SOME CONTEMPORARY ADVANCES IN PHYSICS 105 



manner, and differing by virtue of slight intelligible differences in the 

 atoms which emit them, may be expected to help greatly in making 

 clear the major features of atomic structure. 



Two phenomena, first accurately examined by A. H. Compton, 

 afford a striking illustration of the way in which classical electro- 

 magnetic theory and quantum theory are alternately successful in 

 explaining the qualities of radiation. On the one hand, Compton 

 has been the first to apply accurate wave-length measurements to 

 scattered X-rays, and finds that they are a mixture of two kinds of 

 X-rays — one having exactly the same wave-length as the primary 

 X-rays, the other a wave-length slightly greater and varying with the 

 angle between the primary and the secondary rays. According to the 

 classical theory, scattered X-rays are simply radiation sent out in 

 all directions by electrons inside the atoms of the scattering sub- 

 stances, vibrating under the influence of the primary X-rays, and 

 hence vibrating necessarily with the same frequency as the primary 

 X-rays. This could account for one of the components of the scat- 

 tered X-rays, but not the other. The other can be accounted for by 

 assuming that the primary X-ray quanta of frequency n are perfectly 

 elastic spheres which travel with the velocity of light, have mo- 

 mentum hn/c and energy hn, and collide with the atoms just as one 

 elastic sphere collides with another (that is, under conditions of 

 conservation of translatory kinetic energy and of momentum) ; they 

 depart from the collision with less energy and less momentum than 

 they initially had, and consequently with a diminished frequency. 

 But this does not explain the first-mentioned component, leaving the 

 two theories balanced. On the other hand, in the Philosophical 

 Magazine paper, Compton describes the total reflection of X-rays by 

 glass, silver and lacquer — a phenomenon of exactly the type which the 

 classical theory explains far more easily and naturally than the 

 quantum-theory. 



In glass and lacq-uer, the highest natural frequency of any of the 

 electrons in any of the constituent atoms — to speak the language of 

 the classical theory — is far below the frequency of available X-rays; 

 we are, in optical terminology, on the high-frequency or anomalous- 

 dispersion side of the highest-frequency absorption-band; the well- 

 known dispersion formula reduces to a single term, 



H — 1— Ne 2 /2irmn 2 



where N is the total number of electrons able to vibrate in unison 

 with the X-rays, and /x is the index of refraction of the X-rays of 



