§ 28. Between the differentials of the original coordinates and the new coordinates which we are going to introduce we have the relations

(30) |

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)^{[1]}

or

Further we have for the infinitely small quantities ^{[2]} defined by (19)

and in agreement with this for the components of a vector expressed in -units

so that we find from (25)^{[3]}

Interchanging here and , we obtain

and

(31) |

The quantity between brackets on the right hand side is a second order minor of the determinant and as is well known this minor