- 
148 OBSERVATIONS ow tHe THEORY, 
he fully fhews the common theory to have been very 
defective; but, I believe, none have fince pointed. out 
wherein the deficiency lay, nor how to correct it; and 
now we fee the agreement of the true theory with the re-. 
fult of his experiments. 
] might proceed with this correCtion through feveral 
propofitions, ce. and fhew their coincidence with thofe 
experiments; but muftgeave that, at prefent, for fuch as. 
have more leifure; my view being only to fhew where this 
perplexing difficulty crept in, in order that thofe who may 
have occafion to ule the theory in future, or inftruct. 
young men in the principles of mechanics, may make- 
any ufe of thefe hints they pleafe: I will, however, juft. 
add one problem, as} bave it by me; though it may not, 
be the moft fuitable I could have chofen.. 
Prop. HI. Fig. ty Plate 4; 
Given, the momentum (M) and volocity (V) of the; 
fluid at I, the place of impa@; the radius (R=IS) of the: 
wheel ABC; the radius (r=DS) of the {mall whecl DEF 
on the fame axle or thaft; the weight (W): or refiftance to’ 
be overcome at D, and the Friction (f) or force neceflary 
to move the wheel without the. weight; reguired the velo=. 
city (x) of the wheel, &c. 
Here we have V: V—x::M:-MxS*=the ading 
force at I in. the direGtion KI, as before. (prop. 2.) now, 
Riri: W: =the power atl neceflary to counterpoife 
the weight W; hence, W.4E— the whole refiftance oppofed_ 
to the action of the fluid at I; which dedu@ed from the 
moving force, leaves Mx4>—="—F,= the accelerating 
force of the machine; which, when the motion becomes. 
uniform, will be evanefcent or=O; therefore, Mx*="¥+ 
F, which gives x=Vx1 ‘W_F =the true velocity required ;_ 
or, if we reject the fridtion, then x=Vx' — x is the the~ 
orem 
