172 CELESTIAL MECHANICS. I. hi. 14. 



communication of motion, ** reaction is always equal and 

 contrary to action." And it is found by observation that 

 this principle holds good with respect to all forces in 

 nature. 



[Scholium 1. All the forces in nature, with which we 

 are acquainted, act reciprocally between different masses 

 of matter, so that any two bodies, repellin'g or attracting 

 each other, are made to recede or approach with equal 

 momenta. This circumstance is generally expressed by 

 the third law of motion, that action and reaction are equal. 

 There would be something peculiar, and almost inconceiv- 

 able, in a force which could affect unequally the similar 

 particles of matter; or in the particles themselves, if they 

 could be possessed of such different degrees of mobility, 

 as to be equally moveable with respect to one force, and 

 unequally with respect to another. For instance, a 

 magnet and a piece of iron, each weighing a pound, will 

 # remain in equilibrium when their weights are opposed to 

 each other by means of a balance ; they will be separated 

 with equal velocities, if impelled by the unbending of a 

 spring placed between them ; and it is difficult to conceive 

 that they could approach each other with unequal veloci- 

 ties in consequence of magnetic attraction, or of any other 

 natural force. The reciprocality of force is, therefore, a 

 necessary law in the mathematical consideration of mecha- 

 nics, and it is also perfectly warranted by experience. 

 The contrary supposition is so highly improbable, that the 

 principle may almost as justly be termed a necessary axiom, 

 as a phenomenon collected from observation. 



Scholium 2. 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 



