ON THE MOTIONS OF SIMPLE MASSES. 43 



supposition is so highly improbable, that the principle may almost as 

 justly be termed a necessary axiom, as a phenomenon collected from 

 observation. 



Sir Isaac Newton * observes, in his third law of motion, that " reaction 

 is always contrary and equal to action, or, that the mutual actions of two 

 bodies are always equal, and directed contrary ways." He proceeds, " if 

 any body draws or presses another, it is itself as much drawn or pressed. 

 If any one presses a stone with his finger, his finger is also pressed by the 

 stone. If a horse is drawing a weight tied to a rope, the horse is also 

 equally drawn backwards towards the weight : for the rope, being dis- 

 tended throughout, will, in the same endeavour to contract, urge the horse 

 towards the weight and the weight towards the horse, and will impede the 

 progress of the one as much as it promotes the advance of the other." Now 

 although Newton has always applied this law in the most unexceptionable 

 manner, yet it must be confessed that the illustrations here quoted are 

 clothed in such language as to have too much the appearance of paradox. 

 When we say that a thing presses another, we commonly mean, that the 

 thing pressing has a tendency to move forwards into the place of the thing 

 pressed, but the stone would not sensibly advance into the place of the 

 finger, if it were removed ; and in the same manner we understand that a 

 thing pulling another has a tendency to recede further from the thing 

 pulled, and to draw this after it ; but it is obvious that the weight which 

 the horse is drawing would not return towards its first situation, with the 

 horse in its train, although the 'exertion of the horse should entirely cease ; 

 in these senses, therefore, we cannot say that the stone presses, or that the 

 \veight pulls, and we have no reason to offend the just prejudices of a be- 

 ginner, by introducing paradoxical expressions without necessity. Yet it is 

 true in both cases, that if all friction and all connexion with the surround- 

 ing bodies could be instantaneously destroyed, the point of the finger and 

 the stone would recede from each other, and the horse and the weight would 

 approach each other with equal quantities of motion. And this is what we 

 mean by the reciprocality of forces, or the equality of action and reaction. 



The quantity of action of two attractive or repulsive bodies on each 

 other is partly dependent on their magnitude. When the bodies are of the 

 same kind, their mutual action is in the compound ratio of their bulks ; 

 that is, in the ratio of the products of the numbers expressing their bulks. 

 For instance, if two bodies, each containing a cubic inch of matter, attract 

 or repel each other with a force of a grain, and there be two other bodies, 

 the one containing two inches, the other ten, of the same matter, then the 

 mutual attraction or repulsion of these will be expressed by twenty grains ; 

 for each of the 10 inches is attracted by each of the two with a force of a 

 grain. And the mutual action of 3 and 10 will be 30, of 4 and 10, 40 ; so 

 that when one of the bodies remains the same, the, attraction will be 

 simply as the bulk of the other. Hence the quantity of matter, in every 

 body surrounding us, is considered as proportional to its weight ; for it is 

 inferred from experiment that all material bodies are equally subject to the 

 power of gravitation towards the earth, and are, in respect to this force, of 

 * Principia, Lib. I. 



