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A paper entitled, " An Inquiry as to the Coefficient of 

 LabouringFoice in Overshot Water-Wheels, whose diameter 

 is equal to, or exceeds the total descent due to the fall ; and 

 of Water-Wheels moving in Circular Channels," was read 

 by Robert Mallet, Esq., Mem. Ins. C. E., M. R. I. A. 



This paper is partly mathematical and partly experimen- 

 tal. The investigation which it describes, the results of 

 which are given in ten tables, had in view principally to ob- 

 tain definite experimental answers to the following ques- 

 tions : 



1st. With a given height of fall and head of water, or in 

 other woi-ds, with a given descent and depth of water in the 

 pentrongh, will any diameter of wheel greale?- than that equal 

 to the fall give an increase of labouring force (i. e. a better 

 effect than the latter), or will a loss of labouring force result 

 from such increase of diameter ? 



2nd. When the head of water is necessarily variable, un- 

 der what conditions will an advantage be obtained by the 

 use of the larger wheel, and what will be the maximum ad- 

 vantage ? 



3rd. Is any increase of labouring force obtained by causing 

 the loaded arc of an overshot wheel to revolve in a closely 

 fitting circular race or conduit, and if so, what is the amount 

 of advantage, and what the conditions of maximum effect? 



The author briefly reviews the history of our knowledge 

 of this branch of hydrodynamics, the experimental researches 

 of Da Borda, Smeaton, &c., and the more recent improve- 

 ments in the theory of water-wheels, due to the analytic 

 investigations of German and French engineers, and tlie 

 admirably conducted experiments of Poncelet, Morin, and 

 the Franklin Institute. 



Smeaton, in his paper on water-wheels, read to the Royal 

 Society in May, 1759, and Dr. Robison of Edinburgh, in his 

 treatise on water-power, lay down as a fixed principle, that no 

 advantage can be obtained by making the diameter of an over- 



