28 Law of the Induction of an Electric Current upon itself. 
current through any fibre will be inversely as the length of the 
shortest chord that can be drawn in the cross section through that 
* 
- The equation (F’”) gives us the inductive force for any 
sii within the wire. For a point exterior to it, the quan- 
tity ¢ or z does ap ‘in the process of integration, elimin- 
ate itself from ‘ge '? dz inthe same manner as before, but 
2 now becomes an pie of the limits of the second integra- 
tion with reference to y, or in other words, the interval between 
the lower and upper limits of ¢ is confined to the angle subtended 
by the cross section of the wire, and if this angle be denoted by 
8, the integration a us for an exterior point 
(FD pened “ =4CKRx°8, 
which shows that ion a henna following the law of development 
just deduced, the exterior inductive force at different distances is 
directly as the angle subtended by the cross section of the wire. 
The inverse ratio of the distance from the centre would require 
it to be as the sine of half the subtended angle, so that inthe 
very near vicinity of the wire the induction could not be estima- 
ted as if the current were all generated through the axis of the 
wire 
15. Ina conducting wire having its cross section an ellipse, a 
law of development would obtain perfectly analogous to that of 
the cylindrical wire. Let ADG, fig. 7, rep- 
rae the cross section and E any point in 
Draw the chord GEF making any an- 
oy with a given line, and let HEK be the 
chord which 36 bisected in E, and _ parallel 
to GEF and HEK draw the diameters ACM 
and BCN, and draw DCL bisecting GEF 
in O. Let CA=r, OF =cr and OE=z. 
The Pain of the ellipse give us 
HE? GH. EP 1,cta =o? 
BC? AC? re 
If then i rate of development through E be always equal to. 
ans = 1(° 28 =e 
ae this be substituted in (F’), we shall have for the induetive bc 
force’ at any point within the section 
Geach f? ce ‘one ylas)aenicney 
