Pressure of Fluids. 301 



others, one vertical and the other horizontal, each vertical force 

 will be represented by the truncated prism which has for its 

 base the projection of the trapezoid upon the horizontal plane 

 XZ, and for its inclined base, this trapezoid itself. Therefore 

 the sum of the vertical forces, or the single vertical force that 

 would result from them, will be represented by the sum of all 

 the truncated prisms ; and as the same reasoning is applicable to 

 each horizontal stratum, we conclude, that if a vessel ABCDF, 

 of any figure, whatever, Refilled with a fluid to any line AF, there will 

 result from all the pressures exerted by this fluid upon the several 

 points of the vessel, no other vertical force than that which is repre- 

 sented by the bulk of this fluid, or rather by its weight. 



(2.) That if a body, as ACDBM,/or example, of which AIBFpig.204. 



is the greatest horizontal section, be immersed in a fluid to any depth 

 whatever, the pressure exerted upon the superior part AMB being left 

 out of consideration, the vertical effort of the fluid to raise the body, 

 is equal to the weight of a volume of this fluid comprehended between 

 the level XZ, the surface AIBFC, and the convex surface terminated 

 by the perpendiculars let fall from the several points of the perimeter 

 AIBF upon the plane XZ. 



If we next consider the pressure exerted upon the surface above 

 the greatest horizontal section, it will be seen, by the same kind of 

 reasoning, that there would result from the pressure of the fluid 

 upon this surface in a vertical direction, a downward effort equal 

 to the weight of a bulk of the fluid comprehended between this 

 same surface, that of its projection Jl'F'B'I', and that terminated 

 by the perpendiculars let fall from the several points of the pe- 

 rimeter AIBF. Accordingly, if from the first vertical effort, we 

 subtract the second, it will be seen that the body is urged ver- 

 tically upward by an effort equal to the weight of a bulk of this 

 fluid of which it occupies the place. 



419. We hence derive the general conclusion, that if a body 

 be immersed in any fluid whatever, it loses a part of its weight equal 

 to the weight of the fluid displaced, or equal to the weight of its own 

 bulk of this fluid. 



420. There remain now two things to be inquired into, the 

 first is to determine through what point the vertical effort, result- 



