45 6 Mr. smeaton on Mechanic Power . 
which they were conftru6led, when applied to great 
works, as well as upon a fmaller fcale in models. 
Refpe£ting the explanatory deduction of desag u- 
liers in the firft example abovementioned, which, in- 
deed, 1 have found to be the commonly received doctrine 
among theoretical mechanics, it is fhewn, Phil. Tranf. 
vol. li. p. 120, i 21, and 123. part 1. maxim 4. that, 
w'here the velocity of water is double, the adjutage or 
aperture of the iluice remaining the fame, the effect is 
eight times ; that is, not as the lquare but as the cube of 
the velocity; and the fame is inveftigated concerning the 
power of the wind arifing from difference of velocity, 
p. 156. being part 3. maxim 4. 
The conclulion in the fecond example abovemen- 
tioned, adopted both by desaguliers and maclaurin, 
is not lefs wide of the truth than the foregoing; for if 
that conclulion were true, only ^-ths of the w r ater ex- 
pended could be raifed back again to the height of the 
refervoir from which it had defcended, exclulively of all 
kinds of friction, See. which would make the adtual 
quantity raifed back again ftill lefs; that is, lefs than 
one-feventh of the whole; whereas it appears, from table 
1. p. 1 15. of the faid volume, that in fome of the expe- 
riments there related, even upon the fmall fcale on which 
they were tried, the work done was equivalent to the 
railing back again about one quarter of the water ex- 
pended; and in large works the effect is If ill greater, ap- 
proaching towards half, which feems to be the limit for 
the underlhot mills, as the whole would be the limit for 
the 
