867 
then we get the conjugate tensor with covariant components 
VgP™ Jey Wap: ople 
En VgP** VYyP Vgkh™ 
Peat (=) VoP™ —VY9P" VoP" 
a VYgP” —VoP" —VYgP" 
By multiplying by the velocity vector and contracting, 
dx) 
S 
= (6) wb Peo, 
we get a vector. This vector clearly vanishes in a stationary point, 
because wi, w®), wd, and „Pes vanish, and it therefore always 
vanishes. Thus we conclude that we shall always have 
0 = w?) gP** — w®) V¥gP** + YoP*, (16.1) 
and similar relations for cyclic permutations of the figures 123. It 
is thus confirmed that where w/gPe* (a= 1, 2,3) are polarization 
components, the other components of this tensor consist of compo- 
nents of the corresponding RONTGEN-vector. 
16.2. Apply a similar reasoning to the magnetization tensor. 
Multiply by the velocity vector and contract: 
) dix) 
we Mab — >(b) 
ds ds 
This will be a vector vanishing in stationary points, since 2,, w‚, 
w,, and ,J/*4 vanish. Therefore it will always vanish, and we 
shall have 
da 
= (be) Jbc wy, Mab, 
0=w, MW? + w, MP Lw MY. (cycl. 123). (16.2) 
Here we meet the polarization of moving magnetism, Vg M%*, in terms 
of Met. We know from §§ 8, 9 that W/g Met must contain, besides 
the components of the magnetization and of £¢, the components of 
the RöxraeN-vector corresponding to the polarization of moving mag- 
netism also. 
This will afford us means completely to express the polarization 
of moving magnetism in terms of the magnetization and k of moving 
matter (§ 19). 
Comparison with Other Theories. 
17. In constructing the polarization tensor Einstein, following 
Minkowski, starts from the vector /” defined in §15.2, and he puts 
for his tensor *) 
h Die formale Grundlage der allgemeinen Relativildtstheorie, Berl, Sitz, 41, 
p. 1065, 1914. 
