246 LECTURE XXVII. 



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 me- 

 chanical power which it possesses must be measured by the product of 

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

 ple, a hogshead of water capable of descending from a height of 10 feet, 

 possesses the same power as 10 hogsheads descending from a height of one 

 foot ; and a cistern filled to the height of 10 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 overshot wheel is far 

 preferable to an undershot wheel, and where the fall is too small for an 

 overshot wheel, it is most advisable to employ a breast wheel, which par- 

 takes of its properties, its floatboards 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 con- 

 tented with an undershot wheel ; it is recommended, for such a wheel, that 

 the floatboards 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 propels Mr. Symington's steam-boatt has only six 

 floatboards in its whole circumference. (Plate XXII. Fig. 291, 292.) 



Since the water escaping from an undershot wheel still retains a part of 

 its velocity, it is obvious that this may be employed for turning a second 

 wheel, if it be desirable to preserve as much as possible of the force. In this 

 case, by causing the first wheel to move with two thirds of the velocity of 

 the stream, the whole effect of both will be one third greater than that of a 

 single wheel placed in the same stream ; but it must be considered that 

 the expense of the machinery will also be materially increased. 



Considerable errors have frequently been made by mathematicians and 

 practical mechanics in the estimation of the force of the wind or the water 

 on oblique surfaces ; they have generally arisen from inattention to the 

 distinction between pressure and mechanical power. It may be demon- 

 strated that the greatest possible pressure of the wind or water, on a given 

 oblique surface at rest, tending to turn it in a direction perpendicular to 

 that of the wind, is obtained when the surface forms an angle of about 55 

 with the wind ; but that the mechanical power of such a pressure, which 

 is to be estimated from a combination of its intensity with the velocity of 

 the surface, may be increased without limit by increasing the angle of 

 inclination, and consequently the velocity. The utmost effect that could be 

 thus obtained would be equal to that of the same wind or stream acting on 

 the floatboards of an undershot wheel : but since in all practical cases the 



* Smeaton, Ph. Tr. li. 116, 131 ; and Ixvi. 450. 

 f See Journal of the Royal Institution, vol. i. 



