Page:Elektrische und Optische Erscheinungen (Lorentz) 079.jpg

 § 54. The presupposition, that no derivatives with respect to x, y, z occur, has led us to equation (65), from which the rotation of the polarization plane does not arise. Thus it is necessary, as it was already indicated earlier to assume (at least in the expression $$F_{1}(\mathfrak{M})$$) derivatives with respect to the coordinates. The most simple is, to add to the second term of (65) another vector $$\mathfrak{R}$$, whose components do linearly and homogeneously depend on the first derivatives of $$\mathfrak{M}_{x},\ \mathfrak{M}_{y},\ \mathfrak{M}_{z}$$. Magnitude and direction will now again be closely determined by isotropy. Namely, if we imagine at any point of space a line, that represents the vector $$\mathfrak{M}$$, and in addition in the considered point the vector $$\mathfrak{R}$$, then after an arbitrary rotation of that entire figure, $$\mathfrak{R}$$ must still fit to $$\mathfrak{M}$$. Only the assumption

$$\mathfrak{R}=j\ Rot\ \mathfrak{M}$$,

is in agreement with this,