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Taking also into consideration the opposite side we find for the contributions

This may be applied to each of the three pairs of sides not yet mentioned under ; we have only to take for successively 1, 2, 3.

Summing up what has been said in this § we may say: the components of the vector on the left hand side of (10) are

§ 27. For the components of the vector occurring on the right hand side of (10) we may write

if is the component of the vector in the direction expressed in -units, while represents the magnitude of the element in natural units. This magnitude is

so that by putting


we find for equation (10)


The four relations contained in this equation have the same form as those expressed by formula (25) in my paper of last year[1]. We shall now show that the two sets of equations correspond in all respects. For this purpose it will be shown that the transformation formulae formerly deduced for and follow from the way in which these quantities have been now defined. The notations from the former paper will again be used and we shall suppose the transformation determinant to be positive.

  1. Zittingsverslag Akad. Amsterdam, 23 (1915), p. 1073; translated in Proceedings Amsterdam, 19 (1910), p. 751. Further on this last paper will be cited by l. c.