STRESS, ENERGY, ETC.

Now, the scalar part of this ternary product is

SRnL - SEVnL = - (RVnL) = (nVEL), so that, by (4),

JSEnL = -($)n). Consequently, the full product will be

It will be convenient to combine this with (40) into one forn Let cr be a real, but otherwise arbitrary scalar, and let us i: duce for the moment the auxiliary quaternion

k = to- H- n. Adding iff times (4*1) to (70), we have

L O*

c c

This is valid for any /£, that is, for any direction of n and foi value of o-.

Since (2) transforms into itself, i.e. into J?'= - JR'[J9']L' for legitimate system *S", the same thing is true of the equatio energy (3) and of the formula for the ponderomotive force Both are invariant with respect to the Lorentz transformation. ' we have, in *V,

on . t <\\M p p = — — div it)

and

TV ^o r"7' ./v

P = -Tvy-V/,

where g' = JJ'/^ and where $}', ?/, / are determined by the pre formulae, i.e. also by (8) with dashed letters. Remember that the stress-operator in *$", so that if n' is a unit vector, fri = the pressure on a unit area whose normal is n'.

What are the connexions between |J', */, / on the one sidi J3, ?/, / on the other side ? To answer this question, return t

nP<e»lr«3k fXr If ft •nVixrcir-al m intern inn <»