304 Hydrostatics. 



to jBC, since D, /, are the middle points of AB, AC, respectively. 

 Consequently, they will destroy each other. The resultant then 

 must be the same as that of the two forces h and k ; and as these 

 are parallel, being each perpendicular to CB, their resultant 

 must be equal to their sum, and perpendicular to J5C; that is, 

 (1.) It will be represented by BO + 00 or by C; and (2.) 

 being perpendicular to BC, and passing, as we have just seen, 

 through the centre F of the circle circumscribed about ABC, it 

 passes through the middle point BC. 



Fig.206. This being premised, the resultant p of the two forces p, <?', 

 will be perpendicular to the middle of BE, and be represented 

 by BE. For the same reason, the resultant p' of the two forces 

 p, p', and consequently of the three forces p, q', p', will be per- 

 pendicular to the middle of BD and be represented by BD. 

 Lastly, the resultant g" of the forces p', q, and consequently of 

 the forces p, <(,$> q, will be perpendicular to the middle of DC 

 and be represented by DC; it will accordingly be equal and 

 directly opposite to the force r; therefore all these forces will 

 destroy each other. The same reasoning will evidently be appli- 

 cable, whatever the number and magnitude of the sides. Hence 

 we derive the general conclusion, that the efforts which result in a 

 horizontal direction from the pressure of a heavy fluid exerted perpen- 

 dicularly upon the surface of a body immersed in it, mutually des- 

 troy each other. 



422. The pressures upon any given surface being considered 

 by themselves, the distance at which the resultant, or the centre 

 of pressure passes, is readily found. The forces exerted upon 

 the several points being as the distances respectively of these 

 points from the surface of the fluid, they are as the forces that 

 would arise from the motion of this surface about the intersection 

 of its plane with the surface of the fluid as an axis. But we have 

 seen that the distance of the resultant in this case is that of the 



357 centre of percussion or oscillation. Hence the distance of the 



centre of pressure of any given surface from the surface of the 



fluid, is the same as that of the centre of percussion. Accord- 



Fig.neJngly, the centre of pressure on the side of a perpendicular pris- 



365. matic vessel, is one third of the height from the bottom. 



