70 LECTURE IX. 



without entering minutely into the consideration of the subject, and which 

 appears, when first we examine its foundation with accuracy, to lead to 

 material errors, is in great measure justified by a more profound investi- 

 gation. 



To seek for a source of motion in the construction of a machine, betrays 

 a gross ignorance of the principles on which all machines operate. The 

 only interest that we can take in the projects which have been tried for 

 procuring a perpetual motion, must arise from the opportunity that they 

 afford us to observe the weakness of human reason ; to see a man spending 

 whole years in the pursuit of an object which a week's application to 

 sober philosophy might have convinced him was unattainable. The most 

 satisfactory confutation of the notion of the possibility of a perpetual 

 motion, is derived from the consideration of the properties of the centre of 

 gravity : we have only to examine whether it will begin to descend or to 

 ascend, when the machine moves, or whether it will remain at rest. If it 

 be so placed, that it must either remain at rest or ascend, it is clear, from 

 the laws of equilibrium, that no motion derived from gravitation can take 

 place : if it may descend, it must either continue to descend for ever with 

 a finite velocity, which is impossible, or it must first descend and then 

 ascend with a vibratory motion, and then the case will be reducible to 

 that, of a pendulum, where it is obvious that no new motion is generated, 

 and that the friction and resistance of the air must soon destroy the 

 original motion. One of the most common fallacies, by which the super- 

 ficial projectors of machines for obtaining a perpetual motion have been 

 deluded, has arisen from imagining that any number of weights ascending 

 by a certain path on one side of the centre of motion, and descending in 

 the other at a greater distance, must cause a constant preponderance on 

 the side of the descent : for this purpose the weights have either been fixed 

 on hinges which allow them to fall over at a certain point so as to become 

 more distant from the centre, or made to slide or roll along grooves or 

 planes which lead them to a more remote part of the wheel, from whence 

 they return as they ascend : but it will appear, on the inspection of such a 

 machine, that although some of the weights are more distant from the 

 centre than others, yet there is always a proportionally smaller number of 

 them on that side on which they have the greatest power ; so that these 

 circumstances precisely counterbalance each other. (Plate VI. Fig. 78.) 



LECT. IX. ADDITIONAL AUTHORITIES. 



Lagrange, Hist, et Mem. de Berlin, 1773, p. 85. Landen, New Theory of Ro- 

 tatory Motion, Ph. Tr. 1777, p. 266 ; 1785, p. 311. Vince, Ph. Tr. 1780, p. 546. 

 Robison, Encyc. Brit. Art. Rotation. Fra^ais sur le Rotat. d'un Corps, 4to, Par. 

 1813. Raeb, De Motu Gyratorio, Trajecti adRhenum, 1834. 



Rotation with Progression, D. Bernoulli, Comm. Petr. xiii. 94. Euler, xiii. 220, 

 and Acta Petr. ii. II. 162 ; 1781, v. II. 131 ; 1782, vi. I. 117, II. 107 ; 1783, I. 

 119 ; 1787, v. 149. Fuss, ibid. 176, and 1788, vi. 172. Prony sur le Mouvement 

 d'un Corps sollicite par des Puissances quelconques, 4to, 1800. 



