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



forces; they have the same acceleration. Next, suppose they 

 form parts of a single body; the acceleration will " evidently " 

 be the same as before, &c. (Third Law of Motion assumed.) 

 Hence accelerations being equal, force varies as mass. 



This method has been discredited of late, chiefly through 

 the influence of Thomson and Tart's ' Natural Philosophy,' so 

 that we may omit further discussion upon it. 



It may be remarked, however, that those who have most 

 emphatically declared against the statical measure of force do 

 not seem to perceive what is logically implied in that course. 

 (Cf Professor Tait's Lecture on Force.) 



Consider next the idea of mass. 



The definition based on the weight of bodies is open to the 

 same objections as the corresponding method in the case of 

 force. 



If we define mass by reference to chemical affinity *, or to 

 volumetric observations, we in the first place lose the sim- 

 plicity of the kinetic method, and secondly we adopt a con- 

 ception of mass which is different from the actual conception 

 of modern science. This is demonstrated if we ask ourselves: 

 Supposing experiment to show a discrepancy between the 

 mass as measured kinetically and as measured otherwise, 

 which method should we call inexact ? If the former, Kine- 

 tics could no longer be considered an exact science. 



Consider next the reference system, and the idea of true rest. 

 The most obvious arbitrary definition of the system to which 

 the motions of bodies in Dynamics are to be referred is to look 

 on the centre of gravity of the Solar system as the fixed 

 point, and the directions of certain fixed stars as fixed direc- 

 tions. The objections are, first, this would be a very incon- 

 venient system in discussing the cosmical Dynamics ; second, 

 it is not the actual conception of the science of the present day. 

 If one of the stars chosen were found to have a motion com- 

 pared with the average position of neighbouring stars, we 

 should certainly conclude that its direction was not " fixed " 

 in the dynamical sense. 



It has been suggested to take as a fixed direction that of 

 the perpendicular to the " invariable plane of the Solar system." 

 This really is not an independent definition, and is open to 

 the objections we previously urged against such, when isolated 

 from the fundamental law of Experimental Dynamics. 



The foregoing methods have been well criticised by 

 Streintz | ? who propounds in their stead a method of re- 



* See Maxwell's ' Matter and Motion/ art. xlvi. 



t Die physikalischen Gruncttagen der Mechanik. Leipzig, 1883. 



