September 8, 192 1] 



NATURE 



63 



things as, say, phase difference produced by total 

 reflection, or conical refraction, and consequently 

 there are not many people aware of the extremely 

 high degree of agreement attained. It has not 

 been quite so successful in dealing with the emis- 

 sion and absorption of light; this, however, can- 

 not be ascribed so much to a defect of the theory 

 as to our ignorance of the structure of matter. 



Newton's theory being out of the question, and 

 there being no definite alternative offered, we must 

 attempt to explain the phenomena of X-ray ener- 

 getics on the wave theory. This is not so difficult 

 as is supposed, for in previous discussions import- 

 ant facts have usually been left out. 



In the first place the wave theory does not limit 

 us to the harmonic-wave trains of the elementar}- 

 text-books. It certainly permits of the passage of 

 energy in pulses which widen out ver}- little as 

 they travel. In some signalling experiments a 

 beam of light has been used which was 2 in. wide 

 at one end and 5 ft. wide at the other at a dis- 

 tance of five miles. There would be no difficulty 

 "^ in supposing this repeated on an atomic scale, if 

 we could only imagine a mechanism for getting 

 the beam started. Perhaps electrons vibrating 

 with suitable phase differences on a space lattice 

 might do. In any case it is a matter of arranging 

 the interfering sources suitably ; a hint to the pro- 

 perties of the Fourier integral is here enough. 

 White light on the modern view consists of pulses, 

 and we can easily make calculations on the inter- 

 ference, diffraction, and dispersion of such pulses. 

 For example, a single pulse is changed by its pas- 

 sage through a dense flint plate of i cm. thickness 

 into a group of about 500 visible waves. 



Also it is not necessary that the pulse should be 

 as narrow as the electron in order that all the 

 energy in it should be absorbed by the electron. 

 The analog\' of a large metal plate coated with 

 soot is very misleading in this respect. Lord Ray- 

 leigh has shown {Phil. Mag., August, 1918), or at 

 least made it plausible, that an electron captures 

 all the energy passing through an area compar- 

 able with X^jir, where A is the wave-length. 



There is difficulty on the wave theory about 

 starting the energy off along one line, since it 

 would require elaborate and improbable conditions 

 in the source. So It seems preferable to fall back 

 on the other explanation, namely, that of " trigger 

 action." 



The spherical wave, uniform throughout its 

 front and diverging from a single point source, is 

 a mathematical fiction, used only in the interests 

 of simplicity. What we have in reality is always 

 a superposition of wavelets from a number of 

 electrons, say n, included within a small region 

 and vibrating simultaneously. These wavelets in- 

 terfere. If their amplitudes were all the same and 

 equal to a, the resultant intensity would vary from 

 {no)- to o, according to the degree of reinforce- 

 ment present, the lower values being more prob- j 

 able and the average being na~. There are thus 

 singular points in the wave-front. The ionisation 

 cannot depend on the intensity of the resultant 

 wave, because this brings us up against the diffi- i 

 NO. 2706. VOL. I08I 



culty numbered 3 (a) above. As a result of the 

 interference, though, changes of phase and 

 different rates of change of intensity will be 

 produced, and it is natural to suppose that some 

 complicated combination of these produces the 

 critical conditions ; by an accurately timed series 

 of impulses the electron is thrown out of its orbit, 

 and an atomic explosion follows. Thus the objec- 

 tions above headed (1) and (2) are met. 



The strongest argument in favour of the " trig- 

 ger action " theory is undoubtedly the numerical 

 value of Planck's constant itself. There has been 

 comparatively little attention given to the mean- 

 ing of the quantum itself, or to the connection 

 between the atomicity of energy, or rather action 

 it signifies, and the atomicity of electricity already 

 established. The tendency has been rather to take 

 the quantum for granted and to quanticise every- 

 thing. There has also been a widespread assump- 

 tion that the quantum is inexplicable in terms of 

 the concepts already existing. 



Suppose, however, that we take a sphere of 

 positive electricity of uniform density p and radius 

 a, and assume that inside the sphere there is one 

 electron which oscillates about its centre through 

 the positive electricity. Let v be the frequency of 

 the oscillations, and suppose the radius of the 

 sphere just large enough to neutralise the electron. 

 Then 



v= ^ I \ ^ — ) and e = ^n(i^p. 

 \' V3ir//// 3 



Now suppose that the electron starts from rest on 

 the surface of the sphere and falls towards the 

 centre. Let v be the velocity acquired by the time 

 it reaches the centre. Then v = 2Trav. On elimin- 

 ating p and a these three relations give 



■H~h 



If an electron has one quantum kinetic energy, its 

 velocity is given by 



'=(vt)''- 



The difference between the two formulae for v 

 amounts to the sixth root of v, an amount which 

 would scarcely matter if only the visible spectrum 

 were in question, but is much too great when we 

 take the X-ray region also into consideration. But 

 there is a surprising numerical agreement. If we 

 fix our attention on two wave-lengths, (i) that of 

 sodium in the visible spectrum, and (ii) the wave- 

 length io~* cm. in the X-ray region, we find that 

 the two expressions for v give in the case of (i) 

 929 X 10^ cm. /sec. and 8*64 x 10^ cm. /sec, and in 

 the case of (ii) i"68xio^ cm. /sec. and 6*64 x 10® 

 cm. /'see, the second value in each case being 

 given by the quantum formula. Thus there is fair 

 agreement for sodium, but the new formula gives 

 only one-quarter of the correct value in the X-ray 

 region. 



The agreement, such as it is, cannot be a chance 

 one. It means that. if we construct a model atom 

 in the simplest manner possible, so as to respond 



