strained condition imposed by the nature of the gas. Hence the spectrum must be complex under these circumstances.

At a very low pressure, however, on account of the simpler conditions that prevail, the modes of motion must be fewer, and the corresponding spectrum also simpler in consequence.

2. Under these circumstances also an application of a magnetic field is more likely to result in an effect being produced than under ordinary conditions. Moreover, if a vortical spin is associated with the structure of an atom and each period of a spin corresponds to a line in the spectrum, a change in the spin, conceivably produced by an impressed magnetic field, and a corresponding change in period must lead to a displacement of the lines.

It will follow also that the gas ought to show a simplified spectrum, which may be the same for all gases.

Experiments, so far as they have gone, tend to confirm these conclusions.

3. When photographs of spectra of air are taken at different pressures, it is found (Pl. IV. fig. 1., spectra of air for pressures between 33 to 3 mm.) that there is no change up to a pressure of of millimetre in a tube of length 145 cm. with an induction-coil giving a spark-length of 29 mm. in atmospheric air.

1

4. At a pressure of about millimetre, however, the character of the spectrum seems suddenly to change, giving a partially simplified spectrum (Pl. IV. fig. II., spectra 2, 4), while a simple spectrum of four lines, consisting of four of the original lines, is obtained when the pressure is about 10% of a millimetre (Pl. IV. fig. V., spectrum 3). Figs. III. and IV. represent intermediate stages.

On introducing the magnetic field there seems to be a small shift, which, however, requires further examination (Pl. IV. fig. V., spectra 1, with the magnetic field on, 2, with the field reserved, 3, without the field).

5. If this shift is not fortuitous, it ought to prove of great theoretic interest. Larmor has shown that on his (or any other) dynamical theory of the electromagnetic field, an effect ought to be observable in a strong magnetic field, which, however, Lodge failed to detect.

It may be observed that if any such effect is to be observed it is more likely to be detected under the simpler conditions that obtain in high vacua than in those in Lodge's experiments.

6. It will be noticed that at a certain low pressure the magnetic field produces increased illumination (Pl. IV. figs. IV., v.). When a simplification of spectrum occurs at a

higher pressure than this, the effect of the magnetic field is to restore the original spectrum (Pl. IV. fig. II., spectra 1, 3).

The explanation of the increased illumination and restoration of the original spectrum seems to be that the magnetic field forces more ions through the gas-from one electrode to the other, which were previously proceeding direct to the sides of the vessel, and the consequent increase in ionization and in the number of collisions will naturally produce increased illumination as well as restore the conditions for a complex spectrum, as compared with those that obtained before the application of the magnetic field.

7. Experiments with hydrogen, so far as they have gone, seem to give similar results. It should be noted, however, that, as is well known, spectra of hydrogen generally present features which are difficult to analyse. The results for hydrogen, therefore, have to be tested by further experiments before we can be sure of their accuracy. We accordingly withhold the detailed results for hydrogen till these are duly tested.

8. Various investigators have studied the spectra of electric discharge through gases. These researches relate mostly, however, to discharge under high pressure. Thus, according to W. J. Humphreys, an increase of pressure causes all isolated lines to shift towards the red end of the spectrum, but the lines of bands are not apparently shifted. Also, different series of lines of a given element are displaced to different extents, but similar lines of an element, though not belonging to any recognized series, are displaced equally, the pressure-shifts of similar elements being periodic functions of the atomic weights. In a later paper he suggested that there might be a direct connexion between the pressureshift and the Zeeman effect; but R. Rossi, who employed pressures of 15, 30, 50, and even 100 atmospheres, failed to detect any relation between them.

9. Influence of pressure upon absorption spectra has been studied by A. Dufour and others, while in the case of arcspectra W. G. Duffield has shown that increase of pressure from 1 to 201 atmospheres broadens all silver lines, and J. Barnes has noticed an increase in the intensity of the spark lines of Al and Mg, and a diminution in the number of arc lines of Cu under reduced pressure. Reference should also be made in this connexion to the single-line spectra of metals Hg, Zn, Cd, studied by Frank and Hertz and McLennan and Henderson. They have shown that when heated vapour of these elements is traversed by electrons

possessing kinetic energy above a certain limiting value, they emit a single-line spectrum of determinate wave-length. 10. It is interesting to note that low-pressure effects on spectra have not engaged the attention of physicists to the same extent. Considerable attention has, however, been devoted in recent years to the investigation of the spectra of metals in vacuo.

11. Coming, finally, to the case of discharge in vacuumtubes, reference should be made to the work of R. W. Lawson, who found that variation of the current density and voltage in the discharge-tube did not produce any change in the relative intensity of the nitrogen bands, but considerable difference resulted from pressure changes. In the case of air, oxygen lines were not discernible, the spectrum being the same as that of nitrogen. It appears, accordingly, that no previous worker has (so far as we have been able to discover) noticed the simplification of the spectrum of air in a dischargetube with which the present paper deals.

Our thanks are due to the authorities of the Presidency College for offering us facilities for carrying on these researches in the Presidency College Laboratory, Calcutta.

XXIV. On Maxwell's Stresses. By MEGH NAD SHAHA, M.Sc., Research Scholar in Mathematical Physics, Sir T. N. Palit College of Science, Calcutta *.

1. M

AXWELL † has shown that the mechanical action between two electrical systems at rest can be accounted for by assuming the existence of certain stresses distributed over a surface completely enclosing one of the systems. If be the potential at any point due to the whole system, the X-component of the mechanical force on one of the systems can be shown to be

where the integration extends over the space occupied by the first system.

2. If the force is really due to the presence of stresses on a surface enclosing the first system, we have

where X, Xy, X, &c. . . . are the various surface-tractions,

...

* Communicated by Prof. D. N. Mallik.

+ Maxwell, Electricity and Magnetism,' vol. i. chap. v.

and (l, m, n) are the direction cosines of the normal to the

surface.

Maxwell concludes from this that a system of stresses

X= — (X' —Y'—Z'), Y,= _—_— (Y'—z—x'),

8п

1

1

·(Y2 X3),

8π

1

1

(Z2—X2—Y2), X‚=—-XY, Y.-—YZ,

Xy:

=

distributed over the surface S account for the mechanical action quite satisfactorily, and therefore provide a concrete physical representation of the mechanism of electrostatic

action.

*

3. But the expressions (4) are not complete solutions of the integral equation (3). Maxwell himself points out that they can at best be regarded as a first step towards the solution of equation (3). Many investigators, including Sir J. J. Thomson †, have pointed out that æther cannot possibly be at rest under these stresses. Lorentz ‡ goes so far as to say that the stresses are simply mathematical fictions, which can be conveniently utilized for the calculation of radiation pressure and other allied phenomena. The object *Loc. cit. p. 165 et seq.. † Loc. cit. p. 165, footnote.

Theory of Electrons,' p. 31.

Phil. Mag. S. 6. Vol. 33. No. 195. March 1917.

S

of the present paper is to show that the stresses cannot account for the energy of electrification, if the medium is to be regarded as an elastic solid.

4. The energy of a charged system can be expressed as a volume integral,

Maxwell states that the quantity W may be interpreted as the energy in the medium due to the distribution of stresses; but the statement is not proved. The only rational meaning which we can attach to this assertion is that the energy of electrification arises from the elastic displacement of æther particles. I am not aware whether any other interpretation has been or can be given to Maxwell's statement, but it has generally been taken in this sense, though Maxwell himself is rather vague on the point. We should naturally expect that energy calculated on this understanding would lead to the expression (5), but that this is not the case will be presently shown.

5. If u, v, w be the elastic displacements of a particle of the dielectric medium, the energy of deformation or the train-energy function is

(Xxxx+Yy¤yy+Zzzz + Xy€xy+Yz€yz+Zxzx)dx dy dz.

Assuming the æther to be isotropic and to behave as an elastic