On the Physical Units of Nature. 381 



appears at once on putting his case in mathematical form. 

 He supposes two particles ; m and mf, moving in the same 



fl V dx^ 



straight line (say the axis of x) with velocities -j- and -5— , 



and acting on each other with equal and opposite moving- 

 forces F. Then the Force Function, during any time Bt, is 



F^St-Y^St. 

 dt dt 



According to Dr. Lodge, this is always = 0. But, as is well 

 known, the true equation is 



-ndx ~, -^ dx' ~ dx d /dx\ ~ ,dx f d /dx f \ ~ 



where the left-hand side, taken negatively, is the Potential 



Energy, and the right-hand side is the change in the vis viva 



or Kinetic Energy of the system. This right-hand side clearly 



d v dx 

 varies according to the values of-^> -7- or of the velocities. 



& dt dt ' 



If these velocities are equal (assuming the masses also equal), 

 then the right-hand side vanishes, and we have as a particular 

 case that which Dr. Lodge assumes to hold universally. What 

 does hold universally is that the sum of the two sides (i. e. of 

 the Potential Energy and the Kinetic Energy) is constant ; 

 and this, and this only, is the principle known as the Conser- 

 vation of Energy. 



"Waltek E. Beowne. 



LII. On the Physical Units of Nature. By G. Johnstone 

 Stoney, D.Sc, F.R.S., Vice-President of the Roy cd Dublin 

 Society*. 



1. \ IT HEN mathematicians apply the sciences of measure- 

 W ment to the investigation of Nature, they find it 

 convenient to select such units of the several kinds of quantity 

 with which they have to deal as will get rid of any coeffi- 

 cients in their equations which it is possible in this way to 

 avoid. Every advance in our knowledge of Nature enables 

 us to see more distinctly that it would contribute to our 

 further progress if we could effect this simplification, not only 

 with reference to certain classes of phenomena, but through- 

 out the whole domain of Nature. 



* From the 'Scientific Proceedings' of the Royal Dublin Society of 

 February 16, 1881, being a paper which had been read before Section A 

 of the British Association, at the Belfast Meeting in 1874. Communicated 

 by the Author. 



