A. B. (^uinhy on the Overshot Water- fVheel- 30^^ 



Let us now suppose the wheel om6E, to be entirely [vce 

 to turn — the circunnference sliding closely against the shoul- 

 der at a, of the conduit, and closely, also, against the shoul- 

 der at b, of the branch vtb. And, further, suppose the part 

 ambtc, 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 &;c. 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, suppose each particle of water that shall strike 

 the wheel at a, to adhere to the circumference until it arrive 

 at the lower point b. 



These conditions being all granted, and the conduit being 

 now supposed full of water, let us consider the effect which 

 a given quantity of water, descending from F, and acting 

 through the part amb of the conduit, upon the circumference 

 of the wheel, will have in giving motion to the series of par- 

 ticles in the branch btc 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 Fam6, of the conduit, will 

 communicate to the circumference of the wheel a velocity 

 equal to that which is due to the height oF ; and, conse- 

 quently, as the same velocity that shall be communicated to 

 the circumference of the wheel, will (from the conditions 

 stated) also, necessarily, be communicated to the series of 

 particles in the branch btc, it follows that the velocity com- 

 municated by the water in the part Famb, of the conduit, to 

 the series of particles in the branch btc, will be equal to that 

 which is due to the height aF. Wherefore it is plain that 

 each particle of water that shall pass through the conduit, or 

 down upon the wheel, will be ejected at c, with a velocity 

 that will raise it to the point a, in the original summit level 

 FGd And, as this will be true for any number of particles, 

 or for any capacity whatever of the conduit amble* it fol- 

 lows, as b}' 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 v.'ater through the same vertical height. 



* The capacity of this conduit may be increased at pleasure, by ii^ 

 creasing the length of the buckets, or the width of the wheel. 



