MAY 19, 1923 MATHEWS: PHYSICAL DIMENSIONS 201 
intensity factor, however, is again the pressure this molecule can exert 
per square centimeter, or M/LT?, and this being equal to L?/T?, 
M = L’. The intensity of an electrostatic field is M/LT?; from 
whence again M = L’, 
Hence since everywhere intensity of energy has the same dimensions, 
L?/T?, the dimensions of mass are found to be L’, just as they were 
found from the electrical constitution of matter. 
The great gain made in reducing mass and electric quantity to the 
dimensions of (L’) and (L?) respectively will be apparent. If we keep 
mass and electricity fundamental dimensions, (M) and (E), as Fournier 
does, there is no indication of any relation between them or of their 
real meaning. But if we write mass as (L), it is clear at once that it 
represents space or volume, that it consists of three components, and 
in addition that it contains electric quantity, or (L?) and a length or 
self induction, (L). The relation between mass and electricity is seen 
at once. Similarly, writing electricity as (e), exhibits nothing of its 
qualities, whereas (L?) makes it a surface phenomenon, and relates it 
at once to its peculiarity of accumulating on surfaces and to its surface 
3 
density. The relations between quantity of magnetism (Z) elec- 
tricity (L?), and mass (L’), are clear by simple inspection. For 
example, magnetic flux is (L?/T), while electric current is (L?/T). 
This shows at once that magnetic flux is the product of current by its 
length. And electric quantity or, L?, is magnetic flux x (T/L). 
That is, it is magnetic flux times the square root of K, the specific 
inductive capacity. The specific inductive capacity has the dimen- 
sions of the ratio of electric quantity to quantity of magnetic flux. 
The results of considering T equivalent to L, are considered on 
page 206. 
IV. THE DIMENSIONS OF THE ETHERIAL CONSTANTS 
; a M: perks : 
Since », magnetic permeability, = Tien ak 1 and so has no dimen- 
L; 
) K being the specific inductive capacity: 
Mo 
Hee 
[2 
(16) od @®) i= (7) 
These are the dimensions already ascribed to K by Fournier d’Albe. 
And as he has pointed out, all the phenomena of refraction and disper- 
sions, and (u K) = 
