MAY 19, 1923 MATHEWS: PHYSICAL DIMENSIONS 197 
dimensions of (e), quantity of electricity, may be (L?). Lewis and 
Adams? in the manner of the relativists reduced space and time to one 
dimension, an interval, I; but kept mass, M, as a dimension. They 
thus equate time with length. On this basis and disregarding specific 
inductive capacity which now, with velocity, has no dimensions, they 
attempt to explain several exact numerical agreements they have 
found between various constants. These agreements will be con- 
sidered in a later paper. 
In all these attempts to reduce the number of dimensions, mass 
has been the principal stumbling block. The discovery of the electrical 
constitution of matter enables us, however, to write mass in terms of 
electricity and self induction and reduce it to the dimensions of space, 
or (L’). Fournier d’Albe* has already shown how the dimensions of 
magnetism may be written in those of electricity, but he still keeps 
electric quantity, or (e), as a fundamental unit along with mass. 
His identification of magnetism with electricity in motion, however, 
practically involves the conclusion that magnetic permeability, u, 
which is generally considered to be a density, has no dimensions, and 
that accordingly mass and space are identical. 
Since electricity appears to be the most fundamental quantity of all, 
the first step is to reduce it to the dimensions of L?. 
I. THE DIMENSIONS OF QUANTITY OF ELECTRICITY, (e) 
Matter is composed of electrical charges, the atoms being essentially 
electrical doublets; positively charged nuclei or spheres, accompanied 
by an equal quantity of negative electricity, negative electrons. 
By matter we express three fundamental concepts, namely space, 
weight and inertia. Matter is that which occupies space, and possesses 
, Oy piri : ; 
Capacity, S = E = ary = displacement per unit pressure 
Coefficient of resistance = — = -——~ = impulse or momentum per unit volume 
Magnetomotive force = 4 nC = To current 
Reluctance = 1/yA = L?/M = area/inertia 
Magnetic induction, I = M/T = moment of momentum per unit area 
Coefficient of induction (self or mutual) 1/C = M/L? = inertia per unit area 
8 Lewis and Adams: A Theory of Ultimate Rational Units; numerical relations 
between elementary charge, Wirkungs quantum, constant of Stefans Law. Physical 
Review, 1914, Ser. 2, III, p. 92. 
