The denominator of this fraction is the product of the squares of the semi-axes of the surface
.
If we put
|
(5)
|
and if we make
, then
|
(6)
|
It is easy to see that
and
are the semi-axes of the central section of
which is conjugate to the diameter passing through the given point, and that
is parallel to
, and
to
.
If we also substitute for the three parameters
their values in terms of three functions
defined by the equations
|
(7)
|
then
|
(8)
|
148.] Now let
be the potential at any point
, then the resultant force in the direction of
is
|
(9)
|
Since
, and
are at right angles to each other, the surface-integral over the element of area
is
|
(10)
|
Now consider the element of volume intercepted between the surfaces
, and
. There will be eight such elements, one in each octant of space.
We have found the surface-integral for the element of surface intercepted from the surface
by the surfaces
and
,
and
.