§ 28. Between the differentials of the original coordinates and the new coordinates which we are going to introduce we have the relations
and formulae of the same form (comp. § 10) may be written down for the components of a vector expressed in -measure. As the quantities constitute a vector and as
we have according to (28)
Further we have for the infinitely small quantities  defined by (19)
and in agreement with this for the components of a vector expressed in -units
so that we find from (25)
Interchanging here and , we obtain
The quantity between brackets on the right hand side is a second order minor of the determinant and as is well known this minor
- ↑ Comp. § 7, l. c.
- ↑ For the infinitesimal quantities occurring in (19) we have namely (comp. (30))
and taking into consideration (19) and (20), i e.
and formula (7) l. c, we may write (comp. note 2, p. 758, l. c.)
- ↑ Put . Then we have
and similar formulae for the other three parts of (25).