. The Cambridge course of elementary natural philosophy; being the demonstrations of the propositions in mechanics and hydrostatics in which those persons who are not candidates for honours are examined for the degree of on a fluid, the part immersed : the whole body:: the specific gravity of the body : the specific gravityof the fluid. Let a solid of uniform density float on a fluid with Mcubic inches of it above the horizontal yj\ plane of the surface, and N cubic inches y — -----—^ggp below that surface. z==r^^Jfr-,^JiSS^ Let S= (Specific Gravity) of the solid; S= the fluid.
. The Cambridge course of elementary natural philosophy; being the demonstrations of the propositions in mechanics and hydrostatics in which those persons who are not candidates for honours are examined for the degree of on a fluid, the part immersed : the whole body:: the specific gravity of the body : the specific gravityof the fluid. Let a solid of uniform density float on a fluid with Mcubic inches of it above the horizontal yj\ plane of the surface, and N cubic inches y — -----—^ggp below that surface. z==r^^Jfr-,^JiSS^ Let S= (Specific Gravity) of the solid; S= the fluid. Then, (M+ N) x S = weight of the solid. Prop. x S= fluid displaced. But, because the body floats, these two weights areequal, Prop. vi.; .{M+N)-Si ^^J, or N1: M + N :: S : S; i. e.; The part of it immersed : the whole of the body:: S. G. of the body : S. G. of the fluid, q. e. d. 16. Prop. ix. When a body is immersed in afluid, the weight lost : whole weight of the body ::the specific gravity of the fluid : the specific gravityof the body. Let M be the number of cubic inches contained in abody of uniform density which is whollyimmersed in a fluid; S the S. G. of the body,S the S. G of the Then the pressure downwards of the solidis its weight; and if the solid be removed, andthe space it filled be occupied by an equal bulkof the fluid, equilibrium will still remain. And if the fluidso added become solid, the equilibrium will continue, andthe pressure upwards of the surrounding fluid will remainthe same as before. HYDROSTATICS. 55 Now the pressure downwards produced by the fluidthat becomes solid is its weight. And since the pressureupwards of the surrounding fluid supports this weight, thatpressure must be exactly equal and opposite to it. The pressure downwards, therefore, before it was im-mersed, of the original solid, (i. e. its weight MS, Prop, vu.),must, by the solid having been immersed, have been di-minished by a pressure upwards, arising fro
Size: 1563px × 1598px
Photo credit: © Reading Room 2020 / Alamy / Afripics
License: Licensed
Model Released: No
Keywords: ., bookcentury1800, bookdecade1840, bookpub, booksubjecthydrostatics
