Page:The principle of relativity (1920).djvu/118

 then the fundamental equations for electromagnetic processes in moving bodies are

{A} lor [function] = -s

{B} log] F* = 0

{C} ω[function] = εωF

{D} ωF* = μω[function]*

{E} s + (ω[=s]), w? looking below para.] = - σωF.

ω ω̄ = -1, and ωF, ω[function], ωF*, ω[function]*, s + (ωs|F1: or not blemish, looking {E} above?])ω which are space-time vectors of the first kind are all normal to ω, and for the system {B}, we have

lor (lor F*) = 0.

Bearing in mind this last relation, we see that we have as many independent equations at our disposal as are necessary for determining the motion of matter as well as the vector u as a function of x, y, z, t, when proper fundamental data are given.

§ 13.

Finally let us enquire about the laws which lead to the determination of the vector ω as a function of (x, y, z, t.) In these investigations, the expressions which are obtained by the multiplication of two alternating matrices

[function] = | 0 [function]_{12} [function]_{13} [function]_{14} |
 * [function]_{21} 0 [function]_{23} [function]_{24} |
 * [function]_{31} [function]_{32} 0 [function]_{34} |
 * [function]_{41} [function]_{42} [function]_{43} 0 |

F = | 0 F_{12} F_{13} F_{14} |
 * F_{21} 0 F_{23} F_{24} |
 * F_{31} F_{32} 0 F_{34} |
 * F_{41} F_{42} F_{43} 0 |