119 



fluids, no one will question ; but that it should be retained there 

 by a projectile force, is contrary to analogy, and cannot be de- 

 monstrated. 



If, then, we find that a body put in motion by one impulsive 

 action must ultimately come into a state of rest without any 

 resisting medium, how much sooner must it exhaust its force if 

 opposed by other forces, and especially if the latter should be 

 constant ! A straight line divided into equal parts is one thing, 

 but to produce a force to describe such parts in equal times is 

 another ; the former is controlled by the laws of geometry, the 

 latter by the laws of physics. This is the secret link which has 

 been used to preserve the curvilinear doctrine of gravitation; 

 without which tie it could not stand, and must be well known 

 to those who have studied the 'Principia.* Is this a legitimate 

 connexion? 



We may observe that it was once proposed as a prize ques- 

 tion by the Academy of Sciences at Berlin, to determine whether 

 the laws of motion were necessary or accidental ; that is, whether 

 they were to be considered as mathematical or as physical truths. 

 An attempt was made to deduce them from a metaphysical prin- 

 ciple of the minimum of action in a very complicated and fanciful 

 nature, the intricacy of which only tended to envelope the sub- 

 ject in still greater obscurity than is found in the c Principia;' 

 while the fundamental laws of motion are easily demonstrable 

 from the simplest physical truths. 



Besides the disagreement which exists between the rectilinear 

 motions of the e Principia ' and those of terrestrial physics, there 

 is another point connected with the composition of two forces, 

 viz. the compound of the tangential and centripetal forces. We 

 find that the diagonal of the parallelogram of two forces repre- 

 sents the magnitude and direction of the compound ; but we 

 must always bear in mind the distinction which exists between 

 statics and dynamics. In the former it matters not how the 

 sides of the parallelogram are accumulated, whether slow or 

 quick, by small quantities or by large quantities ; as long as the 

 amount of the forces is represented by the length of the sides, 

 a straight diagonal will represent the compound when in a state 

 of equilibrium. The laws of dynamics are not confined to the 

 extreme limits or the mere gross amount of the forces, but they 



