236 
MR. G. H. LIVENS ON THE 
of this quantity with the magnetism hides its true character, particularly as regards 
its dependence on the velocity of the medium. 
Nevertheless many of the relations of the theory will be considerably simplified if 
this procedure is adopted. 
12. The question of forces on fictitious magnetic poles moving in an electric field is 
easily resolved l)y imparting to such poles a substantiality sufficient to allow us to talk 
of forces on them, and then applying any of the general methods used in this theory. 
The Lagrangian function of the system is still of the form 
r.+ y 
L being that part of it which is not directly determined by the conditions in the field 
and which will as usual he assumed to be a function of the positions and velocities 
of the electric and magnetic elements only. The sequence of changes is then best 
described by the fact that the action integral 
taken between fixed time limits is stationary subject to the implied conditions of the 
field. If we assume generally that there are a number of discrete electric particles as 
well in the field, these conditions may be written in the form 
div E —IttSc = 0, 
div (B-H) + 47r 
Curl —2c., 
c dt c 
dB dH , .. 
dt dt 
0, 
= 0, 
= U, 
wherein e is the charge of the typical electron and its velocity, m is the strength of 
tlie typical magnetic particle whose velocity is and the sum 2 in each equation is 
taken per unit volume at each place over the respective elements indicated in it. 
We now introduce four undetermined Lagrangian multiplying functions, two scalar 
quantities 0] and and two vector quantities Ai and A^, it is thus the variation of 
dt 
L + 
Stt 
dv 
B=^-EW20, div E + 20, div (B-H) 
n / \ 1 TT C^E \ 2 / A 6?B dH 
-2 Ai, Curl H-— + - As—- 
\ c dt I c dt dt /J 
87r2c0i + 87r27n0.^ + — 2e (Ai.,) — (Ao.,,,) 
