354 PHILOSOPHICAL TRANSACTIONS. [aNNO 175Q. 



greater than to describe a semi-circumference, while a body let fall from 

 the top of the wheel vvill descend through its diameter; nor indeed quite so 

 great, as a body descending through the same perpendicular space cannot 

 perform the same in so small a time when passing through a semi-circle, as 

 would be done in a perpendicular line. Thus, if a wheel be l6 feet 1 inch 

 high, a body will fall through the diameter in one second: this wheel 

 therefore can never arrive at a velocity equal to the making one turn in 2 seconds; 

 but, in reality, an overshot wheel can never come near this velocity ; for when 

 it acquires a certain speed, the greatest part of the water is prevented from en- 

 tering the buckets ; and the rest, at a certain point of its descent, is thrown 

 out again by the centrifugal force. This appears to have been the case in the 

 first 3 experiments of the foregoing specimen ; but as the velocity, when this 

 begins to happen, depends on the form of the buckets, as well as other circum- 

 stances, the utmost velocity of overshot wheels is not to be determined gene- 

 rally : and indeed it is the less necessary in practice, as it is in this circum- 

 stance incapable of producing any mechanical eiFect, for reasons already 

 given. 



FI. On the Greatest Load that an Overshot fVheel can Overcome. 



The greatest load an overshot wheel will overcome, considered abstractly, is 

 unlimited or infinite : for as the buckets may be of any given capacity, the more 

 the wheel is loaded, the slower it turns ; but the slower it turns, the more will 

 the buckets be filled with water; and consequently, though the diameter of the 

 wheel, and quantity of water expended, are both limited, yet no resistance can 

 be assigned, which it is not able to overcome : but in practice we always meet 

 with something that prevents our getting into infinitesimals ; for when we really 

 go to work to build a wheel, the buckets must necessarily be of some given ca- 

 pacity ; and consequently such a resistance will stop the wheel, as is equal to the 

 effort of all the buckets in one semi-circumference filled with water. 



The structure of the buckets being given, the quantity of this effort may be 

 assigned ; but is not of much consequence to the practice, as in this case also 

 the wheel loses its power , for though here is the exertion of gravity on a given 

 quantity of water, yet being prevented by a counterbalance from moving, is 

 capable of producing no mechanical effect, according to our definition. But, in 

 reality, an overshot wheel generally ceases to be useful before it is loaded to that 

 pitch ; for when it meets with such a resistance as to diminish its velocity to a 

 certain degree, its motion becomes irregular ; yet this never happens till the 

 velocity of the circumference is less than 2 feet per second, where the resistance 

 is equable, as appears not only from the preceding specimen, but from experi- 

 ments on larger wheels. 



Scholium. Having now examined the different effects of the power of 



