and
, which are purely imaginary.
[8]That this specialization lies in the nature of the case will be evident later.
Special Lorentz Transformation. We obtain the simplest transformations of the type of (24) and (25) if only two of the co-ordinates are to be transformed, and if all the
, which determine the new origin, vanish. We obtain then for the indices 1 and 2, on account of the three independent conditions which the relations (25) furnish,
This is a simple rotation in space of the (space) co-ordinate system about
