482 Mr. R. F. Muirhead on the Laws of Motion. 



the axis, where co is the angular velocity in the first theory, 

 and t is the distance of any point from the axis *. But we 

 reject the latter theory on account of its greate?* complexity. 

 It is incorrect to say that the one is true and the other false. 



It follows that there is no essential difference between a 

 hypothesis and a theory, or what is called a law of nature. 

 One may be less exact than another, or less simple, or less 

 sufficiently tested, but the difference is one of degree. 



Now there are two opposite methods of stating dynamical 

 principles ; the one employing independent definitions of the 

 various conceptions, the other that adopted in this Essay. 

 Both, so far as observation has tested them, correspond equally 

 to the facts. The question is, then, Which is the simpler ? 

 Which comprehends the various relations with the least 

 expenditure of mental energy ? 



According to the former method, force, mass, time measure- 

 ment, and " true rest " would be defined as preliminaries to 

 the science of Dynamics, and independently of that science. 

 According to the latter, these conceptions are defined by 

 means of one Law or Hypothesis. 



Probably to learners unaccustomed to abstract reasoning, 

 who do not probe the processes of proof employed to the 

 bottom, the former method may be preferable because its 

 conceptions are more concrete ; but to one who has mastered 

 the essential relations of the subject, the latter will be found 

 superior. 



Let us discuss the idea of force. What are the alternatives 

 to the kinetic definition of force and force-measurement ? 

 We might take some arbitrary standard, such as a spring- 

 balance having a graduated scale. This would obviously have 

 the disadvantage of want of permanence, or, to speak more 

 accurately, that of liability to invalidate all our other methods 

 of reckoning force, by reason of some physical change occur- 

 ring in the standard balance. Further, such a method would 

 be incapable of accuracy sufficient for many of our physical 

 problems, where we deal with forces so small as to be insen- 

 sible to our present observing powers on such a standard; 

 forces whose magnitude, therefore, we could not define, even 

 theoretically. And, besides, any such arbitrary definition of 

 force would be contrary to our whole tendency in modern 

 science. Suppose, for instance, experiment were to disclose 

 that Newton's Second Law was untrue, the forces being thus 



* We might either suppose these new forces not conformable to the 

 law of the equality of Action and Reaction, which would then have to be 

 modified ; or we might suppose the reactions to observed actions to exist 

 in the fixed stars, and to be beyond our present means of observation. 



