826 On Systems with "Propagated Coupling." 



to another. For example, in Cartesian co-ordinates it 

 becomes 



/1-rV 

 ( ^=-(l + ^)V' 2 Vdf + dz*) + l—ty dt2 - 



It cannot be too clearly recognized that the difference 

 between the two forms of the line element given in (2) 

 and (10) depends only upon the way in which we agree 

 to measure the radial distance r. The form (10) can 

 therefore give no physical result which is independent 

 of radial measurements which is not already implied in (2). 

 For example, the equation of the orbit of a particle is 

 obtained from 



#+^S4=° -^ 



For a particle moving in the plane Q — \<n, the form 

 (10) gives 



W +u = h^HT ; •,.••'• (13) 



while (2) gives the more usual form 



d 2 u m 



^ + u=£ + W, (14) 



where, as usual, u=l/r. 



These two differential equations have different solutions ; 

 but if we investigate a fact Avhich does not depend upon 

 radial measurement, the advance of the apse line per 

 revolution, (13) and (14) agree in giving 3m 2 /h 2 . 



LXXYII. On Systems with " Propagated Coupling " 



To the Editors of the Philosophical Magazine. 

 Gentlemen, — 



Professor A. W. Porter, F.R.S., and Mr. R. E. Gibbs, 

 B.Sc ., have published in No. 243 of the Philosophical 

 Magazine a paper " On Systems with Propagated Coupling" 

 (March 1921, p. 432). In the first part of this communi- 

 cation some interesting experiments are described, but in the 

 second part (p. 434), in the paragraph headed " (ii.) Simple 



