It will be seen that the values of σ in this case are somewhat smaller than those obtained for the two former alloys.

Also from fig. 4, which represents the relation between σ and 6, it appears that the Thomson effect vanishes at about · 190° C.

IX. Experiments with Alloy No. 4.

This alloy contains 23.6 per cent. tin.

Mean diameter of rods =5.50 mm.

Mean resistance of rods =0·0000425 ohm per mm. Some observations taken are shown in Tables IX. and X.

TABLE IX.-Thomson Effect.

It will be seen that the values of σ in this case are less than half those obtained for the previous alloy.

Also from the values of σ and plotted in fig. 5, it appears that, for the range of temperatures employed, the Thomson effect in this alloy is proportional to the absolute temperature.

X. Summary of Results.

We are now in a position to infer the manner of the variation of the magnitude of the specific heat of electricity with composition in the case of these alloys.

From fig. 6, which represents the relation between σ and percentage of tin, we see the striking effect of the addition of a very small amount of tin to bismuth, the Thomson effect in an alloy containing 1 per cent. tin being more than 12 times as large as in pure bismuth.

With the addition of more tin, the value of the Thomson effect continues to increase until the alloy contains about 3 per cent. tin, when the effect is about 15 times as large as for bismuth. When the percentage of tin is increased

beyond this amount, the value of the specific heat of electricity begins to decrease this diminution goes on as the amount of tin becomes greater, until finally the Thomson effect in the case of pure tin has fallen to a value which is only about 300 part of that which holds in the case of bismuth.

It may, indeed, happen that traces of substances other than tin in bismuth produce a considerable change in the value of the Thomson effect, and any discrepancies between the values obtained for different specimens of bismuth may well be attributed to the presence of such impurities (see p. 570).

[These experiments also indicate that in the case of alloys at any rate the specific heat of electricity is not necessarily proportional to the absolute temperature. A similar result has been previously pointed out by Haga, whose experiments Phil. Mag. S. 6. Vol. 7. No. 41. May 1904.

2 R

showed that in the case of platinum the Thomson effect vanishes at 70° C. *]

In conclusion I desire to express my best thanks to Prof. J. J. Thomson for his advice and suggestions throughout the course of the work, and to my brother, Mr. H. E. Laws, to whom I am indebted for the analyses of the specimens used.

Cavendish Laboratory,
March 25th, 1904.

LXIII. On the Intensity of the Natural Radiation from Moving Bodies and its Mechanical Reaction. By Prof. J. LARMOR, Sec.R.S.†

HE subject of the pressure of radiation, which was first reduced into a definite formula by Maxwell, was placed in new and most fruitful light when Boltzmann showed, by following out an idea of Bartoli, that it stood in intimate relation to the law connecting the radiation of a body with its temperature. In a recent memoir Poynting has based very remarkable results, as regards cosmical dynamics, on the operation of a retarding force due to the back pressure of its own radiation when the radiating body is in motion. The main object of the present note is to treat this aspect of radiation-pressure by more direct methods, and thereby confirm the expression for the mechanical reaction against a moving radiating surface, that has been deduced by Poynting from general considerations, naturally somewhat uncertain, relating to flux of energy.

The pressure exerted by radiation is essentially connected with opacity to it. From formulæ developed on other occasions § it appears that, in the case of a medium which may vary in its properties in any manner along the direction of propagation, when it is the seat of electric disturbances of simple harmonic period 2π/n, polarized so that the electric force is (0, Q, 0) and the magnetic (0, 0, y), the dynamical equations being thus in Maxwell's notation

Haga, loc. cit. iii. p. 48.

† Reprinted from the Boltzmann-Festschrift. Communicated by the Author.

Roy. Soc. Proc. 1903; Phil. Trans. ibid.

Phil. Trans. 1897 A; or more fully in Ether and Matter,' Camb. Univ. Press, 1900, pp. 130–133.

the mechanical force acting on any block or segment of it is representable by pressures of intensity

where 70 and Qo represent the amplitudes of y and Q. When the amplitudes are diminished owing to gradual absorption as the disturbance travels onward, there is thus steady mechanical force exerted in the medium in the direction of propagation. When the electric disturbance is incident on a transparent reflector there is no resultant force on the reflecting surface itself, because y and Q both remain. continuous in crossing it. When, however, the reflector is nearly perfectly opaque, the electric forces in front of it in the incident and reflected disturbances almost cancel each other, while the magnetic force just outside is doubled by its presence there must thus be disturbance of the nature of alternating electric flux in the skin-layer of the reflector such as will annul this magnetic field in its interior, and it is the electrodynamic forces acting on this layer of current that constitute the aggregate electric pressure, which can be shown to agree with Maxwell's formula.

From this way of considering the mechanical force, it is readily verified that when the incidence on the reflector is oblique, Poynting is right in taking the incident and reflected wave-trains each to exert their full oblique thrust on the reflector along their directions of propagation.

For radiation to exert steady non-alternating pressure on a small body, it must be of opaque material. A dielectric mass constituted of perfectly elastic elementary vibrators should not be repelled by radiation. In illustration, consider the simplest type of vibrator, an electric doublet consisting of charges + and -e separated by a varying distance l, parallel to a, so that its moment M is el. When it is subjected to a simple wave-train travelling along a with

Loc. cit. p. 133.

† Loc. cit.