August i8, 1923] 



NATURE 



239 



r 



Light-Quanta and Interference. 



In a very important and stimulating paper on the 

 scattering of X-rays by light elements {Phys. Review, 

 May 1923), Prof. A. H. Compton suggests that a study 

 of the problem of scattering by atoms with tightly 

 bound electrons and by groups of atoms may shed 

 some light upon the difficult question of the relation 

 between interference and the quantum theory. 



In an investigation of this kind it may be useful to 

 keep in mind an important difference between an 

 electron and a light-quantum, which depends on the 

 fact that generally most of the electron's energy is 

 unavailable, while the whole energy hv of a light- 

 quantum seems to be available. This indicates, of 

 course, that a light-quantum is a simpler form of 

 matter than an electron or proton. 



Roughly speaking, a light-quantum possesses a 

 large amount of available energy and a small momen- 

 tum, while a moving electron generally possesses a 

 small amount of available energy and a comparatively 

 large momentum. As a rule, then, we cannot expect 

 a free or lightly bound electron to absorb the whole 

 energy of a light-quantum. It is indeed possible, 

 according to the theory of Compton and Debye, for 

 an electron which encounters a light-quantum hv to 

 move away with a kinetic energy equal to hv if the 

 electron has an initial kinetic energy nearly equal to 

 hv, but this case is not of much physical interest. 

 When, however, an electron is tightly bound to an 

 atom, so that some of the energy of an impinging 

 quantum may be transformed into potential energy, 

 there is a possibility that the whole energy of the 

 quantum may be absorbed in a single impact. 



If we admit that the energy of a quantum can be 

 absorbed bit by bit, it does not follow that the type 

 of absorption considered by Compton is the only one 

 which can occur. Let us suppose that a quantum hv 

 after encountering an atom is transformed into a 

 quantum h{v - dv) travelling in the same direction as the 

 original quantum. Assuming that the atom (of mass 

 m) acquires the energy hdv and momentum hdvjc lost 

 by the quantum, the centre of mass of the atom may 

 be supposed to move forward with velocity hdvjmc 

 and a kinetic energy h^{dvYJ2mc^, which is generally 

 negligibly small in comparison with hdv. The 

 acquired energy hdv may therefore be energy of 

 small oscillations about a state of steady motion. To 

 ascertain the nature of these oscillations we repre- 

 sent the incident quantum by a field of type 



E^ = H„ = o, 



where 



/(/)= C""" COS {pt + a.)dp. 

 Jo 



'). 



(See Nature, April 28, p. 567.) 



The emergent quantum may be represented by a 

 field of the same type with v -dv instead of v, while the 

 field which is really effective in producing the oscilla- 

 tions is the difference of these two, and is of the same 

 type with 



f{^)= T'" COS{pt + a)dp. 



Jzniv — di/) 



When dv is very small, this represents approxi- 

 mately a homogeneous train of waves of frequency v. 

 The small oscillations set up in the atom are thus 

 specified approximately by a trigonometrical function 

 of type 2-irdv cos {2irvt + a) and are practically un- 

 damped and of frequency p. The phenomenon of 

 interference may, then, be quite compatible with 

 quantum theory, for it may depend really on an inter- 



NO. 2807, VOL. I 12] 



ference of small oscillations produced in the atoms 

 by the quanta. If a number of quanta in phase 

 strike the same atom, the small oscillation may be- 

 come large and eventually result in a quantum jump, 

 but the growth of an oscillation may depend, of 

 course, on the phenomenon of resonance. 



Since we have endowed a quantum with a field, a 

 single quantum may produce small oscillations in a 

 large number of atoms in accordance with Compton's 

 idea, and so a second difficulty in the theory of inter- 

 ference may not be so great as it seems at first sight. 



H. Bateman. 



Institute of Technology, 

 Pasadena, California. 



A Mountain Mirage. 



As part of a magnificent view from Ben More of 

 Mull on July 13, my sister and I saw a striking mirage 

 on the Coolins of Skye. To begin with, Skye and 

 all the Highlands to the eastward of it were. covered 

 by a level sheet of white cloud, with the highest 

 peaks just showing clear and sharp above it. Then, 

 starting from the sea, this cloud gradually melted 

 away, and revealed a magnificent prospect extending 

 far past the Coolins into the mountains of Ross. 

 But as the cloud first melted it left the Coolins 

 strangely transformed, each of their jagged crests 

 drawn up into a fantastic spire. In the course of a 

 very few minutes this effect died away and the 

 Coolins took on their natural outline. 



This was about 6.30 p.m., summer time. Pre- 

 sumably the mirage had some connexion with the 

 cloud sheet ; at one stage of its absorption the sheet 

 must have been represented by a refracting layer, 

 which would be very nearly at our eye-level. The 

 air was remarkably clear, not only to the north but 

 also to seaward. For some time a long line of the 

 Outer Hebrides, from about South Uist to Barra 

 Head, was visible, pale but perfectly clear-cut. 



E. Leonard Gill. 



Royal Scottish Museum, Edinburgh, 

 July 18. 



Probable Aeolian Origin of Grey wether Sandstone. 



On reading Mr. C. Carus-Wilson's note (Nature, 

 March 3, p. 292) referring to the long tubular 

 holes seen in sarsen stones, which he says suggest 

 ' ' the work of marine annelids, anterior to the con- 

 solidation of the rock," it struck me that some 

 important light may be thrown on this subject by 

 observations made on this side of the globe. First 

 of all one might suggest that if these were annelid 

 burrows they would have an average diameter, and 

 there seems to be no evidence that the greywether 

 sandstone, with its once softer siliceous matrix, was 

 of marine origin. In Australia we have a great 

 extent of country along the coast and inland, covered 

 with dune formation, and these deposits enclose 

 enormous quantities of vegetation. Plants that are 

 growing on or near these dune areas, sometimes 

 under swampy conditions, are covered over with 

 sand, which is being blown about the stems of such 

 grasses, reeds, and shrubs so as to completely enclose 

 them. When the dune rock, some of which dates 

 back to the early Pleistocene, has consolidated, a 

 fracture reveals tubular holes which might suggest 

 worms, but from their positions, at all angles, as 

 well as vertical, and from their varied diameter and 

 outline, are easily traced back to plant origin. 



From many years' observations upon our Australian 

 dunes, I cannot help thinking that here we have a 

 similar process going on, which obtained during the 

 arid interludes of the Eocene in the south of England. 



