by the steel bar method as recommended by the National Physical Laboratory. In the experiments on steam, described in the last communication, the tube constant was found to have changed slightly. The change, which was the only one ever recorded throughout this work, may be ascribed to the fact that steam was the last of a series of six gases to be investigated in the same tube. The constant used was 0.0180 instead of 0.0186.

Tube C. The alundum furnace tube, using a frequency of 2992.

Tube D. The pythagorascompo tube, used with slight improvements to the oscillator and a change of frequency to 30185 per second.

The values of Ce, plotted in fig. 1, show the results obtained with tubes B, C, and D. Tubes B and C have, respectively, correction factors approximately ten times and three times greater than that demanded by Kirchhoff's formula, whilst that of tube D is less than the theoretical value. From the excellent agreement of the final values of C, for the three tubes, we thus confirm previous workers' conclusions that the Kirchhoff-Helmholtz formula cannot be applied generally.

The differences in the tube constants can be explained qualitatively by a consideration of the nature of the tubes. The two factors mentioned by Kirchhoff probably account. for the greater part of the differences. They are (a) the nature of the inner surface of the tube, (b) the heatexchange between the tube and the gas. Tube B was of silica with a glazed inner surface, whilst the surface of C was very rough. Tube D had a very uniform and smooth surface, but was not glazed as in the case of B. The thermal conductivities of the tubes B, C, D are respectively 0.00082, 0.00833, and 0.00169. The measurements are comparative and are taken from the Norton Company's handbook *. Thermal conductivity seems to play a relatively large part. Thus, the excellent surface of the silica tube B is more than counterbalanced by its very low thermal conductivity. Hence a large correction factor. With the alundum tube the thermal conductivity is very high, but the extremely rough and porous surface increased what would otherwise probably have been a very small factor. The pythagorascompo tube-a mixture of aluminium oxide and fireclay-had a conductivity probably greater than that given above, which is the value for fireclay. It had an excellent inner surface. Hence the very small correction factor. The metal tubes used by Norton Refractory Laboratory Ware,' 1926, p. 9.

Cornish and Eastman would have very high thermal conductivity and presumably a fairly smooth surface. The tube correction thus might easily have coincided with the theoretical value, but coincidence with theoretical values in a single piece of research work does not seem to us sufficient grounds for dismissing as entirely wrong the work of many previous investigators and for claiming overwhelming evidence in favour of the minority. Particularly does this apply when the limitations of the theory were pointed out by its originator.

Summary.

The molecular heats of air, nitrogen, and oxygen have been determined over a temperature 0° C. to 1000° C. by a method depending on the measurement of the velocity of sound in the chemically pure gases. Further measurements for air up to 1300° C. are added, and a reply is given to criticism of the method of determining the tube constant.

I

Chemistry Department,

East London College,
University of London.

XCI. The Effect of Refraction on Electron Diffraction.
By G. P. THOMSON, M.A.*

Na very valuable and important paper on the diffraction of electrons by thin metal films, E. Rupp† considers that his results can be best explained by attributing a refractive index to the metal for electron waves and calculates its value in certain cases. These values have recently been used by Rosenfeld and Witmer in a theoretical paper. While the hypothesis that a metal shows a refractive index for electrons is intrinsically probable, and seems by far the best way of accounting for some of Davison and Germer's experiments with reflected electrons, it appears that there is an oversight in Rupp's method of calculation which greatly modifies the conclusions which can be drawn from his experiments. The problem is as follows:-Electrons are assumed to be guided by waves whose wave-length in free space is λ=h/nw. They pass at normal incidence through a thin film of metal and are diffracted by the atoms of the crystals composing it, a pattern being formed analogous to • Communicated by the Author.

† E. Rupp, Ann. der Phys. lxxxv. p. 981 (1928).

Rosenfeld and Witmer, Zeit. f. Phys. xlix. p. 534 (1928).

μ

a Debye-Scherrer pattern for X-rays. How will the pattern be modified if the wave-length in the metal is not λ but λ=λ/p where u is a quantity analogous to an optical refractive index? When 1 the electrons are reflected whenever they are incident on a crystal plane at an angle O satisfying Bragg's law

nλ= 2d sin 0,

and a diffracted beam occurs with a deviation =20. $20. If μ 1 this becomes (fig. 1, a)

nλ/μ=2d sin 0',

and this is the relation (in my notation) which Rupp uses to find 'the new angle of reflexion. For the deviation he

takes 20', and it is here that the error lies. If the wavelength is modified in the metal, there must, by Huyghen's principle, be a bending of the rays on emergence. In the actual case where the incidence is normal there is no bending on entering the metal, but a becomes λ and the deviation in the metal is 20', which is the angle of incidence on the second surface. The angle of refraction d' is given by

Thus for e, e' small the effects compensate, and for larger angles the small effect is in the opposite direction to that given by Rupp's calculation.

It has been suggested that the diffraction actually observed in these and similar experiments occurs at the inner surfaces of holes in the metal film (fig. 1, b). While holes are undoubtedly present in the films I used, and may have occurred in Rupp's films also (see, for example, Smekal's paper in the 'Transactions of the Volta Centenary' on the imperfection of crystals), it does not seem likely that these really play an important part. If the rays were really reflected from planes parallel to the inner face of one of these holes, the effect of refraction would be expressed by a formula found by Darwin for the analogous case with X-rays, namely,

where is the new glancing-angle outside the metal, and μ-1 is small. Now in my experiments † with electrons of

1

the order of 40,000 volts, 1 was of the order, thus

(01-0)/0~502(μ—1).

But Bragg's law held in its simple form to better than 1 part in 50, thus

where E the kinetic energy of the electron and the potential of the metal, then gives <7 volt. This is very small compared with the 18 volts found by Davison and Germer and with any theoretically probable value. In addition there is very little difference between patterns taken with my original films which had obvious holes, and with films which I have been using recently made by spluttering, which appear quite continuous under the microscope.

In criticizing Herr Rupp's calculations of the effect of the refractive index I should like to emphasize that I am not trying to minimize the importance of the exceedingly beautiful work he has done in showing that comparatively slow electrons can show well-marked diffraction patterns through metal films. The supposed effect of refractive index is only a few per cent. in any case, and Herr Rupp himself says

C. G. Darwin, Phil. Mag. xxvii. p. 320 (1914).

+ 'Nature,' cxx. p. 802 (1927); Proc. Roy. Soc. A, cxvii. p. 600 (1928).

that it is on the limit of the accuracy of the experiments. The discrepancy left, when the calculation is made as indicated above, may perhaps be accounted for by a slight systematic error in the measurement of the electron velocities. Aberdeen,

Sept. 27, 1928

XCII. Notices respecting New Books.

"Glüh

Handbuch der Radiologie: Vierter Band, Dritter Teil. electroden," von O. W. RICHARDSON; "Technische Anwendung der Glühelectroden," von H. RUKOP; "Flammenleitung," vou ERICH MARX. Zweite Auflage. [Pp. xvi+724, mit 190 Figuren und Abbildungen im Text.] (Leipzig: Akademische Verlagsgesellschaft m.b.H., 1927. Price, brosch. M.48; geb. M.50.)

THE

HE third part of the second edition of Bd. iv. of the 'Handbuch der Radiologie' comprises three monographs. The first is a translation, by Prof. A. Karolus, of Richardson's well-known work on the emission of electricity by hot bodies. This has been brought up to date where necessary by a 32 page appendix, contributed by E. Rupp. The second monograph, by Prof. Rukop, written for the new edition of the Handbuch, is an account of the technical applications of thermionic emission. It is naturally concerned to a large extent with the theory and the various practical applications of the triode valve and of tubes with special characteristics--tubes with multiple grids, tubes used in conjunction with magnetic fields, &c. Extending to 138 pages, this monograph deals with the subject in a very comprehensive

manner.

The third monograph, by the Editor of the Handbuch, deals with the conduction of electricity in flames. Since the appearance of the first edition, the theory of temperature ionization, advanced by M. N. Saha to explain the phenomena of stellar spectra, has gained general acceptance. This theory was shown by H. A. Wilson and Noyes to be applicable to the problem of conduction in flames. A full account of the theory and of its applications to electrical conduction in flames has been included in the new edition; the theory has enabled some matters, which were controversial at the time of the first edition, to be settled and the relevant sections have therefore been omitted. The monograph provides a valuable summary of the present position of practice and theory with respect to the phenomena of electrical conduction in flames.

Although the process of subdivision has been carried further in the second edition than the first, there does not appear to be any particular advantage in publishing these three monographs in one volume. If each were obtainable separately the sales would undoubtedly benefit.