a word, whatever be the manner in which the bodies may affect each other, 

 whether by collision, traction, attraction, or repulsion, or by whatever other 

 name the phenomenon may be designated, still it is an inevitable consequence, 

 that any motion, in a given direction, which one of the bodies may receive, 

 must be accompanied by a loss of motion in the same direction, and to the same 

 amount, by the other body, or the acquisition of as much motion in the contrary 

 direction ; or, finally, by a loss in the same direction, and an acquisition of 

 motion in the contrary direction, the combined amount of which is equal to the 

 motion received by the former. 



From the principle, that the force of a body in motion depends on the mass 

 and the velocity, it follows that any body, however small, may be made to move 

 with the same force as any other body, however great, by giving to the smaller 

 body a velocity which bears to that of the greater the same proportion as the 

 mass of the greater bears to the mass of the smaller. Thus a feather, ten thou- 

 sand of which would have the same weight as a cannon-ball, would move with 

 the same force if it had ten thousand times the velocity ; and, in such a case, 

 these two bodies, encountering in opposite directions, would mutually destroy 

 each other's motion. 



The consequences of the property of inertia, which have been explained in 

 the present and previous lecture, have been given by Newton in his Prin- 

 cipia, and, after him, in most English treatises on mechanics, under the form 

 of three propositions, which are called the " laws of motion." They are as 

 follow : 



i. 



" Every body must persevere in its state of rest, or of uniform motion in a straight line, 

 unless it be compelled to change that state by forces impressed upon it." 



ii. 



" Every change of motion must be proportional to the impressed force, and must be in 

 the direction of that straight line in which the force is impressed." 



HI. 



" Action must ahrays be equal, and contrary to reaction ; or the actions of two bodies 

 upon each other must be equal, and directed toward contrary sides." 



When inertia and force are defined, the first law becomes an identical propo- > 

 sition. The second law cannot be rendered perfectly intelligible until the stu- 

 dent has read the discourse on the composition and resolution of forces ; for, in 

 fact, it is intended as an expression of the whole body of results in that dis- 

 course. The third Jaw has been explained in the present lecture, as far as it 

 can be rendered intelligible in the present stage of our progress. 



We have noticed these formularies more from a respect for the authorities by 

 which they have been adopted, than from any persuasion of their utility. Their 

 full import cannot be comprehended until nearly the whole of elementary me- 

 chanics has been acquired, and then all such summaries become useless. 



The consequences deduced from the consideration of the quality of inertia in 

 this lecture, will account for many effects which fall under our notice daily, and 

 with which we have become so familiar that they have almost ceased to excite 

 curiosity. One of the facts of which we have most frequent practical illustra- 

 tion is, that the quantity of motion, or moving force, as it is sometimes called, 

 is estimated by the velocity of the motion and the weight or mass of the thing 

 moved conjointly. 



If the same force impel two balls, one of one pound weight, and the other of 

 two pounds, it follows, since the balls can neither give force to themselves nor 



