49 51] PRINCIPLES OF MECHANICS. UNITS AND DIMENSIONS. 95 



The vector acceleration, a, may be defined as the resultant of 

 the components a x , a y , a z , and accordingly its modulus is 



This is not in general equal to -y- which is the acceleration of 



ctt 



the scalar velocity. The direction of a is given by its direction 

 cosines 



a a a 



51. Physical Axioms. The results of universal experience 

 with regard to motion are summed up by Newton in his three Laws 

 of Motion or Axioms of Physics. An axiom is defined by Thomson 

 and Tait* as a proposition, the truth of which must be admitted 

 as soon as the terms in which it is expressed are clearly under- 

 stood. These physical axioms rest, not on intuitive perception, 

 but on convictions drawn from observation and experiment. 



LEX I. Corpus omne perseverare in statu suo quiescendi vel 

 movendi uniformiter in directum, nisi quatenus a viribus impressis 

 cogitur statum suum 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 apart of its different parts may be neglected, the motion 

 is uniform if 

 xx dx _ dy _ dz _ 



~dt~ Cl> ~dt~^ di = C3) 



that is 



^ = ^-^-0 

 dt* dt*~dt*~ 



* Thomson and Tait, Natural Philosophy, 243. 



