862 
We shall call this the polarization of moving magnetism. It explains 
why no current is set up in a moving magnet on account of a 
motion perpendicular to its own internal induetion field, so that 
with sliding contacts no current can be taken off. Thus, e.g., if we 
take a circular spring, the two ends pressing together, we can put 
a long magnet into it. Suppose that we can draw the magnet across 
the ring, the ends of the spring giving way and making a sliding 
contact: there will arise no current in the ring if we do it. 
Again, this polarization is responsible for the electric force set 
up in a homogeneous magnetic field if the magnets producing the 
latter acquire a uniform motion at right angles to the field. The 
magnetic field may remain stationary and homogeneous: neverthe- 
less an electric force will be induced by the motion of the magnets. 
Afterwards these problems will be treated more adequately when 
we shall have explained the character of our deductions from the 
relativity point of view (see below § 20). 
Then we shall also define a distinction between the di-electric pola- 
rization which is independent in itself, and the polarization of moving 
magnetism. 
The Invariancy of the Results. 
13. Thus far we did not want to refer to a single theorem of 
the theory of relativity to deduce our results. Nevertheless they 
possess the property of complete invariancy, not only in EiNstwIN- 
Minkowski’s theory of restricted relativity, but also in EiNsTEIN’s 
theory of general relativity. We proceed to show this. 
This theory ascribes to a four-dimensional track the length ds: 
ds* = = (ab) gap dat da), 
if dart (a=1..4) define the increments of the coordinates and time. 
The determinant of the gas is called gy, and its minors divided by 
g are denoted get. 
What is the character of Nw«? Remembering the definition ($ 3 :) 
Vg NdV dae 
Vg dV dal) ’ 
we notice that NdV is a number, dz“ is a contravariant vector 
and WgdV de constitutes a scalar. Thus Nw° is a contravariant 
vector multiplied by Yq. 
6r* is a contravariant vector too, and so 
Ort Nw — Or? Nw 
is an skew-symmetrical contravariant tensor, multiplied by g. (This 
is sometimes called a volume-tensor or a tensor-density, after Wry). 
Nwe= 
Then we know that 
