September 25, 1919] 



NATURE 



85 



because of the shortest wave-lengths, or so-called 



K spectrum, which its perturbations emit. And in 



^(■ending the series of elements, as the nucleus gets 



longer by addition of units, the electron in this 

 innermost or K ring must revolve faster and faster 

 to counterbalance the greater attracting force. Its 

 orbit will accordingly get smaller and smaller, in the 

 proportion proper to the law of inverse square. .\nd 

 the frequency will increase for both reasons, i.e. for 

 both the greater speed and the shorter journev. The 

 spectrum accordingly, while preserving the same type, 

 ascends the ladder of frequency. 



Suppose the atomic number, or strength of the 

 nucleus in atoms of successive elements, increases in 

 arithmetical progression N— i, N, N+i, etc., then 

 the radius of the given type of orbit may shrink in 

 the same proportion, so that rN is constant ; and the 

 velocity v may increase in the same proportion, so 

 that rv is constant ; or, in other words, so that the 

 moment of momentum in corresponding rings of 

 different atoms is thq same. There is good evidence 

 that such is the case. The law, so far as it is a law, 

 is styled by Prof. Millikan the atomicity of angular 

 momentum. If the value of mvr or mr'w differs in 

 different rings, it differs by finite steps. 



The frequency of orbital revolution will depend on 

 V directly and on r inversely, so the frequency 

 (vl-mr) will increase in the proportion of N^ ; and 

 this, in some form of other, is known as Moselev's 

 law. 



The energy, \ynv- in a given tyf>e of ring, will also 

 depend upon N" in different atoms, and is therefore 

 simply proportional to the frequency. The orbital 

 energy is half the energy with which a particle breaks 

 loose (or is driven to infinity) whenever a convulsion 

 occurs. The convulsion can be stimulated bv X-ravs 

 or ultra-violet light of the right frequency ; their 

 energy appears to be stored by resonance until the 

 critical breaking-up point is reached. The ratio of 

 emission energy to frequency is a remarkable uni- 

 versal constant, and is called h, the quantum. It is 

 not energy, but the accumulation or integral of energv 

 for a certain time ; and . it is permissible to write 

 mv^ = iviiC = hn\ because the emission velocity u (the 

 velocity from infinity) is sj ^ times the orbital velo- 

 r' city r. But h, or rather 11/277, mav also be taken as 

 i' representing the orbital angular momentum mvr 

 (more strictly, if the orbit is at all elliptical, nivp) 

 for the ring whence the particle came. It would be 

 rather convenient if the designation h were transferred 

 to h/2jr before it is too late; but I must leave this 

 minor change to the approval of leaders in this 

 subject. 



I mav 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. .4nd, if a coincidence, it is 

 odd that the symbol h should have been used both 

 for Kepler's r'dOldt and for an atomic quantity which 

 is also r'dO/dt multi|)lied by 2-m. 



Within each atom Kepler's laws must presumably 

 hold; so r'/t', or rv'. 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 rv' of an element is 

 1 pniportional to the central attracting force, and there- 

 fore proportional to N. Hence it goes up step by 

 step in the .series of atoms, as N does. 



Summary. 

 \ is Moseley's atomic number, and equals the 

 number of orbital electrons, or the number of un- 

 b.ilanced positive charges in the nucleus. The con- 



NO. 2604, VOL. 104] 



stant rv' is characteristic of all the rings in one atom 

 (N being constant). The product rv 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 rv 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 pro- 

 duct 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 ... ... ri/^ is constant. 



Angular momentum for 



the rings in one atom ... rv cc .Jr 



Energv for the same ... v^ oc 1/1- 



For any Ring in any Atom. 



Central force for any ring 

 in any atom rv- o: N 



For the same Type of Ring in Different Atoms. 



Radius of given t\'pe of 



ring in any atom ... r ex i/N 



Orbital velocity in ring of 



that type ... ... v cc N 



Moment of momentum in 



given type of ring ... rv \s const, as regards N. 

 Frequency in that type of 



ring ... ... ... v/r cc N- 



Energy in same ... ... v' oc N- 



So for a given type of ring in different atoms the 

 orbital energy is proportional to the frequency ; which 

 is a curious result thoroughly consistent with Moseley's 

 law, ascertained by experiments on emission, and 

 true, at any rate, for emission energy. The ratio 



emission energv ;//?'- ., , 



— ,. s^-- = =27rmvr=2n.?//r^.2T!-r=2nlQ> 



frequency ■z//27ir 



So if we call this h, or a multiple of h, then on our 

 hypothesis h/27T is the indivisible unit of angular 

 rhomentum for an orbital electron. 



The speed with which an electron is ejected is very 

 high, something like o-g of light, so the increase of 

 mass at high speeds must be taken into account in 

 propounding a reason for the emission of corpuscles. 



Radiation Heterodoxy. 



In considering the radiation from an atom, I have 

 virtually made the hypothesis that so long as orbits 

 are circular they do not radiate, but that if perturbed 

 into ellipses, with corresponding fluctuation of S[)eed 

 — as they would be by the influence of a flying charge 

 passing through or near them — then they would 

 radiate, with the proper orbital frequency, until 

 the eccentricity disappears again and they resume 

 their stable circular orbit once more, though, of 

 course, they might be so much perturbed as to eject 

 a particle. .iXny one of the rings, if perturbed at all, 

 may radiate and give appropriate spectral lines. ."Xn 

 external synchronous alternating field will also cause 

 them to absorb energy, even though they were not 

 radiating any until the extra energy arrived. 



This hypothesis, if at all regarded, is equivalent to 

 a request to mathematicians to -.-econsider their theory 

 of electronic radiation.- Radiation intensity is known 

 to be proportional to the square of acceleration (Sir 

 Joseph Larmor, and to some extent FitzGerald and 

 Hertz, established this), and I must admit that the 

 reasoning seems to make this law applicable to every 

 kind of acceleration ; but my rash suggestion is that 



