488 Mr. B. F. Muirhead on the Laws of Motion. 



space and time which the mind has been able to form " is unwar- 

 ranted. 



Kirchhoff in his Mechanik appears to adopt a view somewhat 

 similar to that set forth in this Essay. In his preface we find him 

 stating as the problem of Mechanik, " die in der Natur vor sich 

 gehenden Bewegungen vollstandig und zwar auf die einfachste 

 Weise zu beschreiben." 



This author uses the term force only as a convenient means of 

 expressing equations shortly in words. Mass appears as a coeffi- 

 cient in the equations of motion, and thus receives a kinetic defi- 

 nition. But no explanations are given as to time-measurement, or 

 as to the axes of reference. 



Note B. — Newton's Absolute Space and Time. 



My criticisms of the Newtonian scheme of Definitions and Axioms 

 have been directed not so much against what I suppose to be 

 Newton's meaning, as against the form in which it is put, especially 

 as against that form on the supposition that force is to be measured 

 kinetically. 



Thus, instead of looking on the Second Law as a mere definition 

 of force-measurement, we might suppose that Newton had in his 

 mind some non-kinetic conception of force-measurement ; in which 

 case the Second Law would be a real and not an illusory statement 

 of physical fact, though imperfect through the want of any speci- 

 fication of how force was to be measured. 



Again, take the question of absolute space and time, with respect 

 to which Newton's laws are stated. 



There are three ways of looking at it. Some characterize these 

 terms as mere metaphysical nonsense (Mach, p. 209). Streintz* 

 quotes the Hypothesis I. from the third Book of Newton's Prin- 

 cipia to show that by absolute rest Newton means rest relative to 

 the centre of gravity of the universe. But Newton evidently places 

 this Hypothesis in a different category from his laws of motion. 



I think the meaning of the terms amounts simply to this, that 

 Newton looked on Dynamics as an abstract science. " In rebus 

 philosophicis abstrahendum est a sensibus" t, "loca primaria moveri 

 absurdum est " f. And an abstract science is one which deals 

 with a certain body of conceptions, every relation in which holds 

 with absolute exactness. The point at which considerations as to 

 degree of exactitude may arise, is its application to experience. 



If this be the correct view of Newton's meaning, then the fore- 

 going Essay has been simply the explicit and developed statement of 

 that meaning. 



Thomson and Tait, while in various ways improving the form in 

 which they state the Newtonian theory, entirely ignore his idea of 

 " absolute space and time," which, as I have tried to show, is the 

 germ of the true theory. 



* Physikalische Grundlagen, p. 10. 

 t Scholium to Bejlnitiones. 



