242 Prof. J. G. MacG-regor on the 



based upon the belief that dynamical reference systems are 

 means of describing velocities absolutely. 



This is the method which Streintz employs in the work re- 

 ferred to above. He accepts Newton's conclusion* that it is 

 possible to recognize absolute motion of rotation, and possible, 

 therefore, apart from all reference to surrounding bodies, to 

 recognize a body as not rotating. He consequently assumes 

 that the fundamental body, by reference to which the motion 

 of other bodies must be specified in order that the first law 

 may hold, must be a body which is undergoing no rotation f ; 

 and he holds that such a body may be recognized by the 

 application of the Foucault's pendulum test and by other 

 similar experimental tests. 



While Streintz's method leads him to a correct, though a 

 particular, result, as tested by the results of legitimate methods, 

 it is based upon an assumption which, when the relativity of 

 the laws of motion is admitted, may readily be shown to be 

 erroneous, viz. that the absence of centripetal forces enables 

 us to recognize a body as being absolutely without rotation. 

 The widespread confidence in the conclusion which Newton 

 drew from the behaviour of his rotating bucket of water 

 seems to me to be an instance of the confusion of thought 

 which has its origin in the non-recognition of this rela- 

 tivity %. That a particle which is moving in a curved path 

 must be acted upon by a resultant force which has a com- 

 ponent directed towards the centre of curvature, is a deduction 

 from the second law of motion. Without specification of 

 axes the deduction has no definite meaning ; for a path 

 which is curved relatively to one set of axes may be differently 

 curved or even straight relatively to others. Obviously, 

 however, the axes by reference to which motion is assumed 

 to be specified are axes by reference to which the second law 

 holds. Fully enunciated, the proposition would therefore read 

 thus : — A particle which, relatively to a dynamical reference 

 system, is moving in a curved path, must be acted upon by a 

 force having a component directed towards the centre of cur- 

 vature. If, therefore, in any case we can detect the action or 

 the non-action of such force, we may assert that the particle 

 is moving or is not moving, respectively, in a path which is 



* Principia : Scholium to Definitions. 



f Prof. Tait proposes a similar mode of specification (Properties of 

 Matter (1885), p. 92). 



\ Writers who accept Newton's conclusion usually deny the possibility 

 of recognizing absolute translation. Yet if we regard the laws of motion 

 as holding for absolute space, which we must do in order to accept his 

 conclusion, it follows that the translational acceleration of a body deter- 

 mined bv the second law must be an absolute acceleration. 



