320 HISTORY OF MECHANICS. 



the smallness of the point of contact. 3 But the most common mistake 

 of this period was, that of supposing that as force is requisite to move 

 a body, so a perpetual supply of force is requisite to keep it in motion. 

 The whole of what Kepler called his " physical" reasoning, depended 

 upon this assumption. He endeavored to discover the forces by which 

 the motions of the planets about the sun might be produced ; but, in 

 all cases, he considered the velocity of the planet as produced by, and 

 exhibiting the effect of, a force which acted in the direction of the 

 motion. Kepler's essays, which are in this respect so feeble and un- 

 meaning, have sometimes been considered as disclosing some distant 

 anticipation of Newton's discovery of the existence and law of central 

 forces. There is, however, in reality, no other connection between 

 these speculations than that which arises from the use of the term 

 force by the two writers in two utterly different meanings. Kepler's 

 Forces were certain imaginary qualities which appeared in the actual 

 motion which the bodies had ; Newton's Forces were causes which 

 appeared by the change of motion : Kepler's Forces urged the bodies 

 forwards ; Newton's deflected the bodies from such a progress. If 

 Kepler's Forces were destroyed, the body would instantly stop ; if 

 Newton's were annihilated, the body would go on uniformly in a 

 straight line. Kepler compares the action of his Forces to the way in 

 which a body might be driven round, by being placed among the sails 

 of a windmill ; Newton's Forces would be represented by a rope pull- 

 ing the body to the centre. Newton's Force is merely mutual attrac- 

 tion ; Kepler's is something quite different from this ; for though he 

 perpetually illustrates his views by the example of a magnet, he warns 

 us that the sun differs from the magnet in this respect, that its force is 

 not attractive, but directive. 4 Kepler's essays may with considerable 

 reason be asserted to be an anticipation of the Vortices of Descartes ; 

 but they can with no propriety whatever be said to anticipate New- 

 ton's Dynamical Theory. 



The confusion of thought which prevented mathematicians from 

 seeing the difference between producing and preserving motion, was. 

 indeed, fatal to all attempts at progress on this subject. We have 

 already noticed the perplexity in which Aristotle involved himself, by 

 his endeavors to find a reason for the continued motion of a stone 



3 In speaking of the force which would draw a body up au inclined plane he ob- 

 serves, that " per communem animi sententiam," when the plane becomes hori- 

 zontal, the requisite force is nothing. 



4 Epitome Astran. Copem. p. 176. 



