216 OUTLINES OF NATURAL PHILOSOPHY. 



mi a? A i 8 <a T C S d fl C 



1 he effect, when a maximum, is - a 2 h x T ^= > 



y o *i 



that is, eight twenty-sevenths of the quantity of mo- 

 tion expended on the machine. 



In different falls of water, that act on wheels moving 

 with a velocity in a given ratio to that of the water, 

 if the expenditure be the same, the forces will be 

 as the velocities simply, ( 297.), and the effects 

 of the machines driven by them as the squares of 

 the velocities. 



If the sections of two streams are the same, their 

 forces will be as the squares of their velocities, or as 

 the heights due to the velocity of the water, ( 297.), 

 and the effects of the machines driven by them, will 

 be as the cubes of their velocities, or as the heights 

 due to those velocities multiplied into their square 

 roots. 



These conclusions, all except the first, are remarka- 

 bly verified by the experiments of Mr SMEATON. 

 He found, that an undershotwheel, when working 

 to the greatest advantage, had a velocity which va- 

 ried from one-third to one-half the velocity of the 

 stream ; and was, in great machines, nearer to the 

 latter of these limits than the former. Also, that 

 the load, when the effect was greatest, approached 

 very near to the weight of the whole column of wa- 

 ter striking on the wheel. It is found above to 

 he eight-ninths. 



When 



