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s!iot wheel greater than that ofthe total descent, minus so much 

 as is necessary to give the water a proper velocity on reaching 

 llie wheel. The author, however, contends that the reasoning 

 by which the latter writer upholds this is inconclusive, — that 

 there are some circumstances which he points out necessarily 

 in favour of the larger wheel, and that conditions may occur 

 in practice in which it is desirable to use the larger wheel, 

 even at some sacrifice of power; and that hence it is of im- 

 portance to ascertain its value in use, as compared with 

 Smeaton's size for maximum effect. 



The author states the general proposition, " that the la- 

 bouring force [travail of French authors, or mechanical power 

 of Snieaton) of" any machine, transferring the motive power 

 of water, is equal to that of the whole moving power em- 

 ployed, minus one-half of the vis viva lost by the water on 

 entering the machine, and minus one-half of the vis viva due 

 to the velocity of the water on quitting it." He then obtains 

 general equations expressing the relations between the fall, 

 the velocity, the weight of fluid, the power, &c. in overshot 

 water-wheels, at whatever point the water may first reach 

 the wheel, and whether the latter move naked, or in a cix'- 

 cular channel or course. From these he deduces, that — 



1st. If the portion ofthe total descent passed through by 

 the water, before reaching the wheel, be given, the velocity of 

 the circumference should be one-half that due to this height. 



2nd. If the velocity of the circumference be given, the 

 water must descend through such a fraction ofthe whole fall, 

 before reaching the wheel, as will generate this velocity. 



3rd. The maximum of labouring force is greater as the 

 velocity of the wheel is less, and its limit theoretically ap- 

 proaches that due to the whole fall ; general equations are 

 then given, expressing the amount of labouring force in all 

 the conditions considered by the author, and their maxima. 



One of the principal advantages of using an overshot 

 wheel greater in diameter than the height of the fall, is the 



