ELECTRIC AND MAGNETIC INDUCTIONS IN THE SURROUNDING FIELD. 301 
hypothesis of movement of magnetic induction, may also be obtained without any 
special hypothesis as to the motion of the induction tubes, merely assuming that 
growth of induction through a curve is accompanied by electric intensity round the 
curve. Instead of connecting L, M, N with the number of tubes which have cut the 
axes, we start with the following definitions :— 
Let L, M, N denote the time integrals of the components of the electric intensity 
parallel to the axes since the origin of the system, so that 
then 
l=|m 
M= 
N= 
jib A 
ii 
Cs+ ' 1 r 1 
Q= 
fZM 
dt 
R= 
dS 
dt ' 
If a, b, c be components of magnetic induction, since the growth of induction 
through a curve is equal to the line integral of the electric intensity round a curve in 
the negative direction, we have 
da _d _ d_R_d_Um_cm 
dt dz dy dt\dz dy 
with corresponding equations for ~ and 
Integrating with respect to t from the origin of the system, when all the quantities 
were zero 
dM_dN~' 
dz dy 
c£N_ dM 
dx dz 
dL_dM 
dy dx ^ 
(O 
equations the same in form as equations (1). 
As before we obtain equations (3), (4), and (5), while instead of (6) we have the 
simple equations P=and the two others. 
Substituting for — we obtain an equation of the same form as (7), which may also 
CLL 
be put into the form (8). Equations (9) and (10) will also follow. 
Just as we have obtained equations by considering the growth of the magnetic 
induction to its present state so we may obtain corresponding equations by considering 
the growth of the electric induction. 
Let ——be the algebraic sum of the number of electric induction tubes 
2 R 
MDCCCLXXXV. 
