274 
PAUL BIEFELD 
where m is the mass in motion, m^ the mass at rest of the electron. 
The principle is, however, not only true in connection with 
masses of electrons but also with respect to every ponderable 
mass as will be shown later. 
Returning now to equations (3) and (3a) we will introduce 
the so-called ‘light time,’ l=ct; using this, these equations be- 
come : 
2( — Al-) =0 
(9) 
2(Ax'=— Ar-)=o 
v ' 
(9a) 
and the Lorentz transformation makes (9) a covariant equation 
which is satisfied with reference to every inertial system K', hav- 
ing a uniform rectilinear motion relative to K, if it is satisfied in 
the system K to which we have referred the two events : emission 
and reception of electromagnetic radiations or light. 
At this point the genius of Mincowski steps in, introducing. the 
time coordinate: x^=il (i=V - 1) 
and equation (9) becomes: 
2x“ =0 V from 1 to 4 
y 
(10) 
and (9a) 
' . 
2x'-=o V from 1 to 4 
(10a) 
r 
Thus putting at once the time coordinate formally on the same 
footing as the space coordinates Xo, x,. We say formally only 
because the relation of rationality must be considered. The space- 
time frame of reference of (10) and (10a) is Euclidean with one 
imaginary coordinate. 
A point x^, X., x^, x^ is called a ‘world-point’ and the line gener- 
ated by the same a ‘world-line,’ and the continuum th'^ ‘world.’ 
All events present themselves to the observer as intersections of 
world lines. Thus the event “twelve o’clock” as observed on a 
watch comes to us as the intersection of a world line through a 
point on the dial with a world line through -a coincident point on 
the hands of the watch. 
We shall now give another interesting consequence of the re- 
stricted theory. 
According to this theory the conservation of mass, or more 
