OHM ON THE GALVANIC CIRCUIT.
413
|
, | |
then
|
. | |
Thirdly, since
and
is equal to the part of
which extends from
to the line
, we have
|
, | |
whence
|
, | |
or, since
and
,
|
. | |
If now for
,
,
we substitute their values
|
we obtain | |
|
; | |
and if by
we represent a line such that
|
![{\displaystyle CD:F''X''=\lambda '':x''}](https://wikimedia.org/api/rest_v1/media/math/render/svg/1e7ba1df298f9b75ecec9e48818175f01d04b83e) | |
we have
|
. | |
These values of the ordinates, belonging to the three distinct parts of the circuit and different in form from each other, may be reduced as follows to a common expression. For if
is taken as the origin of the abscissæ,
will be the abscissa corresponding to the ordinate
which belongs to the homogeneous part
of the ring, and
will represent the length corresponding to this abscissa in the reduced proportion of
. In like manner
is the abscissa corresponding to the ordinate
which is composed of the parts
and
belonging to the homogeneous portions of the ring, and
,
are the lengths reduced in the proportions of
and
corresponding to these parts. Lastly
is the abscissa corresponding to the ordinate
, which is composed of the parts
,
,
belonging to the homogeneous portions of the ring, and
,
,
are the lengths reduced in the proportions of
,
,
. If in consequence of this consideration we call the values
,
,