ON MOTION. 17 



from the actual rotation of the earth on its axis, which is not, indeed, an 

 undisturbed rectilinear motion, but which is equally applicable to every 

 practical purpose. Hence we obtain, by astronomical observations, the 

 well-known measures of the duration of time implied by the terms day, 

 hour, minute, and second. 



Now the equality of times being thus estimated from any one motion, all 

 other bodies moving without disturbance will describe equal successive parts 

 of their lines of direction in equal times. And this is the second law of 

 motion, which, with the former law, constitutes Newton's first axiom 

 or law of motion :* " that every body perseveres in its state of rest or 

 uniform rectilinear motion, except so far as it is compelled by some force to 

 change it." It appears that this second law is strictly deducible from the 

 axioms and definitions which have been premised, and principally from the 

 consideration of the relative nature of motion, and the total deficiency of a 

 , criterion of absolute motion. For, since the velocity of a body moving 

 without resistance or disturbance is only a relation to another body, if the 

 second body has no mechanical connexion with the first, its state with 

 respect to motion can have no effect on the velocity of the first body, how- 

 ever great its comparative magnitude may be : and if a body is at rest, there 

 is nothing to determine it to begin to move either to the right hand or to 

 the left ; if it is at rest with respect to any other bodies it will remain in 

 the same condition, whatever the relative motions of those bodies may be 

 when compared with the surrounding objects ; and these relations can only 

 be preserved by its continuance in uniform rectilinear motion. This law is 

 also confirmed by its perfect agreement with all experimental observations, 

 although it is too simple to admit of an immediate proof. For we can 

 never place any body in such circumstances as to be totally exempt from 

 the operation of all accelerating or retarding causes ; and the deductions 

 from such experiments as we can make, would require in general, for the 

 accurate determination of the necessary corrections, a previous knowledge 

 of the law which we wish to demonstrate. 



When, indeed, we consider the motion of a projectile, we have only to 

 allow for the disturbing force of gravitation, which so modifies the effect, 

 that the body deviates from a right line, but remains in the same vertical 

 plane ; whence we may infer that, in the absence of the force of gravita- 

 tion, the body would continue to move in every other plane in which its 

 motion began, as well as in the vertical plane ; since in that case all these 

 planes would be indifferent to it ; it must, therefore, remain in their com- 

 mon intersection, which could only be a straight line ; so that by thus 

 combining arguments with observation, we may obtain a confirmation of 

 the law of the rectilinear direction of undisturbed motion, partly founded on 

 direct experiment. Its uniformity is, however, still less subjected to im- 

 mediate examination : yet, from a consideration of ttye nature of friction 

 and resistance, combined with the laws of gravitation, we may ultimately 

 show the perfect coincidence of the theory with experiment. The ten- 

 dency of matter to persevere in this manner in the state of rest or of 

 uniform rectilinear motion is called its inertia. 



* Principia, lib. i. 

 c 



