## Extract

*Introduction and Summary*.—In Maxwell’s equations of the electromagnetic field, ∂e/∂t ═ curl h (*a*) ∂h/∂t ═ — curl e (*b*) div e ═ 0, div h ═ 0 (*c,d*)} the properties of the field, in regions containing no charges, are described in terms of two vectors, e and h, which in the general case may have arbitrary magnitudes and directions at any given point of space and time. Although e and h are the quantities most closely related to experiment, they are not the only ones in terms of which the field can be described. The description can in fact be given in terms of any definite functions of e and h by making the appropriate substitutions in (1). The equations obtained by such a transformation cannot of course describe properties of the field which are not ultimately implied in Maxwell’s equations; they may nevertheless lend themselves more readily to determining what these properties are. It is shown in this paper that this is the case with a certain transformation in which, instead of in terms of e and h, vectors making an arbitrary angle with each other, the equations are expressed in terms of two vectors, R and u, at right angles to each other, and of a scalar function of position, α. The equations obtained reveal that the most general electromagnetic field in regions not containing charges can be represented by a vector R of invariant magnitude, the lines of which at each point are in motion at right angles to themselves with a definite velocity *u* relatively to the observer. They show further that small moving elements of the field can be constructed which can be regarded as keeping their identities permanently as they move. The movement of these elements takes place under the action of a simple form of stress in accordance with the fundamental laws of dynamics. In addition to their translatory motions and independent of them, the elements exhibit in the general case co-ordinated rotational movements. By their translatory and rotary movements, and the changes of shape which result from them, they fix definitely the local time rates of change of the field. In fact every property of the field can be specified directly in terms of these moving and rotating elements. A field element is a space section constructed in a natural way from, the four dimensional entity which constitutes the field in space-time. Considered in space-time as a four dimensional element, it appears as an element of *action*, and it is a result of the analysis that the general electromagnetic field can always be divided in a natural way into such elementary units of action. The properties which characterise them are of a kind which suggests and is consistent with the possibility that both field elements and the corresponding elements of action may have a finite magnitude in the field.

## Footnotes

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- Received August 10, 1926.

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