owing to the shortening of the waves, the velocity in this vibration is changed, and therefore the volume-density of vibratory energy in the æther is modified as above. And the Lorentz transformation has shown us what is not so immediately obvious, that also on the electric view which considers the sources to be constituted of vibrating electrons, though their relative motions are not affected by the uniform translation as again Carnot's principle demands, yet the vibratory energy emitted from them is modified in the manner here described.

Cambridge, September 21, 1903.

[Note added Dec. 26.-As the intensity of the pressure of radiation depends on the instantaneous state of the adjacent medium, it may be expected to remain equal to the energy per unit volume, as above assumed, whether the body that it acts on is at rest or in motion.

We may verify in detail for a plane-polarized wave-train with electric force (0, Q, 0), current (0, v, 0), and magnetic force (0, 0, y), incident directly on an absorbing face perpendicular to . Then *the mechanical force in the absorber per unit volume is

v being the velocity of the material medium, with which the axes of coordinates travel. Thus

X'2

Let the slice between a and a be an indefinitely thin one containing the absorbing interface; as Q is continuous across it, dQ/dt is very small outside it; thus, y being finite, the last term is negligible, and the mechanical force acting on the slice is equal to the value of y2/8π just outside it, where Q is null; thus it is equal to the energy-density just outside, whether the absorber is in motion or not.

From the way of considering the origin of this mechanical *' Æther and Matter,' 1900, § 65.

force above, as acting on the interfacial current-sheet, it is not difficult to verify that when the incidence is oblique, the incident, reflected, and refracted wave-trains exert independently on the reflecting surface their full oblique thrusts in their own directions of propagation, as is implied in Prof. Poynting's calculations referred to at the beginning.

The result here verified, that motion of a material body does not affect the pressure exerted on it by the ambient radiation, has been rejected by Prof. Poynting in a later postscript added to the memoir above referred to, on the ground that radiation shot out of a radiator A into a moving absorber B would, according to it, alter the store of momentum of the two bodies. But if the bodies are in thermal equilibrium, other compensating events are at the same time occurring, viz. the absorber B is also radiating towards A. And indeed if the temperatures of A and B are unequal, the aggregate momentum of both admittedly does change on account of their radiation.

If the present argument is right, the view which considers a ray to be a simple carrier of momentum from the one body to the other cannot therefore be maintained. It may be noticed, in connexion with that 584 supra, P. 584 for the same amplitude of ionic excursions in the vibrating molecule, as determined by its maximum electric moment, and for the same periodic time, it follows from Hertz's formulæ for a simple radiator, and may be generalized by the theory of dimensions, that the radiation emitted per unit time is proportional to the refractive index of the surrounding medium, and therefore the equilibrium-density of the radiation in that medium is proportional to the square of the same index, in accordance with Balfour Stewart's law derived from the doctrine of equilibrium of exchanges between sources at uniform temperature.]

LXIV. Note on the Measurement of Small Inductances and Capacities, and on a Standard of Small Inductance. By J. A. FLEMING, D.Sc., F.R.S., Professor of Electrical Engineering in University College, London*.

LA

on the

AST year a paper was read before the Physical Society by the present writer and Mr. W. C. Clinton, "Measurement of Small Capacities and Inductances" †. In that paper we described two forms of motor-driven commutator for the measurement of small capacities and *Communicated by the Physical Society: read March 25, 1904. + See Proc. Phys. Soc. Lond. vol. xviii. p. 386; also Phil. Mag. May 1903, p. 493.

inductances. Since that date, these appliances have been extensively used for this purpose in the Pender Electrical Laboratory at the University College.

In the measurement of small inductances lying in value between 100,000 and 10,000 centimetres, it is essential to use in connexion with the modification of the Anderson method *, described in our paper, a very sensitive galvanometer; and when small inductances of this order are being measured we have since found that the stray field from the motor employed to drive the commutator produces, by a dynamo action, a small electromotive force in the commutator which makes itself evident in the galvanometer circuit, and so gives rise to an irregularity, vitiating the results. The remedy for this, of course, is to employ an enclosed iron-clad motor, or else to place the commutator at a greater distance from the motor, connecting the two by a long shaft. This has already been done and has been found to be effective.

Meanwhile, in the course of the experiments to overcome these difficulties, the attempt was made to use a telephone in place of the galvanometer and a simple interrupted current in the battery-circuit. In the bridge arrangement described by Prof. Anderson (loc. cit.) we substituted an ordinary buzzer in the battery-circuit to interrupt the current at the rate of about 100 per second, and in the bridge-circuit an ordinary Bell telephone for the galvanometer, the commutator being abolished. Under these circumstances, it was found that an observer with sharp hearing could obtain a very good balance when a coil having small inductance was placed in one arm of the bridge, and a condenser of suitable capacity placed as described by Prof. Anderson (see fig. 1).

Mr. J. C. Shields, who has been engaged in experiments on this matter in the Pender Laboratory, found that with this arrangement he could make very quick and fairly accurate determinations of small inductances, the accuracy of the reading being determined by the limits within which a value could be assigned to r in the equation given by Prof. Anderson, viz. :

L=C{r(R+S) +RQ},

the value of being that of a resistance inserted in the bridgecircuit, which is varied until no sound is heard in the telephone.

In the above equation L is the inductance and R the resistance of the coil being measured, C the capacity of the condenser, and S and Q the resistances of the adjacent

* See Phil. Mag. vol. xxxi. p. 329 (1891).

and opposite bridge-arms, and the resistance inserted in series with the telephone in the bridge-circuit.

When was adjusted to produce silence in the telephone, it was found that variations to the extent of about 1 per cent. either way, and sometimes much less, caused the sound to reappear in the telephone, and hence gave the limits within which the inductance L could be determined.

In the experiments here described, the capacity generally employed consisted of two leyden-jars, the joint capacity of which had been determined carefully with the FlemingClinton commutator, and found to have the value 0·00272 microfarad. The tests of this telephone method were made by Mr. J. C. Shields on a number of coils of silk-covered copper wire, each of which consisted of one layer of the wire wound uniformly and in closely adjacent turns upon a wooden or glass circular-sectioned rod. One coil, much employed, consisted of a wooden rod about two metres in length wound over as above described with one layer of no. 32 s.w.G. wire in closely adjacent turns. The mean diameter of one circular turn of this wire was 4096 centimetres, and the length of the solenoid or spiral wire was 200-3 centimetres, and the number of turns of wire 5000 in all, and hence

the number of turns per centimetre of length of the spiral was 24.96.

This long coil belonged to a resonance apparatus designed by Seibt, and is hence alluded to as the long Seibt coil. The resistance of the wire on this coil was about 152 ohms, and it was connected to a Wheatstone's bridge (as shown in fig. 1), the other arms of which are denoted by P, Q, and S.

The arrangement of apparatus used, consisted therefore of an ordinary Post-Office plug Wheatstone's bridge having the spiral of which the inductance was to be determined. connected to it. The battery-circuit contained the buzzer, and the bridge-circuit a telephone in series with a plug resistance-box, affording values for r. The condenser consisted of one or more leyden-jars or a mica condenser. The steady balance was obtained first in the usual way with a galvanometer and steady current.

The following Table gives the values of the bridge-arms, the bridge resistance r, the capacity used, and the inductance L calculated from the formula given by Anderson.

The Table contains two sets of measurements, one set marked A, made by Mr. Shields with the Fleming-Clinton commutator, and the other marked B, made with the telephone and buzzer as above described.

TABLE I.-Results of Inductance Measurements of a
Long Coil, having a Dimension ratio of 50: 1.

Mean of A readings=19.7 × 106 cms.

Mean of B readings=19.9 × 106 cms.

Value calculated from the formula L=(Dt) (πDN)=20·6×10 cms.

By numerous observations on coils of this kind, sometimes 50 diameters long or even less, the wire being wound in a single layer and in closely adjacent turns, the writer has