between the wave-lengths of the spectral lines, make it seem probable that if matter is to be considered as an electrical system, it must be much more complex than a system composed entirely of electrons separated by distances great in comparison to their size. It becomes therefore of interest to see whether any relations can be found between the mass of an electric system in general, and any of its other properties. It will be found that a general relation does exist, which is not only of considerable interest in itself, but also suggests other relations.
3. The straightforward calculation of the mass of an electric system possessing any distribution of charge and any internal velocities below that of light presents considerable difficulty; for such calculation involves the use of the scalar and vector potential, and these are not effective instantaneously at all parts of the system. Any expression for the mass of the system calculated in this way will therefore involve terms which vary in an extremely complicated way with the internal velocities when these are not very small. The same is true with respect to the velocity of the system as a whole. In the following discussion the problem is attacked in an entirely different way, which is not open to this objection.
As the constraints of the system are intimately involved, it will be well first to consider them.
4. The position of internal constraints in general electrical theory is a very fundamental one. By "constraints" are meant rigid connexions of any kind. These act merely as reactions to the electrical forces, and do not contribute to the virtual work. If the electrical laws are to hold universally, i. e., for minute distances as well as for greater ones, it is obvious that no electrical system can exist as such unless there are such constraints to balance the electrical forces. Even a single electron would dissipate itself through the mutual repulsion of its elements, were it not for some form of internal constraint. Besides holding the system together, as it were, these constraints also act in another important way. They may become, in common with all geometrical constraints, paths of energy flow. We are accustomed to think of the Poynting vector as representing completely the energy flow in a purely electrical system, but of course this is not in general true.
Take as a simple example the case of a large plane aircondenser moving in a direction perpendicular to the plane of its plates. If the condenser is charged there is obviously a transference of energy at a rate equal to the internal energy multiplied by the velocity of movement. The Poynting
