320 LECTURE XXVII. 



or empty itself into the first when it has ascended again to its original situa- 

 tion. The action of a column of water, inclosed in a pipe, is of a nature- 

 nearly similai- to that of such a reservoir, excepting that the apparatus is 

 more liable to friction; the arrangement of its parts is nearly similar, although 

 in an inverted position, to that which is more commonly employed for rais- 

 ing welter by means of pumps. But both these methods of employing the 

 weight of water, are in great measure confined to those eases in which it is 

 to be procured in a small quantity, and may be allowed to descend through a 

 considerable height, and when the circumstanceis do not allow us to employ 

 machines which require a greater space. 



We have seen that in order to determine the effect of any force employed 

 in' machinery, we must consider not only its magnitude, but also the velo- 

 city with which it can be brought into action, and we rnujs^t estimate the ul- 

 timate value of the power, by the joint ratio, or the product, of the force and 

 the velocity. Thus, if we had a corn mill, for example, in which we wished 

 the millstone to revolve with a certain velocity, and to overcome a given 

 resistance, and supposing that this eifect could be obtained by means of 

 a certain train of wheels from a given source of motion; if the velocity 

 of the motion at its source be reduced to one- half, we must double the 

 diameter of one of the wheels by which the force is communicated, in 

 order to give the millstone the desired velocity, and thus we must introduce 

 a mechanical disadvantage, which can only be compensated by a double in- 

 tensity in the force at its origin. 



If we apply this estimation of effect to the motion of an overshot wheel, 

 we shall find that the velocity of the wheel, and consequently its breadth, and 

 the magnitude of its buckets, is perfectly indifferent with respect to the 

 value of its operation : for supposing the stream to enter the buckets with the 

 uniform velocity of the wheel, the quantity of water in the wheel at any one 

 time, and .consequently the pressure, must be inversely as the velocity, so. 

 that the product of the force into the velocity will be the same, however 

 they may. separately A'ary. If, however, the velocity were to become very 

 considerable, it would be necessary to sacrifice a material part of the fall, in 

 order that the water might acquire this velocity before its arrival at the wheel; 

 but a fall of one foot, or even less, is sufficient for producing any velocity 



