ELECTRIC AND MAGNETIC INDUCTIONS IN THE SURROUNDING FIELD. 295 
induction passing through it is equal to the excess of the number which have moved 
in over the number which have moved out through the boundary since the beginning 
of the formation of the field, suggests a historical mode of describing the state of the 
field at any moment. 
Let a, b, c be the components of magnetic induction at any point O. Consider a 
small area dy dz close to the point, then the number of tubes passing through the 
area dy dz will be ady dz. This will be equal to the difference between those which 
have come in and those which have gone out. 
Fig- 6. 
Let L dx, M dy, N dz denote the numbers of tubes which have cut the lengths 
dx, dy, dz since the beginning of the system, those being positive which have tended 
to produce electric intensity in the positive direction along the axes, and those being 
negative and therefore subtracted which have tended to produce intensity in the 
opposite direction. Let us consider the number which have come into the area 
OBCD = dy dz (fig. 6). The number which have come in across OB is—M dy 
(—because the movement of tubes passing through dy dz in the positive direction 
must be outwards to produce E.I. along OB). The number which has passed out 
across CD is— dzjdy. The difference is—^dy dz. The number which has 
come in across OC is+Ncfe (+ because the movement of tubes passing through dy dz 
in the positive direction must be inwards to produce E.I. along OC). The number 
which has passed out across BD is -{-—dy^jdz. The difference is —~-dy dz. 
The number still passing through dy dz is therefore l~-~^jdy dz. 
Equating this to the actual induction through the area, viz., 
ady dz 
and performing the same process for the corresponding areas dz dx, dx dy, we obtain 
<m 
dz 
dy 
dN 
dL 
dx 
dz ' 
dL 
dM 
'dy 
dx 
2 q 2 
(0 
