is,4 Perkins: Absolute Units and Relativity Principle 345 
Let us define a gram as this apparent mass of an electron 
10 28 
multiplied by g-^-. The manner specified for measuring the 
mass of the electron (that is, that the electron shall be at 
rest relative to the observer), does not specify any particular 
“frame” for the observer and electron. The apparent mass 
so determined is constant according to the Relativity Principle 
itself. The pure number can hardly be expected to 
vary with the “frame,” so we have an absolute definition of 
the gram, in the sense that every quantity in it is independent 
of the “frame. 
An absolute unit of length may be similarly obtained from 
the known properties of a system of two electrons at rest 
relative to the observer. If they are at rest at an apparent 
distance L„ which we need not measure in any units, after a 
short apparent time the apparent distance between them will 
be increased by a length L 2 . During the same time any light 
wave in the neighborhood will have apparently moved a dis- 
tance which we will call L s . Now we know that as we choose 
the interval of apparent time shorter and shorter, the apparent 
L 2 Ik 
length — jA 2 — approaches a constant value absolutely inde- 
JLg 
pendent of our “frame” in space, provided only that there 
is no relative motion between us and the electrons. We 
may now define a centimeter as a length which contains 
(4 774) 2 °f these absolute length units. 6 * * * 
The second may now be defined as the apparent time 
required for light to travel 2.9986 X 10 10 centimeters. Now 
these units are all apparent quantities, but they are also absolute, 
6 The above numerical relation of the centimeter to this absolute unit 
is arrived at as follows: 
acceleration of each electron 
velocity of each 
mL; 
lim. fU e 2 T 
T=0[_ T 
L 3 = cT 
lim. j~ cLi 2 e 2 L 3 
T=0|_ L 3 — m L, c 
lim. fLfU e 2 
t =°L Li 
mLf 
