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



Lastly, let us consider the conception of time-measurement. 



The only rival definition of equal times that need be con- 

 sidered is that adopted by Streintz, and ascribed by him to 

 D'Alembert and Poisson, viz. " Times are equal in which 

 identical processes take place." The difficulty here would be 

 to distinguish when we have identical processes going on. 

 We find that practically this will reduce to assuming each 

 rotation of the Earth with reference to the fixed stars a pro- 

 cess identical with all the others. For the " processes " must 

 consist in movements of matter, of which the Earth's rotations 

 are the most " identical " we have experience of. 



But even these we know are not absolutely identical, so 

 that our definition is not practicable. With this definition, 

 what should we mean by saying that the rotation period of 

 the Earth is altering ? We should mean that if identical pro- 

 cesses happened at different dates, their durations measured by 

 sidereal time would differ. But the only identical processes 

 actually available are wrapped up in the general dynamical 

 theory of the Solar system ; so that this theoretically inde- 

 pendent definition of time turns out to involve all our Dynamics 

 implicitly when we try to give it physical meaning. 



In seeking to justify our preference of kinetic definitions 

 over non-kinetic definitions of our fundamental dynamical 

 conceptions, we have found that the latter, besides being 

 theoretically inconvenient, very often have only an illusory 

 independence of Dynamics. 



In fact no one has ever built up a science of Dynamics 

 from independently formed conceptions ; and to do so in a 

 strictly logical manner would require expositions whose length 

 would render them tedious in the extreme. 



We have hitherto made no reference to any scheme of 

 dynamical principles apart from that of Newton, and those 

 various modifications of it proposed by later writers. This 

 course has been adopted in order to concentrate attention upon 

 the principle at issue. 



Systems of Dynamics founded on such principles as Mau- 

 pertius's " Principle of Least Action, " or Gauss's " Principle 

 of Least Coercion " (Kleinsten Zwanges), may be treated from 

 exactly the same point of view, and will not be further re- 

 ferred to. 



Note A. — On Theories and Hypotheses. 



In the preceding Essay we have assumed as known the science of 

 Geometry ; but of course the views put forward in this Essay con- 

 cerning the nature of physical theories apply equally to geometri- 



