108 FERGUSON'S LECTURES. 



volve with a certain velocity, and to overcome a given resistance, 

 and supposing that this effect could be obtained by means of a cer- 

 tain 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 dou- 

 ble the diameter of one of the wheels by which the force is commu- 

 nicated, in order togive the mill-stone the desired velocity ; and thus 

 we must introduce a mechanical disadvantage, which can only be 

 compensated by a double intensity in the force at its origin. 



If we apply this estimation of effect to the motion of an over- 

 shot wheel, we shall find that the velocity of the wheel, and con- 

 sequently its breadth, and the magnitude of its buckets, is per- 

 fectly indifferent with respect to the value of its operation : for, 

 supposing the stream to enter the buckets with the uniform velo- 

 city of the wheel, the quantity of water in the wheel at anv 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 vary. If, how- 

 ever, 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 arival at the wheel ; 

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

 velocity that would be practically convenient : and it is obvious, 

 on the other hand, that a certain velocity may be procured from 

 a wheel moving rapidly, with less machinery than from another 

 which moves more slowly. In general, the velocity of the sur- 

 face of the wheel is between two and six feet in a second ; 

 and whether it be greater or smaller, the force actually applied 

 will always be equal in effect to the weight of a portion of the 

 stream employed, equal in length to the height of the wheel. In 

 order to avoid the resistance which might be occasioned by the 

 stagnant water below the wheel, it is a good practice to turn the 

 stream backwards upon its nearer half, so that the water, when 

 discharged, may run off in the general direction of its motion. 



If we suffer the stream of water to acquire the utmost veloci- 

 ty that the whole fall can produce, and to strike horizontally 

 against the float-boards of an under-shot wheel, or if we wish to 

 employ the force of a river running in a direction nearly horizon- 

 tal, the wheel must move, in order to produce the greatest effect, 

 with half the velocity of the stream. For the whole quantity of 

 water impelling the float-boards is nearly the same, whatever may 

 be the velocity, especially if the wheel is properly inclosed in a 

 narrow channel, and hence it is easy to calculate that the great- 

 est possible effect will be produced when the relative velocity of 



