. 



> ,. 



Jxyx fx*x 



the correction being equal to nothing ; and when a: zr c D or d, we have 



en = 1^*3. (308). 



520. Again, for the horizontal co-ordinate nm, by substituting the 

 above value of y in the second of the equations of condition, we obtain 



here again the correction is nothing, and in the limit when a? = CD or 

 dj we have 



T 3 G L ( 309 )- 



8\/3 



521. It is shown by the writers on mensuration, that the planes com- 

 posing a tetrahedron, are inclined to each other in an angle whose 

 sine is equal to V 2 > an d by the principles of mechanics, the direction 

 of the force applied at m, must be perpendicular to the plane ; itjs 

 therefore inclined to the horizon at an angle whose cosine is $^/2 ; 

 but by the principles of Trigonometry, we have 



sin.^> -v/ 1 cos 2 .0, 

 or by substituting as above, we get 



sin.^ i= v/l f = $ = .33333, 

 corresponding to the natural sine of 19 28' 15". 



Hence it appears, that at whatever point in the plane the retaining 

 force may be applied, its direction will be inclined to the horizon, at 

 an angle of 19 28' 15" ; the third demand of the problem is therefore 

 satisfied, and we have seen that equation (307) fulfils the first, while 

 the second requires the application of equations (308) and (309), and 

 the method of reduction will become manifest from the resolution of 

 the following example. 



2E2 



I 



