470 Sir Oliver J. Lodge [Feb. 28, 



write m v^ = 2 m w- = lin \ because the emission velocity u (the 

 velocity from infinity) is ^2 times the orbital velocity v. But /i, or' 

 rather /i/2 tt, may also be taken as representing the orbital angular 

 momentum, mvr (more strictly, if the orbit is at all elliptical, mv^) 

 for the ring whence the particle came. It would be rather convenient 

 if the designation li were transferred to A/2 tt before it is too late ; 

 but I must leave this minor change to the approval of leaders in this 

 subject. 



I may point out that this constancy of angular momentum in 

 different orbits bears a curious analogy to Kepler's second law about 

 rate of description of areas in the same orbit. And, if a coincidence, 

 it is odd that the symbol li should have been used both for Kepler's 

 r- d 6/d t and for an atomic quantity which is also r^ d B/d t multiplied 

 by 2 TT m. 



Within each atom Kepler's laws must presumably hold ; so r^/t -, 

 or r v^^ is constant for the different circular orbits in each atom ; 

 whence the energy in successive rings of one atom is inversely as their 

 radii ; hence the ring most likely to eject a particle is the innermost 

 or K ring. 



This characteristic constant r v"- of an element is proportional to 

 the central attracting force, and therefore proportional to X. Hence 

 it goes up step by step in the series of atoms, as N does. 



Summary. 



N is Moseley's atomic number, and equals the number of orbital 

 electrons, or the number of unbalanced positive charges in the nucleus. 

 The constant r v^ is characteristic of all the rings in one atom (N 

 being constant). The product r ^' is a constant characteristic of a 

 given type of ring in the whole series of atoms (N going up step by 

 step) ; but in any one atom this product r v ascends from ring to 

 ring in regular arithmetical stages, the same stages as V^- 



The product rv"^ is constant inside each atom and proceeds by 

 steps from atom to atom ; while the product rv is the same for 

 different atoms, but changes inside each atom and proceeds by steps 

 from ring to ring. In fact we may write : — 



For all the rings in one atom. 



Central force . . . . r z^^ is constant. 



Angular Momentum for the rings in 



one atom . . . . . r v cr. ^r 



Energy for the same . . . v^ y. 1/r 



For any ring in any atom. 

 Central force for any ring in any atom ri;- cc N 



