162. If we make a distinction in the forces or powers, by J^L 

 regarding one, q for instance, as giving motion, p as receiving it, 

 and F as a pivot or point of support, we may, in the manner of 

 the ancients, make three sorts of levers, according to the three 

 different situations in which the agent q can be placed with re- 

 gard to p and F. Figure 71 represents what is called a lever of 

 the first kind, in which the agent and the resistance are on op- 

 posite sides of the fulcrum, and the agent will have so much the 

 more advantage according as its distance from the fulcrum is 

 greater than that of the resistance. Figure 72 represents a lever 

 of the second kind, in which the resistance is between the agent 

 and the fulcrum, and which consequently is always favourable 

 to the agent. Figure 73 represents a lever of the third kind, in 

 which the agent is between the resistance and the fulcrum ; in 

 this case, therefore, the power of the agent is always employed 

 to disadvantage ; and such a lever is never to be used, where 

 the object is to augment the effect of the agent ; that is, where 

 -it is proposed to overcome a greater force. But as the purpose 

 to be fulfiled is not always to increase the power of the agent, 

 this circumstance d< es not prevent this third kind of lever being 

 very usefully employed in machinery, where we would avail 

 ourselves of every species of motion that we can dispose of. 

 Thus in turning, in weaving, in spinning, and in various kind of 

 manufacture, where great velocity, and not great force is requir- 

 ed, and where the hands of the labourer are occupied with the 

 more important parts of the work, this species of lever is adopted 

 with obvious advantage, the feet being employed to give motion 

 to the machinery. 



163. Before proceeding farther, we will observe, that setting 

 aside friction, the fulcrum is not to be considered as simply a 

 pivot, or support. Indeed, if the fulcrum F, instead of penetrat- Fig 

 ing into the interior of th,e lever, as represented in the figure, 

 only touched the surface, it is evident that, although the two 

 powers 9, p, were in the inverse ratio of the distances of the 

 perpendiculars FM, FJL, they would still not be in equilibrium, 

 except in the single case, where the direction AF is perpendicu- 

 lar to BD (or to the tangent at F in figure 68) ; for, if JLF were 

 oblique, it would clearly tend to communicate motion to the lev- 

 er in the direction BD. Thus, we should err in supposing, for 



