DYNAMICS. 53 



This conclusion agrees perfectly with all the in- 

 stances in which accelerated or retarded motion can 

 be traced by the senses, and therefore we might 

 conclude, even from analogy, that it holds in those 

 cases where the progress of acceleration escapes ob- 

 servation. When a ball, from being at rest, issues 

 almost in an instant from the mouth of a cannon, 

 with the velocity of 1800 feet in a second, it is not 

 to be imagined, that it has acquired the whole of 

 that velocity, or any part of it, suddenly, and with- 

 out the lapse of time. Could we divide time into 

 small enough portions, and did we perfectly under- 

 stand the Law of the Force produced by the in- 

 flammation of gunpowder, we should be able to de- 

 termine the point of time, and the place in the in- 

 terior of the gun, at which the ball had any as- 

 signable velocity from to 1800 per second ; when, 

 for instance, it had a velocity of one foot per 

 second ; of two, of 100, of 1200, &c. The same 

 holds of the direction of motion ; a body from moving 

 in one direction, does not come to move in another, 

 without describing a portion of a curve, and taking 

 in its motion every possible direction from the one 

 to the other. 



b. The notion of the continuity of motion seems first 

 to have occurred to GALILEO. LEIBNITZ introdu- 

 ced it as a leading principle in his philosophy, and 

 he proved the necessity of it by a metaphysical, but 

 conclusive argument. If a body receive an in- 

 crease of its motion without the lapse of time, then 

 the same body, at the same indivisible instant, is in 

 two different states, which is impossible. If, for in- 

 stance, 



