Page:CunninghamPrinciple.djvu/10

The two last equations reducing to those above for y=0 and z=0.

But our hypothesis requires that the equation

$\xi ^{2}+\eta ^{2}+\zeta ^{2}=c^{2}\tau ^{2}\,$

shall be a result of the equation

$x^{2}+y^{2}+z^{2}=c^{2}t^{2}.\,$

This is so if, and only if, c₁, c₂, d₁, d₂ are all zero.

Thus we have arrived exactly at the transformation as given above, and, as Einstein has shown (loc. cit.), in order that the electromagnetic equations may be invariant under this transformation the electric and magnetic vectors in the two systems must be correlated in the manner done in this paper.

Bucherer in the paper referred to does not take into account this necessary modification of coordinates, and therefore when in the latter part of it he evaluates the electromagnetic mass of the electron on the assumption that it is spherical he is in reality considering the Abraham electron, and so obtains Abraham's expression for its mass.