Let a rectangular system (_x_, _y_, _z_, _t_,) of reference be given in space and time. The unit of time shall be chosen in such a manner with reference to the unit of length that the velocity of light in space becomes unity.
Although I would prefer not to change the notations used by Lorentz, it appears important to me to use a different selection of symbols, for thereby certain homogeneity will appear from the very beginning. I shall denote the vector electric force by E, the magnetic induction by M, the electric induction by _e_ and the magnetic force by _m_, so that (E, M, _e_, _m_) are used instead of Lorentz’s (E, B, D, H) respectively.
I shall further make use of complex magnitudes in a way which is not yet current in physical investigations, _i.e._, instead of operating with (_t_), I shall operate with (_i t_), where _i_ denotes √(-1). If now instead of (_x_, _y_, _z_, _i t_), I use the method of writing with indices, certain essential circumstances will come into evidence; on this will be based a general use of the suffixes (1, 2, 3, 4). The advantage of this method will be, as I expressly emphasize here, that we shall have to handle symbols which have apparently a purely real appearance; we can however at any moment pass to real equations if it is understood that of the symbols with indices, such ones as have the suffix 4 only once, denote imaginary quantities, while those which have not at all the suffix 4, or have it twice denote real quantities.
An individual system of values of (_x_, _y_, _z_, _t_) _i. e._, of (_x₁_ _x₂_ _x₃_ _x₄_) shall be called a space-time point.
Further let _u_ denote the velocity vector of matter, ε the dielectric constant, μ the magnetic permeability, σ the conductivity of matter, while ρ denotes the density of electricity in space, and _x_ the vector of “Electric Current” which we shall some across in §7 and §8.
