### Distance element in the
elliptical coordinates

As we found earlier,

We have further

The derivatives are

Please substitute.
Calculation of the tangential unit vector

.
Let us consider two close points on the ellipse:

and

.
The vector connecting these two points is a tangential vector, that is,

.
However, we have to take into account that

and

are
not independent, since they have to be calculated with

,
that is,

Using this we find

Please substitute. After

is found, the normal unit vector can be found as

.