Mr. K. F. Muirhead on the Laws of Motion. 485 



ference to a " Fundamental Korper," which is any body not 

 acted on by external forces and having no rotation. The 

 absence of rotation is to be determined by observations of 

 centrifugal force (as in Newton's experiment of the rotating 

 bucket of water) . Now as Streintz takes the kinetic definition 

 of force, it involves reasoning in a circle to speak at this stage 

 of a body " not acted on by forces." Further, if the observa- 

 tions of centrifugal force are to be made with the whole re- 

 sources of Dynamics, and our knowledge of the laws of nature, 

 this is virtually the kinetic definition of force, but stated 

 in a form which involves reasoning in a circle. If, on the 

 other hand, want of rotation is to be defined as existing when 

 the surface of a bucket of water does not appear to deviate 

 from planeness, then our stock objections to such definitions 

 of dynamical ideas reappear. 



A most instructive discussion relating to this subject is 

 given by Professor Mach in his book Die Mechanik in Hirer 

 Entwickelung , historisch-kritisch dargestellt, pp. 214-222-. Let 

 us quote a sentence on p. 218: — 



" Instead of saying i the direction and velocity of a mass 

 fi in space remain constant,' we can say ' the mean accelera- 

 tion of the mass p with reference to the masses m, m! , m" . . . 



at the distances r, r', r n . . . is = 0, or -j^ -^ — = 0.' The 



at *~iii\ 



latter expression is equivalent to the former, so soon as 

 we take into consideration masses which are great enough, 

 numerous enough, and distant enough. - " 



On the previous page, referring to Newton's bucket ex- 

 periment, he remarks that no one can say how the experiment 

 would come out were we to increase the mass of the bucket 

 continually ; and, further, that we should be guilty of dis- 

 honesty were we to maintain that we know more of the motion 

 of bodies than that their motion relative to the very distant 

 stars appears to follow the same laws as Galileo formulated for 

 terrestrial bodies relative to the Earth. 



Of course this charge of dishonesty cannot be urged against 

 the method of this Essay, as explained in our paragraphs on 

 the nature of theories. And our definition of " true rest " 

 being based entirely on experiment and observation, is not 

 affected by Prof. Mach's strictures on the use of the terms 

 absolute rest, absolute space, &c. 



Though on the principles of this Essay no exception in 

 principle can be taken to Prof. Mach's substitute for the 

 " First Law of Motion above quoted," we reject it because it 

 is not the actual conception which has been historically evolved 

 in Dynamics. 



