. Transactions of the American Philosophical Society. I have it by me ; though it may not:be the moft fuitabk I could have chofen. Proj). III. Fig. I. Plate 4. Given, the momentum (M) and volocity (V) of thefluid at I, the place of impad; the radius (R=IS) of thewheel ABC; the radius (r=DS) of the Imall wheel DEFon the fame axle or fhaft; the weight (W) or refifiance tobe overcome at D, and the Fridion (F) or force neceffaryto move the wheel without the weight; required the velo-city (x) of the wheel, &c. Here we have V : V—x : : M : Mx^= the adingforce at I in the diredion KI, as before, (pro
. Transactions of the American Philosophical Society. I have it by me ; though it may not:be the moft fuitabk I could have chofen. Proj). III. Fig. I. Plate 4. Given, the momentum (M) and volocity (V) of thefluid at I, the place of impad; the radius (R=IS) of thewheel ABC; the radius (r=DS) of the Imall wheel DEFon the fame axle or fhaft; the weight (W) or refifiance tobe overcome at D, and the Fridion (F) or force neceffaryto move the wheel without the weight; required the velo-city (x) of the wheel, &c. Here we have V : V—x : : M : Mx^= the adingforce at I in the diredion KI, as before, (prop. 2.) now,R : r : : W : ^-^= the power at 1 neceffary to counterpoifethe weight W; hence, ^+F= the whole refiftance oppofedto the adion of the fluid at I; which deduded from themoving force, leaves Mx^-^ —F,= the acceleratingforce of the machine; which, when the motion becomesuniform, will be evanefcent or=0; therefore, Mx^=-^+F, which gives x=Vxi ^^ ^= the true velocity required;or, if wc rejed the fridion, then x=Vx^^^ is the the- oreni:. h Pwt i^Mp ??? Of W a T E Pv M 1L L S, &c. r49. orem for the velocity of the wheel. This, by the com-mon theory would be x=Vxf—V^^i which is too little-by Vv^—V~g: No wonder why we have hitherto de--rived fo little advantage from the theory. Corol. i. If the weight (W) or refiftance be required,fuch as juft to admit of that velocity which would producethe greateft effed ; then, by fubflituting -^V for its equi-valent X (by prop. II.) we have ~V=Vxi—^r-^i*, henceW=t=^xR; or, if F=o, W=^^; but theorifls makethisiH?, where the error is ^^_; Corol. 2. We have alfo r = i-^^x^; o**} rejeding fric-tion, r=~t when the greateft effe£t is produced, infteadof r=i!^, as has been fuppofed : this is an importanttheorem in the coiiftrudtion of Mills. WM. WARING^.Ehiladel^hia^ ]thy c^th mo, 1790. A/lronomicaE ( ijo ) :n°. XIX. Afcrononical Ohfervatlons^ Covtmuftirafed bjT)AVID Rit- Obferuations of a hinar Eclipfe,Nov. xd, 1789, and
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