Page images
PDF
EPUB

March 1868, p. 184. See also remarks on that experiment, by the present writer, in the number for May 1868.

VI. Electrostatic Measurement of Resistance. (See Art. 355.) 780.] Let a condenser of capacity C be discharged through a conductor of resistance R, then, if x is the charge at any instant,

[merged small][merged small][merged small][merged small][ocr errors][merged small][merged small]

If, by any method, we can make contact for a short time, which is accurately known, so as to allow the current to flow through the conductor for the time t, then, if E, and E, are the readings of an electrometer put in connexion with the condenser before and after the operation, RC (log, E-log, E1) = t.

(3)

If C is known in electrostatic measure as a linear quantity, R may be found from this equation in electrostatic measure as the reciprocal of a velocity.

If R, is the numerical value of the resistance as thus determined, and Rm the numerical value of the resistance in electromagnetic

[merged small][merged small][ocr errors][merged small][ocr errors][merged small]

Since it is necessary for this experiment that R should be very great, and since R must be small in the electromagnetic experiments of Arts. 763, &c., the experiments must be made on separate conductors, and the resistance of these conductors compared by the ordinary methods.

CHAPTER XX.

ELECTROMAGNETIC THEORY OF LIGHT.

781.] IN several parts of this treatise an attempt has been made to explain electromagnetic phenomena by means of mechanical action transmitted from one body to another by means of a medium occupying the space between them. The undulatory theory of light also assumes the existence of a medium. We have now to shew that the properties of the electromagnetic medium are identical with those of the luminiferous medium.

To fill all space with a new medium whenever any new phenomenon is to be explained is by no means philosophical, but if the study of two different branches of science has independently suggested the idea of a medium, and if the properties which must be attributed to the medium in order to account for electromagnetic phenomena are of the same kind as those which we attribute to the luminiferous medium in order to account for the phenomena of light, the evidence for the physical existence of the medium will be considerably strengthened.

But the properties of bodies are capable of quantitative measurement. We therefore obtain the numerical value of some property of the medium, such as the velocity with which a disturbance is propagated through it, which can be calculated from electromagnetic experiments, and also observed directly in the case of light. If it should be found that the velocity of propagation of electromagnetic disturbances is the same as the velocity of light, and this not only in air, but in other transparent media, we shall have strong reasons for believing that light is an electromagnetic phenomenon, and the combination of the optical with the electrical evidence will produce a conviction of the reality of the medium similar to that which we obtain, in the case of other kinds of matter, from the combined evidence of the senses.

782.] When light is emitted, a certain amount of energy is expended by the luminous body, and if the light is absorbed by another body, this body becomes heated, shewing that it has received energy from without. During the interval of time after the light left the first body and before it reached the second, it must have existed as energy in the intervening space.

According to the theory of emission, the transmission of energy is effected by the actual transference of light-corpuscules from the luminous to the illuminated body, carrying with them their kinetic energy, together with any other kind of energy of which they may be the receptacles.

According to the theory of undulation, there is a material medium which fills the space between the two bodies, and it is by the action of contiguous parts of this medium that the energy is passed on, from one portion to the next, till it reaches the illuminated body.

The luminiferous medium is therefore, during the passage of light through it, a receptacle of energy. In the undulatory theory, as developed by Huygens, Fresnel, Young, Green, &c., this energy is supposed to be partly potential and partly kinetic. The potential energy is supposed to be due to the distortion of the elementary portions of the medium. We must therefore regard the medium as elastic. The kinetic energy is supposed to be due to the vibratory motion of the medium. We must therefore regard the medium as having a finite density.

In the theory of electricity and magnetism adopted in this treatise, two forms of energy are recognised, the electrostatic and the electrokinetic (see Arts. 630 and 636), and these are supposed to have their seat, not merely in the electrified or magnetized bodies, but in every part of the surrounding space, where electric or magnetic force is observed to act. Hence our theory agrees with the undulatory theory in assuming the existence of a medium which is capable of becoming a receptacle of two forms of energy *. 783.] Let us next determine the conditions of the propagation of an electromagnetic disturbance through a uniform medium, which we shall suppose to be at rest, that is, to have no motion except that which may be involved in electromagnetic disturbances.

* For my own part, considering the relation of a vacuum to the magnetic force, and the general character of magnetic phenomena external to the magnet, I am more inclined to the notion that in the transmission of the force there is such an action, external to the magnet, than that the effects are merely attraction and repulsion at a distance. Such an action may be a function of the æther; for it is not at all unlikely that, if there be an æther, it should have other uses than simply the conveyance of radiations.'-Faraday's Experimental Researches, 3075.

783.] PROPAGATION OF ELECTROMAGNETIC DISTURBANCES. 385

Let C be the specific conductivity of the medium, K its specific capacity for electrostatic induction, and μ its magnetic 'permeability.'

To obtain the general equations of electromagnetic disturbance, we shall express the true current C in terms of the vector potential A and the electric potential .

and

The true current C is made up of the conduction current the variation of the electric displacement D, and since both of these depend on the electromotive force &, we find, as in Art. 611,

C = (C + K

d

dt) &.

(1)

But since there is no motion of the medium, we may express the electromotive force, as in Art. 599,

[ocr errors]
[merged small][merged small][ocr errors][ocr errors][merged small][merged small][merged small][merged small][merged small][merged small][ocr errors][merged small][merged small]

But we may determine a relation between C and 2 in a different way, as is shewn in Art. 616, the equations (4) of which may be

written

where

4 πμC = ▼2 A+ VJ,

dF dG dH

J = +

+

dx dy dz

[ocr errors][merged small][merged small]
[merged small][merged small][ocr errors][merged small][merged small][merged small][merged small]

which we may express in the form of three equations as follows

[merged small][merged small][ocr errors][subsumed][merged small][ocr errors][merged small][merged small][merged small][merged small][merged small][merged small][ocr errors][merged small][merged small][merged small][ocr errors][merged small][merged small][ocr errors][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][ocr errors][merged small][merged small][merged small][ocr errors][ocr errors][merged small][ocr errors]

These are the general equations of electromagnetic disturbances. If we differentiate these equations with respect to x, y, and z respectively, and add, we obtain

dJ

μ ( 1 π C + K d ) ( d − ▼2 4 ) = 0.

dt dt

(8)

If the medium is a non-conductor, C= 0, and V2, which is proportional to the volume-density of free electricity, is independent of t. Hence J must be a linear function of t, or a constant, or zero, and we may therefore leave J and out of account in considering periodic disturbances.

VOL. II.

Propagation of Undulations in a Non-conducting Medium.

[merged small][merged small][merged small][merged small][merged small][merged small][ocr errors][merged small][merged small][merged small][merged small][merged small][merged small]

The equations in this form are similar to those of the motion of an elastic solid, and when the initial conditions are given, the solution can be expressed in a form given by Poisson*, and applied by Stokes to the Theory of Diffraction †.

[merged small][merged small][merged small][merged small][ocr errors][merged small][merged small][merged small][merged small][merged small]

point of space at the epoch (t0), then we can determine their values at any subsequent time, t, as follows.

Let O be the point for which we wish to determine the value of F at the time t. With O as centre, and with radius Vt, describe a sphere. Find the initial value of F at every point of the spherical surface, and take the mean, F, of all these values. Find also the dF

initial values of

at every point of the spherical surface, and let dt the mean of these values be

dF

[ocr errors]

dt

Then the value of F at the point O, at the time t, is

[blocks in formation]

785.] It appears, therefore, that the condition of things at the point at any instant depends on the condition of things at a distance Vt and at an interval of time t previously, so that any disturbance is propagated through the medium with the velocity V. Let us suppose that when t is zero the quantities A and Д are

* Mém. de l'Acad., tom. iii, p. 130.

+ Cambridge Transactions, vol. ix, p. 10 (1850).

« PreviousContinue »