146 OBSERVATIONS on tur THEORY, 
Now the miftake confifls in fuppofing the momentum;. 
or force of the water againft the wheel, to be in the dupli=. 
cate ratio of the relative velocity.:- Whereas. . 
Prop. De 
The force of an invariable ftream, impinging againft a: 
Mill-Wheel in motion is.in the /imple direct proportion of — 
the relative velocity. 
For, if the relative velocity of a fluid againft a-fingle - 
plane be varied, either by the motion of, the. plane, or of 
the fluid from a given aperture, or both, then, the num- 
ber of particles acting on the Plane in a given time, and. 
likewife the momentum of each particle, being refpective-. 
ly as the relative velocity, the force on both thefe accounts, , 
muft be in the duplicate ratio of the relative velocity, a- 
greeably to the common theory, with refpeé to this fingle » 
plane ; but, the number of thefe planes, or parts of the 
wheel acted on, in a given time,. will be as the velocity of. 
the wheel, or. znver/ely-as the relative velocity ; therefore, | 
the moving force of the wheel muft be in the fimple dis - 
rect ratio of the,relative volocity. Qs E. D. 
Or, the propofition is manifeft from this confideration; 
that, while the ftream is invariable, whatever be the velo- 
city of the wheel, the fame number of particles or quan- . 
tity of the fluid, muft ftrike it fome where or other ina. 
given time; confequently, the variation of force is only . 
on. account of the-varied-impingent velocity of the fame 
body, occafioned by a change of motion.in the-wheel; that _ 
is, the momentum isas the relative velocity. 
Now, this true principal fubftituted for the erroneous : 
one in ufe, will bring the theory-to agree remarkably - 
with the notable experiments of the-ingenious Smeaton, 
before. mentioned,:. publifhed inthe Philofophical Tranf= 
actions of the Royal fociety of London for the year-1751, 
Vol. 51, for which the honorary annual medal was ad-- 
| | judged 
