88 LECTURE VI. 



little importance or practical utility, but which so far deserves to be 

 noticed, as it has been magnified by some philosophers into a fundamental 

 law of nature. Among all the curves that a body can describe, in moving 

 from one point to another, it always selects that, in which, if its velocity 

 be supposed to be everywhere multiplied by the distance that it describes, 

 the sum of the infinitely small products will be a minimum, that is, less 

 than in any other path that the body could take. For example, if a body 

 move freely, and therefore with a uniform velocity, in any regular curved 

 surface, it will pass from one part of the surface to another by the shortest 

 possible path. This has been called the principle of the least possible 

 action ; it is, however, merely a mathematical inference from the simpler 

 laws of motion, and if those laws were even different from what they are, 

 the principle would be true in another form, and in another sense of the 

 word action.* 



LECT. V. ADDITIONAL AUTHORITIES. 



Confined Motion, Pendulum, Sfc. Becherus de Nova Temporis Dimetiendi Ra- 

 tione, 4to, Lond. 1680. Brook Taylor, Ph. Tr. xxviii. 11. Graham and Camp- 

 bell's Experiments to determine the Difference in the Length of Isochronal Pendu- 

 lums at different Places, Ph. Trans. 1733, p. 302. Courtivron on a Circular Pendu- 

 lum, Hist, et Mem. de 1'Acad. de Paris, 1744, p. 384, H. 30. Lagrange on Iso- 

 chronous Curves, Mem. de 1'Acad. de Berlin, 1765, p. 361; 1770, p. 97. D'Alem- 

 bert, ibid. 1765, p. 381. Landen on Circular Pend. Ph. Tr. 1771, p. 308 ; 1775, 

 p. 287. Maseres, ibid. 1777, p. 215. Legendre, on do. Hist, et Mem. de 1'Acad. 

 de Paris, 1786, pp. 30, 637. Biot, on Tautoch. Curves, Bulletin dela Soc. Philo- 

 matique, No. 73. Carlini sulla Lunghezza del Pendolo, Cesaris Effemeridi, 

 1827, Milan. Bessel Untersuchungen tiber das Secunden Pendul, 4to, Berl.1828. 

 Piola sulla Teoria del Pen. Ces. EfFem. 1831-2. 



Confined Motion with, Resistance. Krafft on the Inclined Plane, Com. Petr. xii. 

 261 ; xiii. 100. Euler, ibid. xiii. 197. Kastner, ibid. Leips. Mag. ii. 1. Euler 

 on a Rotatory Pendulum with Res. A. Petr. 1780, IV. ii. 164. Airy, Transactions 

 of the Cambridge Philosophical Society, III. 111. Plana sur le Mouvement d'un 

 Pendule dans un milieu resistant, 4to, Turin, 1835. Challis. Trans, of the Camb. 

 Phil. Soc. vii. 333. 



Properties of the Cycloid. Pascal, Histoire de la Roulette. Carlo Dati, Let- 

 tera della vera Storia della Cicloide, 4to, Firenze, 1663. Groningius, Historia Cy- 

 cloidis. Lalouere, Geometria Promota, 4to, Tolosae, 1660. Young, An Essay 

 on Cycloidal Curves, 4to, 1800. Peacock's Examples to the Diff. Calc. I. Gre- 

 gory's Do. 134. 



LECTURE VI. 



ON THE MOTIONS OF SIMPLE MASSES. 



HITHERTO we have considered the motions of one or more single points 

 or atoms only, without any regard to the bulk or mass of a moveable body : 

 but it now becomes necessary to attend also to the difference of the masses 



* See p. 16.* Consult also Ampere sur 1' Application du Calcul des Variations 

 aux Prop, de Mec. 4to, Par. 1809. 



