MAY 19, 1923 MATHEWS: PHYSICAL DIMENSIONS 209 
Furthermore electric charge being (L*), shows that it cannot be 
simple, but must be constituted by the product of two coordinates 
(Li) and (L:). It is an interesting question what these two coordinates 
areand whether electric quantity, ore, isinreality (L?), or (L?), or (Li) (Le). 
It should be possible in the latter case to make an electron charge 
either by an increase in L; with less Le, or vice versa. Just as mass can 
be formed by much L? and little L,, or by a smaller amount of elec- 
tricity and a greater inductance. That is, we may have the same 
quantity of mass by moving a large number of electrons slowly; or a 
smaller number with greater velocity. Similarly, e may be formed 
by moving a long distance along L; and a small distance along I», or 
a small interval along L; and a large interval along Lz, or by equal 
intervals of both. The square root of e ine. s. u. is 2.185 x 10-5 un- 
its of interval or L. 
Mass, energy, and moment of magnetism now all have the same 
dimensions. They may be identified as equivalent, provided the 
various spatial coordinates are equivalent, but not if they are not. 
Each has the dimensions of L*. Again it is obvious that each of these 
three has in it electric quantity, L*, and self inductance, L. Further- 
more if these various coordinates are not the same, we can obtain the 
same quantity of mass or energy or magnetic moment by changes in 
velocity or in any of the three intervals. 
Velocity, elasticity, specific inductive capacity, magnetic per- 
meability, intensity of magnetic field, intensity of electrostatic field, 
are now without dimensions. They are but the ratio of two intervals 
L,/Ly. 
Acceleration, sie lr velocity, frequency, coefficient of reer and 
reluctance all have the dimensions of the reciprocal of an interval, = é 
Time, period, length, current, coefficient of self induction, electro- 
motive force, capacity, magnetomotive force, all have the dimension L. 
Moment of inertia is L’*. 
The interpretation of these results may be left for each one to make 
for himself. That they offer an enormous apparent simplification of 
things is obvious. In relativity the attempt has been made already to 
identify mass with energy. Eddington‘ for example says ‘Hence it 
appears that mass (inertia) and energy are essentially the same thing 
or at the most two aspects of the same thing.” 
The foregoing resolution of the dimensions of each to L’*, or space, 
6 Eddington: Space, Time and Gravitation. Cambridge, 1920. 
