At. B. Quinby on the Overshot Water-Wheei- 309 
Let us now suppose the wheel ambE, to be entirely free 
to turn—the circumference sliding closely against the shoul~ 
der at a, of the conduit, and closely, also, against the shou!- 
der at b, of the branch wtb. And, further, suppose the part 
ambte, of the conduit, to be extremely small, so that the 
water contained in it shall be only a succession of single par- 
ticles; and, lastly, suppose the circumference amb &e. to 
have about it an immense number of very small buckets, so 
that each particle of water that shall strike the wheel, at a, 
shall be received into a separate bucket; or, which will be 
equivalent, mae: each particle of water that shall strike 
the wheel at a . adhere to the circumference until it arrive - 
at the lower poin 
These csiniGeons being all granted, and the conduit being 
now supposed full of water, let us consider the Beet = 
a given quantity of water, descending from F, and acting 
— the part amb of the conduit, upon the circumference 
the wheel, will have in giving motion to the series of par- 
ticles i in the branch dtc of the conduit. 
From the conditions that have been stated, and from known 
principles in mechanics, and a known law in hydraulics, it is 
obvious that the water in the part Famb, of the conduit, will 
. stated) also, necessarily, be communicated to the series of 
particles in the branch te, - tiem that A ss velocity com- 
municated by the water in the part Famd,. 
the series of particles in the branch bie; a i Fi. eq 
which is due to the height aF. Wherefore i it is plain that 
each particle of water that shall pass through the conduit, or 
own upon the wheel, will be ejected atc, with a velocity 
that will raise it to the point a, in: the original summit level 
Gd. And, as this will be true for any number of particles, 
or for any capacity whatever of the conduit ambtc,* it fol- 
lows, as by the preceding demonstration, that any quantity of 
water, acting through any fall upon an overshot water-wheel 
which is not the whole height of the fall, will raise an equal 
quantity of water through the same vertical height. 
*The capacity of this conduit may be increased at ae by in- 
creasing the length of the buckets. or the width of the whee 
