*as regards permutation with the indices* (1,2,3,4).

### § 3. The Theorem of Relativity of Lorentz.

It is well-known that by writing the equations I) to IV) in the symbol of vector calculus, we at once set in evidence an invariance (or rather a (covariance) of the system of equations A) as well as of B), when the co-ordinate system is rotated through a certain amount round the null-point. For example, if we take a rotation of the axes round the *z*-axis. through an amount , keeping fixed in space, and introduce new variables instead of , where

and introduce magnitudes

where

and , where

,
, , |

then out of the equations (A) would follow a corresponding system of dashed equations (A') composed of the newly introduced dashed magnitudes.

*So upon the ground of symmetry alone of the equations (A) and (B) concerning the* suffixes *(1, 2, 3, 4), the theorem of Relativity, which was found out by Lorentz, follows without any calculation at all.*

I will denote by a purely imaginary magnitude, and consider the substitution

(1) |

Putting

(2) |