Mr. R. F. Muirhead on the Laws of Motion. 475 



Principia. The Definitions and Axioms therein propounded 

 include all the principles underlying the modern science of 

 Dynamics. Subsequent progress has been either in the 

 direction of mathematical development or application to special 

 problems, or in attempts to improve the form of statement. 



Let us now inquire whether Newton's scheme of Definitions 

 and Axioms is satisfactory. 



We are struck at once b} r the fact (noticed by many 

 writers) that the First Law of Motion is previously stated or 

 implied in the Definition of Inertia. This, however, may be 

 passed over as a mere awkwardness of arrangement. 



Another defect which has been pointed out by several 

 writers, is the absence of any definition of equal times, which 

 renders the expression " uniformiter " in Law I. perfectly 

 indefinite. 



Of course the law implies that all bodies unacted on by 

 force pass through spaces in any interval of time whatever, 

 which are in the same proportion, so that taking any one such 

 body as chronometer, the First Law of Newton may be 

 affirmed of all the rest. We may, however, object to a form 

 of statement which does not directly state, but implies the 

 physical fact. 



Again, " uniform rectilinear motion " has no meaning 

 unless with reference to some base of measurement. And 

 the Law is not true except with reference to bases of a certain 

 type. For instance, the " fixed stars describe not straight 

 lines, but circles, taking the Earth as base of measurement.'" 



Newton's own statement is that the Laws of Motion are to 

 be understood with reference to absolute position and absolute 

 time. 



The only explanation given of absolute time, is that in 

 itself and of its own nature, without reference to anything 

 else, it flows uniformly. 



In explanation of the expressions " absolute motion" and 

 " absolute position,'"' we have the statement that " Absolute 

 and relative motion and rest are distinguished from one 

 another by their properties, causes, and effects. It is a property 

 of rest that bodies truly at rest are at rest among themselves, 

 but true rest cannot be defined by the relative positions of 



bodies we observe The causes by which true 



and relative motion are distinguished from one another are 

 the forces impressed on the bodies to produce motion. True 

 motion cannot change except by forces impressed. 



" The effects by which absolute motion is distinguished 

 from relative are the centrifugal forces of rotation. For 



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