50 LECTURE VII. 



resumed their activity. Some authors have thought it impossible that a 

 quadruped should stand for an instant with both feet of the same side 

 raised from the earth ; but when a horse is walking fast, it may very often 

 be observed that the print of the hind foot is considerably more advanced 

 than that of the fore foot, which has been raised to make way for it. 



From the general law of the equilibrium of the centre of gravity, we 

 may deduce the properties of levers of all kinds. It follows, from the defi- 

 nition of this point, that if two bodies be attached to a straight rod of in- 

 considerable weight, they may be sustained in equilibrium by a fixed 

 point or fulcrum, which divides their distance into portions which are in- 

 versely as their weights. And it is obvious that if any other equivalent 

 forces be substituted for weights, acting at the same distance from the 

 fulcrum, and with the same inclination to the rod or lever, the conditions 

 of equilibrium will be precisely the same. Also, if either of the forces be 

 transferred to an equal distance on the other side of the fulcrum, and act 

 there in a contrary direction, the equilibrium will still remain. Hence we 

 have two principal kinds of levers ; the first, in which the fixed point or 

 fulcrum is between the points at which the forces or weights are applied ; 

 the second, where the forces are applied in contrary directions, on the 

 same side of the fulcrum. (Plate III. Fig. 47.) 



The demonstrations of the fundamental property of the lever have been 

 very various. Archimedes himself has given us two.* Huygens,t Newton,^ 

 Maclaurin, Dr. Hamilton, || and Mr. Vince,1T have elucidated the same 

 subject by different methods of considering it. The demonstration of 

 Archimedes, as improved by Mr. Vince, is ingenious and elegant, but it is 

 neither so general and natural as one of Dr. Hamilton's, nor so simple and 

 convincing as Maclaurin's, which it may be worth our while to notice. Sup- 

 posing two equal weights, of an ounce each, to be fixed at the ends of the 

 equal arms of a lever of the first kind ; in this case it is obvious that there 

 will be an equilibrium, since there is no reason why either weight should 

 preponderate. It is also evident that the fulcrum supports the whole 

 weight of two ounces, neglecting that of the lever ; consequently we may 

 substitute for the fulcrum a force equivalent to two ounces, drawing the 

 lever upwards ; and instead of one of the weights, we may place the end 

 of the lever under a firm obstacle, and the equilibrium will still remain, 

 the lever being now of the second kind. Here, therefore, the weight re- 

 maining at the other end of the lever counterbalances a force of two 

 ounces, acting at half the distance from the new fulcrum ; and we may 

 substitute for this force a weight of two ounces, acting at an equal distance 

 on the other side of that fulcrum, 'supposing the lever to be sufficiently 

 lengthened, and there will still be an equilibrium. In this case the fulcrum 

 will sustain a weight of three ounces, and we may substitute for it a force 

 of three ounces acting upwards, and proceed as before. In a similar 



* Archimedes de ^Equiponderantibus, and de Planorum 



t Demonstratio ^Squilibrii Bilancis, Hist, et Mem. Paris, 1693. 



J Principia, Laws of Motion, cor. 2. View of Newton's Philosophy. 



(I The Properties of the Mechanic Powers Demonstrated, Ph. Tr. 1763, liii. 103. 



|| Ph. Tr. 1794, Ixxxiv. 33. Philosophical Essays, 12mo, Lond. 1767. 



