184 NEWTON S PKINCIPIA. 



body does not pass through the centre of gravity, the 

 resistance itself will tend to cause rotation in the body. 

 To simplify our analysis we shall consider the bodies to 

 be indefinitely small particles. 



The principle on which we proceed is, that the motion 

 of the particle will be the same as if the resisting medium 

 were removed, arid that, first, a retarding force is substi 

 tuted in its stead, which acts along a tangent to the mo 

 tion of the particle, and depends only on the density of 

 the fluid and the velocity of the particle at the moment 

 under consideration, and that, secondly, all the impressed 

 forces are, by the buoyancy of the fluid or other causes, 

 diminished in a known ratio. 



In considering the motions of bodies in vacuo we exa 

 mined the effects of various laws of gravitation besides 

 that which we know to exist in nature. So we may now 

 examine the consequences of supposing the resistance to 

 vary according to different functions of the velocity. 



It is to Newton and Wallis * that we owe the first 

 researches on the theory of the motion of bodies in resist 

 ing media. Wallis, in the same year that Newton pub 

 lished his &quot; Principia,&quot; communicated his reflections on this 

 subject to the Royal Society, who published them in their 

 Transactions for 1687. Wallis, however, does not go so 

 deeply into the subject as Newton did. A little after 

 Newton s book appeared, Leibnitz asserted that he had 

 already discussed these subjects, and that he had commu 

 nicated his opinions twelve years previously to the Academy 

 of Sciences at Paris. Huygens also considered some 

 points in this theory at the end of Traite de la Pesanteur, 

 which appeared in 1690. Finally, everything which had 

 been either proved, or stated without proof, was demon 

 strated by Yarignon by the aid of the modern calculus. 

 * Montucla, Part IV., Lib. VII. 6. 



