12, 13] NEWTON'S LAWS OF MOTION. 21 



Thomson and Tait 1 ) as a proposition, the truth of which must he 

 admitted as soon as the terms in which it is expressed are clearly 

 understood. These physical axioms rest not on intuitive perception, 

 but on convictions drawn from observation and experiment. 



The manner of summing up the results of our experience is to 

 a great extent unimportant, provided that it is sufficiently all- 

 embracing. We are not concerned with the metaphysical question 

 of the causes of motions, but merely with the physical question of 

 stating what is actually found to take place in nature. The statement 

 may be made by means of a single analytical formula, as was done 

 in different ways by Lagrange, Hamilton and Hertz, or we may 

 consider the various assumptions upon which such formulae are 

 founded, making detailed statements, employing conceptions with 

 which we are familiar. 



This is what was done by Newton, and although his laws have 

 received considerable criticism, they have, when properly understood, 

 been generally admitted to be better than anything that has been 

 proposed in their place. 



Lex I. Corpus omne perseverare in statu suo quiescendi vel 

 movendi uniformiter in directum, nisi quatenus a viribus impressis 

 cogitur statum suam mutare. 



Every body persists in its state of rest or of uniform motion 

 in a straight line, except in so far as it may be compelled by force 

 to change that state. 



The property of persistence thus defined is called Inertia. 



This gives a criterion for finding whether a force is acting on 

 a body or not, or in other words a negative definition of force. 

 Force is acting on a body when its motion is not uniform. By 

 uniform we mean such motion that the vector velocity is constant. 

 If the body be a material point, that is a body so small that the 

 distances between its different parts may be neglected, the motion is 



uniform if 



dx _ dy dz 



dt = ~~ C i> d* = = C2 > dt =C ^ 

 38) that is 



Accordingly we see that the force and acceleration vanish together. 

 Integrating the equations 38), 



x = ct-\-di, y = c 2 t+d 2 , = c 3 tf-fd 3 , 

 39) x d l y d z z d s 



1) Thomson and Tait, Natural Philosophy, 243. 



