ON MOTIOK. 21 



tangent: for it meets the curve, but does not cut it, provided that the curva- 

 ture be continued. (Plate I. Fig. 1 ... 3.) 



Having formed an accurate idea of the nature of motion, and of the im- 

 port of the terms employed in speaking of its properties, we may proceed to 

 consider the mechanical laws to which it is subjected, and which are derivable 

 from the essence of the definitions that have been premised. The first is, that 

 a moving point never quits the line of its direction without a disturbing cause : 

 -for a right line being the same witb 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 in- 

 dependent of experimental proof. It was once proposed as a prize question 

 by the academy of sciences at Berlin, to determine whether the law& of mo- 

 tion were necessary or accidental; that is, whether they were to be consider- 

 ed as mathematical or as physical truths. Maupertuis, then president of the 

 academy, wrote an elaborate dissertation, in which he endeavoured to deduce 

 them from a complicated principle of the prodtiction of every eifect in the 

 manner which requires the least possible action^ a principle which he sup- 

 poses to be most consistent with the wise economy of nature. But this prin- 

 ciple has itself been shown to be capable of accommodation to any other 

 imaginable laws of motion, and the intricacy of the theory tends only to en- 

 velope the subject in unnecessary obscurity; 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 produce like effects. If, however, any person 

 thinks differently, he is at liberty to call these laws experimental axioms, col- 

 lected from a comparison of various phenomena; for we cannot easily reduce 

 them to direct experiments, 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 ex- 

 amine. 



Having established the rectilinear direction of undisturbed motion, we 



