446 
MR. 0. HEAVISIDE ON THE FORCES, STRESSES, AND 
(e -f- e 0 ) and (h + ii 0 ) instead of e 0 and h 0 , whilst the Poynting flux requires us to 
reckon only E x and H 1 as the effective electric and magnetic forces concerned in it.* 
But we must develop (Q + U + T) plainly first. We have, by (86), (87), used in 
(103), 
e 0 J + h^G = E (C + I) T - q/fl + H (K + B + q^) — (eJ + h&) A div A E^H^. . . (104) 
Now here we hav 7 e 
CJ = — 4 ED = 4 ED + 4 BE 
dt “ 
= E±> + i (BE 
= ED - I EcE 
— ed — tr c . 
1 
ED) 
> 
J 
(105) 
* It will be observed tlxat the constant 4? r, which usually appears in the electrical equations, is absent 
from the above investigations. This demands a few words of explanation. The units employed in the 
text are rational units, founded upon the principle of continuity in space of vector functions, and the 
corresponding appropriate measure of discontinuity, viz., by the amount of divergence. In popular 
language, the unit pole sends out one line of force, in the rational system, instead of 4?r lines, as in the 
irrational system. The effect of the rationalisation is to introduce 4tt into the formulae of central forces 
and potentials, and to abolish the swarm of 4?r’s that appear in the practical formulae of the practice of 
theory on Earadat-Maxwell lines, which receives its fullest and most appropriate expression in the 
rational method. The rational system was explained by me in ‘ The Electrician,’ in 1882, and applied to 
the general theory of potentials and connected functions in 1883. (Reprint, vol. 1, p. 199, and latex 1 , 
especially p. 262.) I then returned to irrational formulae because I did not think, then, that a reform of 
the units was practicable, partly on account of the labours of the B. A. Committee on Electrical Units, 
and partly on account of the ignorance of, and indifference to, theoretical matters which prevailed at 
that time. But the circumstances have greatly changed, and I do think a change is now practicable. 
There has been great advance in the knowledge of the meaning of Maxwell’s theory, and a diffusion of 
this knowledge, not merely amongst scientific men, but amongst a large body of practicians called into 
existence by the extension of the practical applications of electricity. Electricity is becoming, not only 
a master science, but also a very practical one. It is fitting, therefore, that learned traditions should not 
be allowed to control mattei's too greatly, and that the units should be rationalised. To make a begin¬ 
ning, I am employing rational units throughout in my work on “ Electi’omagnetic Theory,” commenced in 
‘ The Electrician,’ in January, 1891, and continued as fast as circumstances will permit; to be republished 
in book form. In Section XVII. (October 16, 1891, p. 655), will be found stated more fully the nature 
of the change proposed, and the reasons for it. I p oint out, in conclusion, that as regards theoretical 
ti’eatises and investigations, thei’e is no difficulty in the way, since the connection of the rational 
and irrational units may be explained sepai’ately; and I express the belief that when the merits of the 
rational system are fully recognised, there will arise a demand for the rationalisation of the practical 
units. We are, in the opinion of men qualified to judge, within a measurable distance of adopting 
the metric system in England. Surely the smaller reform I advocate should precede this. To pxxt the 
matter plainly, the present system of units contains an absurdity running all through it of the same 
nature as would exist in the metric system of common units were we to define the unit ai'ea to be 
the area of a circle of unit diameter. The absurdity is only different in being less obvious in the 
electrical case. It would not matter much if it were not that electricity is a practical science. 
