282 THE THEORY OF RELATIVITY
paper,* the reader will verify that the above vector is identic
where the quaternions >; and { are as in (B), p. 265, In the homogeneity, therefore, N vanishes, and we have A= -V/J the condition (/3) is satisfied, with the above stress and morr by taking (150) for the ponderomotive force, that is (140) force-quaternion.
In the more general case of a heterogeneous medium we ha to supplement our original P by the vector N, and conseque add to our original F the quaternion
which, like that P itself, is ~<j> since Tfy and Tf, being the of physical quaternions, are invariant with respect to the '. transformation.
Thus we shall have, as a generalization of (140),
f-RCL- EC1] - A (Tr,)*. DK- I (Tfl*. which splits into
P = PE + » and
(Pv) +/= (El)
All requirements being now satisfied, with the above va density and flux of energy, and of stress and momentum, tl thing to be still revised on account of the heterogeneity medium is the Joulean waste. Now, proceeding as befc obtain at once, from (15) and (16),
where