go LECTURE IX. 



we have been considering are adapted : they are not only less active when a 

 certain velocity has once been att:uned, but they are often capable of a tem- 

 porary increase or diminution of intensity at pleasure. We have seen the in- 

 convenience of producing a great final velocity, on account of its endanger- 

 ing the structure of the machine : if therefore our permanent force be calcu- 

 lated according to the common rule, so as to be able to maintain the equili- 

 brium, and overcome the friction, the niomentum or inertia of the weights, 

 when once set in motion, will be able to sustain that motion equably; and it 

 will not be dithcult to give them a sufficient momentum, by a greater exer- 

 tion of the moving force, for a short space of time, at the beginning: and 

 this is in fact the true mode of operation of many machines where animal 

 strength is employed. Other forces, for instance those of wind and water, 

 regulate themselves in some measure, at least with respect to the relative ve- 

 locity of the sails and the wind, or the floatboards and the water ; for we may 

 easily increase the resistance, until the most advantageous effect is produced. 

 Many authors, considering the pressure of a stream of water as analogous to 

 the impulse of a number of unconnected particles, striking the floatboards» 

 and then ceasing to produce any further effect, have inferred, that the force 

 obtained by such an impulse must be as the square of the relative velocity^ 

 and that the effect of an undershot wheel must be the mo&t advantageous, 

 when its velocity is one third of that of the stream : but it will hereafter ap- 

 pear, that this estimation of hydraulic force is by no means accurate. If we 

 compare the greatest velocity with which a man or a horse can run or walk 

 without fatigue, to the velocity of the stream, and the actual velocity of that 

 part of the machine to which the force is applied, to the velocity of the float- 

 boards of a water wheel, the strength which can be exerted may be repre- 

 sented, according to the experiments of some authors, by the impulse of the 

 stream, as supposed to be proportional to the square of the relative velocity ; 

 consequently the same velocity would be most advantageous in both cases, 

 and the man or horse ought, according to these experiments, to move, when 

 his force is applied to a machine, with one third of the velocity with which 

 he could walk or run when at liberty. This, for a man, would be about a 

 mile and a half an hour ; for a horse, two or three miles : but in general both 

 men and horses appear to work most advantageously with a velocity some- 

 what greater than this. 



