From Wikisource
Jump to: navigation, search
This page has been proofread, but needs to be validated.

§ 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)[1]


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



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

  1. Comp. § 7, l. c.
  2. 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.)

  3. Put . Then we have

    and similar formulae for the other three parts of (25).