348 PHILOSOPHICAL TRANSACTIONS. [aNNO 1759. 



Stream, acting on undershot wheels. We now proceed to examine the power 

 and application of water, when acting by its gravity on overshot wheels. 



In reasoning without experiment, one might be led to imagine, that however 

 different the mode of application is ; yet that whenever the same quantity of 

 water descends through the same perpendicular space, that the natural effective 

 power would be equal; supposing the machinery free from friction, equally cal- 

 culated to receive the full effect of the power, and to make the most of it : for 

 if we suppose the height of a column of water to be 30 inches, and resting on a 

 base or aperture of one inch square; every cubic inch of water that issues will 

 acquire the same velocity or momentum, from the uniform pressure of 30 cubic 

 inches above it, that one cubic inch let fall from the top will acquire in falling 

 down to the level of the aperture; viz. such a velocity as in a contrary direction 

 would carry it to the level from which it fell ;* one would therefore suppose, 

 that a cubic inch of water, let fall through a space of 30 inches, and there strik- 

 ing another body, would be capable of producing an equal effect by collision, as 

 if the same cubic inch had descended through the same space with a slower mo- 

 tion, and produced its effects gradually : for in both cases gravity acts on an equal 

 quantity of matter through an equal space ;-{' and consequently, that whatever 

 was the ratio between the power and effect in undershot wheels, the same would 

 obtain in overshot, and indeed in all others : yet however conclusive this reason- 

 ing may seem, it will appear, in the course of the following deductions, that the 

 effect of the gravity of descending bodies is very different from the effect of the 

 stroke of such as are non-elastic, though generated by an equal mechanical 

 power. 



The alterations in the machinery already described, to accommodate the same 

 for experiments on overshot wheels, were principally as follow : 



PL 13, fig. 10, the sluice ib being shut down, the rod hi was unscrewed and 

 taken off. The undershot water-wheel was taken off the axis, and instead of it 

 an overshot wheel of the same diameter was put in its place. This wheel was 1 

 inches in the shroud or depth of the bucket: the number of the buckets was 36. 

 The standards s and t, fig. Q, were raised half an inch, so that the bottom of 

 the wheel might be clear of stagnant water. A trunk for bringing the water on 

 the wheel was fixed according to the dotted lines ig^ fig. 10. The aperture was 



* This is a consequence of the rising of jetts to the height of the reservoirs nearly. 



+ Gravity,it is true, acts a longer space of time on the body that descends slow, than on that which 

 falls quick} but ihis cannot occasion the difference in the effect: for an elastic body falling through 

 the same space in the same time, will, by collision on another elastic body, rebound nearly to the 

 height from which it fell ; or by communicating its motion, cause an equal one to ascend to the same 

 height. — Orig- 



