16 LECTURE II. 



II 

 disturbing causej for a right line being the same with respect to all sides, 



no reason can be imagined why the point should incline to one side more ' 

 than another ; and the general law of induction requires that the moving 

 point should preserve the same relations towards the points similarly 

 situated on every side of the line. This argument appears to be sufficiently 

 satisfactory to give us ground for asserting that the law of motion here laid 

 down may be considered as independent of experimental proof. It was once 

 proposed as a prize question by the Academy of Sciences at Berlin, to determine 

 jj whether the laws of motion were necessary or accidental ; that is, whether 

 they were to be considered as mathematical or as physical truths. Mauper- 

 tuis,* then president of the Academy, wrote an elaborate dissertation, in 

 which he endeavoured to deduce them from a complicated principle of the 

 production of every effect in the manner which requires the least possible 

 action, a principle which he supposes to be most consistent with the wise 

 economy of nature. But this principle has itself been shown to be capable 

 /v of accommodation to any other imaginable laws of motion, and the intricacy 

 of the theory tends only to envelope the subject in unnecessary obscurity ; 

 I the laws of motion appear to be easily demonstrable from the simplest 

 mathematical truths, granting only the homogeneity or similarity of matter 

 with respect to motion, and allowing the general axiom that like causes pro- 

 duce like effects. If, however, any person thinks differently, he is at liberty 

 to call these laws experimental axioms collected from a comparison of 

 various phenomena ; for we cannot easily reduce them to direct experi- 

 ments, since we can never remove from our experiments the action of all 

 disturbing causes; for either gravitation, or the contact of surrounding 

 ^bodies, will interfere with all the motions which we can examine. 



Having established the rectilinear direction of undisturbed motion, we 

 come to consider its uniformity. Here the idea of time enters into our sub- 

 ject. To define time in general is neither easy nor necessary ; but we must 

 have some measure of equal times. Our abstract idea of time depends on 

 the memory of past sensations ; but is obvious that the results of an intel- 

 lectual measure of the duration of time would be liable to the greatest 

 uncertainty. We may observe that on a journey the perpetual succession 

 of various objects will often make a week appear, upon retrospection, as 

 long as a month spent in a continuation of such employments as are uni- 

 form without being laborious ; the multitude of new impressions not only 

 serving to increase the apparent magnitude of the interval, by filling up its 

 vacuities, but tending also to dimmish the vivacity of the ideas which they 

 have superseded, and to give them the character of the fainter recollections 

 of an earlier date. We are therefore obliged to estimate the lapse of time 

 by the changes in external objects ; of these changes the simplest and most 

 convenient is the apparent motion of the sun, or rather of the stars, derived 



* Hist, et Mem. de 1'Acad. de Berl. 1746, jp. 267] Collected Works of Maup., 

 4 vols. Lyons, 1756, vol. iv; p. 31. Compare Leibnitz's Leipsic Acts, 1682. 

 D'Arcy on Maupertuis's Minimum of Action. Hist, et Mem. de Paris, 1749, p. 531. 

 H. 179, 1752, p. 503. Euler on the General Principles of Motion and Rest. Hist, 

 et Mem. de 1'Acad. de Berl. 1751, pp. 169, 199. Bertrand on the least Action, ib. 

 1753, p. 310. Malvezio on the Principle of Maupertuis, Com. Bon. VI. Opuscula, 

 p. 315. Euler, Dissertatio de Principio Min. Act. Berl. 1753. 



