MOV'ING FORCE. 
169 
<iherchoit la force du choc du fluide ; mais il falloit observer Cases of diffi- 
que dans le mouvemeni dont il' s’agit. Taction du Teau ne of 
sVxerce pas contre une palette isolee, mais centre plusieures moving force, 
palettes a la fois, et que ces palettes ferinant tout le passage da 
petit canal et otant au fluide la \Uesse qvTil a de plus qu’elles, 
la quantite du mouvement perdu par ce fluide, et par conse- 
quent le choc qu’cprouvent les palettes, n'est plusproportionnelle 
au cai re de la ditVerence des vt'.esses dn fluide et des palettes, • 
uiais seulcment i la difl'ercnce de ces vi esses*.” 
Mr. Waring’s demonstration is as follows: ‘‘ If the relative 
'Velocity of a fluid against a single plane be vjried, either by 
' the motion of the plane, or of the fluid from a given aperture, 
or both, then, the number of particles acting on the plane in 
a given time, and likewise the momentum of each particle, 
; being respectively as the relative velocity, the force, on both 
I these accounts, must be in the duplicate ratio of the relative 
' velocity, agreeably to the common theory, with respect to this 
single plane •, but the number of these planes or parts of the 
’ wheel, acted on in a given lime, will be as the velocity of the 
ynhve\, oi inversely as the ■> dative velocity •, therefore the mov- 
I ing force of the wheel must be in the simple direct ratio of the 
relative velocity,” and, consequently, the maximum etfcct 
' must be produced when the velocity of the wheel is half that 
of the waterf. 
But this kind of demonstration cannot, 1 think, be very .sa- 
tisfactory. It leads, I apprehend, to this conclusion, that we 
may double the power of any undershot water-wheel, (what- 
ever may be its velocity) by merely doubling the number of 
its floats or planes acted «[)on by the water. Mr. Smeaton, 
how’ever, ever found, that no such advantage was to be gained 
by that means J. 
It mu.st be acknowledged, that the celebrated experiments 
of D’Alembert, Condorcet, and Bossut, furnished results in 
• Memoircs de TAcad. Paris, 176?j p. 274. 
t American Phil. Trans, vol. S. p. 146. 
4 Phil. Trans. 1759, p. 124. 
«0l- 
