Page:The principle of relativity (1920).djvu/53

 and

1/c [part]/[part]t [L, M, N] = - | [part]/[part]x [part]/[part]y [part]/[part]z |  (1) |      X              Y              Z        |,

where [X, Y, Z] are the components of the electric force, L, M, N?] are the components of the magnetic force.

If we apply the transformations in §3 to these equations, and if we refer the electromagnetic processes to the co-ordinate system moving with velocity v, we obtain,

1/c [part]/[part]τ [X, β(Y - (v/c)N), β(Z + (v/c)M)] =

| [part]/[part]ξ [part]/[part]η   [part]/[part]ζ   | |          L        β(M + (v/c)Z)    β(N - (v/c)Y)     |,

and

1/c [part]/[part]τ [L, β(M + (v/c)Z), β(N - (v/c)Y)]

= -| [part]/[part]ξ [part]/[part]η   [part]/[part]ζ   | |          X        β(Y - (v/c)N)    β(Z + (v/c)M)     |,  (2)

where β = 1/[sqrt](1 - v^2/c^2)

The principle of Relativity requires that the Maxwell-Hertzian equations for pure vacuum shall hold also for the system k, if they hold for the system K, i.e., for the vectors of the electric and magnetic forces acting upon electric and magnetic masses in the moving system k,