. Transactions of the American Philosophical Society. , will be — r^Tiftance oppofed to either brachium, to t f be eftimated as if accumulated at i. r from the centre of motion ; confequently equal to the effed at both apertures when reduced to their diftance, QJi, F. This may be obtained independently of fluxions ; by confidering, that the whole quantity of water (rwa) in r the u$^e (—)nf its pafling through the rotatory, acquires a^ 2crv velocity ( ) equal to, and in the diredion of, the aper- t tures, as it is carried with the tube out of its natural courfe; to p
. Transactions of the American Philosophical Society. , will be — r^Tiftance oppofed to either brachium, to t f be eftimated as if accumulated at i. r from the centre of motion ; confequently equal to the effed at both apertures when reduced to their diftance, QJi, F. This may be obtained independently of fluxions ; by confidering, that the whole quantity of water (rwa) in r the u$^e (—)nf its pafling through the rotatory, acquires a^ 2crv velocity ( ) equal to, and in the diredion of, the aper- t tures, as it is carried with the tube out of its natural courfe; to produce which the neceflary force will be , a$ t before. Acquired velocity of the ivaten •, The velocity of the water through the apertures at theJp^inning of rotation is Svh (by the eftablifhed principlesof iiydroftatics) and, as 2 wah: 8^7^^=^64l\ : : * 2(),2g6r^ ^ .—?—: 64hH =the fquare of the augment- lT t- .6i4r- cd velocity; the fquare root of which is 8v/(hH )= the acquired velocity of the water, t ?.• • Proportion. iQo Dr. barkers mill Proportion cf the centralforcs to the Inertia. .6i4r , By fiibrtituting Sv/(hH —jfor v, in —— itbe- \\V V t coines- X V ( \- .6 i 4) = ihe inertia ; and, as the t r 76,75ar- ^ hf- ; xv[ ) : : I : t V i+{- ); that IS, the power gained by centrifugal force is to the obfirudllon oc-calioned by the inertia, in theproportion of i to ^(1 + ); by which it appears that the latter is the great rter, except when t or 11 = 0, or r infinite; cafes nev-er occuriug in practice.; and that the longer the brachia, thelefs the fall of water, and the greaterthe velocity of ro-tation are, the nearer thefe forces approach the ratio ofequality; but as we always find fomething in pradlical ma-chanics to prevent our? running into infiniLccimals, fohere we are particularly limited; for in the AJjiiJiment of the parts and centrifugal force fhould not exceed the gravity of
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