OF WATER-WHEELS. 109 



the stream, striking the float-boards, is equal to the velocity of LECT. 

 the wheel itself. The pressure on the float-boards is equal to fV 

 that of a stream containing the same quantity of water, and 

 striking a fixed obstacle with half the velocity, that is, such a 

 stream as escapes from the wheel, which must be twice as deep 

 or twice as wide as the original stream, since its motion is only 

 one half as rapid ; and a column of such a stream, of twice the 

 height due to its velocity, that is, of half the height of the fall, 

 being as we have already seen, the measure of the hydraulic pres- 

 sure, this force will be precisely half as great as that of a similar 

 column, acting on an over-shot wheel, which moves with the same 

 velocity. But the stream thus retarded will not retain the other 

 half of its mechanical power ; since its greatest effect will be in 

 the same proportion to that of an equal stream acting on an over- 

 shot wheel with one fourth of the fall of the former ; and the re- 

 maining fourth of the power is lost in producing the change of 

 form of the water and in overcoming its friction. In whatever 

 way we apply the force of water, we shall find that the mechanical 

 power which it posesses must be measured by the product of the 

 quantity multiplied by the height from which it descends : for ex- 

 ample, a hogshead of water capable of descending from a height 

 often feet, possesses the same power as ten hogsheads descend- 

 ing from a height of one foot ; and a cistern filled to the height of 

 ten feet above its orifice possesses 100 times as much power as the 

 same cistern filled to the height of one foot only. 



When, therefore, the fall is sufficiently great, an over-shot 

 wheel is far preferable to an under-shot wheel, and where the 

 fall is too small for an over-shot wheel, it is most advisable to 

 employ a breast-wheel, which partakes of its properties ; its 

 float-boards consisting of two portions meeting at an angle, so as 

 to approach to the nature of buckets, and the water being also 

 in some measure confined within them by the assistance of a 

 sweep or arched channel which follows the curve of the wheel, 

 without coming too nearly into contact with it, so as to produce 

 unnecessary friction. When the circumstances do not admit 

 even of a breast-wheel, we must be contented with an under-shot 

 wheel : it is recommended, lor such awheel, that the float-boards 

 be so placed as to be perpendicular to the surface of the water at 

 the time that they rise out of it : that only one half of each 

 should ever be below the surface, and that from three to five 

 should be immersed at once, according to the magnitude of the 

 wheel. Sometimes, however, it has been thought eligible to 

 employ a much smaller number: thus the water-wheel which 



