MAY 19, 1923 MATHEWS: PHYSICAL DIMENSIONS 199 
II. THE DIMENSIONS OF MAGNETISM OR MAGNETIC FLUX 
The electrical theory of magnetism shows that this is nothing else 
than the phenomenon of electricity in motion. The quantity of it, 
that is (M’), or magnetic flux, is determined by, or is nothing else 
than, the quantity of electricity multiplied by its velocity. Hence 
the dimensions of magnetic flux (M’) 
(10) (M’) = (e) X (v) = (1 x}) 
ities ob 
(11) .'. (M’) = 7 
Magnetism is space per second; or it is electric quantity x velocity; 
acd I? L 
or it is electric current, le! times a length; or it is current, (=) x 
inductance (L); or mass X a frequency. 
III. THE DIMENSIONS OF MASS 
The dimensions of mass may be obtained from those of magnetism: 
(12) (M’) = (M12]3/T-1y1/2) 
M 
Substituting for » its dimension i in (6) 
He WS . M 
(13) (M’) = (seven ua) = (*) 
That is magnetism is mass per second. Or in another way, mass) 
(M), is nothing else than magnetic flux-seconds. But as shown in 
(11) magnetic flux is the product of electric quantity by velocity, or 
(M’) = (=). Hence: 
| L3 M 
Ma: (2) - @) 
(15) .*. (M) = (1) 
Mass, therefore, has three dimensions of space. This follows also 
from the dimensions of », magnetic permeability. This, as has been 
shown, is a density, or (+). and it is usually identified with the density 
of the ether (Maxwell, Lodge, Tunzelman, etc.). Since the ether is 
