Page:BatemanElectrodynamical.djvu/14

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286
[March 11,
Mr. H. Bateman

Secondly, we must exclude transformations in which the axes are changed from a right-handed system to a left-handed system, for then equation (1) would imply a change from positive electricity to negative electricity. Such a transformation, however, becomes relevant when equation (1) is replaced by

(1)'

equation (2) by

(2)'

and equation (3) by

(3)'

These relations also imply that the transformation is a spherical wave transformation, and so a transformation which changes a right-handed system of axes into a left-handed system is relevant, but the formulae of transformation of the components of the electric and magnetic force are not the same as before. The sign of θ will be determined later by the condition that a right-handed set of axes is transformed into a lefthanded set. If

corresponding sets of axes are both right-handed or both left-handed. If, on the other hand,

the axes are right-handed in one system and left-handed in the other.

It is easy to establish a relation between the two quantities

and

Since