Pressure of Fluids. 297 



der ECDG, but in order to transport the vessel, an effort would f . J94 

 be required equal to the weight of the entire mass of water con- 

 tained in the vessel. This will be demonstrated in a manner still 

 more general after we have explained the method of estimating 

 the pressure upon oblique plane surfaces and upon curred 

 surfaces. 



414. LetACDF be the vertical section of a vessel terminated Fig.199^ 

 by surfaces either plane or curved, and inclined in any manner 20 - 



to the horizon. If we imagine an infinitely thin stratum a b d c, 

 we can suppose it destitute of gravity, and pressed by the fluid 

 above it. Now this pressure will be distributed equally to all 

 points of the stratum, and will act perpendicularly and equally 

 upon each of the points of the faces a c, b d. Accordingly, as 

 this force is equal to that which a single filament IK would 

 cause, the pressure exerted perpendicularly upon 6 d, will be 

 expressed by b d X IK ; and it is evident that we should arrive 

 at the same result, if instead of b d being considered as a small 

 straight line, we regard it as a small surface. We hence derive 

 the general conclusion, that the pressure exerted perpendicularly 

 upon any infinitely small surface by a heavy homogeneous fluid, has 

 for its expression this surface multiplied by its perpendicular distance 

 from the level of the fluid. 



415. Hence the whole pressure exerted upon any plane sur- 

 face, situated as we please, is equal to the sum of the infinitely 

 small parts of this surface, multiplied each by its distance from 

 the level of the fluid. If we represent these small parts by 

 m, ?i, o, &c., and their distances respectively from the level of 

 the fluid by AA', BE', CC', &c., according to article 76, we shall 

 have 



GG' X (m + n + o -f &c.,) 

 = AA' X m -{- BB' X n -f CO X + &c., 



that is, the sum of these products is equal to the whole surface 

 multiplied by the distance of its centre of gravity from the same 

 horizontal plane. Therefore the pressure exerted by a heavy fluid 

 against an oblique plane surface has for its measure the product of 

 this surface into the distance of its centre of gravity from the line of 

 level of the fluid. 

 Mech. 38 



