Page:The Meaning of Relativity - Albert Einstein (1922).djvu/35

Rh it is assumed that for symmetrical dilatations in all directions, i.e. when

there are no frictional forces present, from which it follows that $$\beta = -\frac{2}{3}\alpha$$. If only $$\frac{\delta u_1}{\delta x_3}$$ is different from zero, let $$p_{31} = - \eta \frac{\delta u_1}{\delta x_3}$$, by which $$\alpha$$ is determined. We then obtain for the complete stress tensor,

The heuristic value of the theory of invariants, which arises from the isotropy of space (equivalence of all directions), becomes evident from this example.

We consider, finally, Maxwell's equations in the form which are the foundation of the electron theory of Lorentz.

{{MathForm2|(19)| $$ \left. \begin{align} \frac{\delta h_3}{\delta x_2} - \frac{\delta h_2}{\delta x_3} & = \frac{1}{c}\frac{\delta e_1}{\delta t} + \frac{1}{c}i_1 \\ \frac{\delta h_1}{\delta x_3} - \frac{\delta h_3}{\delta x_1} & = \frac{1}{c}\frac{\delta e_2}{\delta t} + \frac{1}{c}i_2 \\ & \cdots \\ \frac{\delta e_1}{\delta x_1} + \frac{\delta e_2}{\delta x_2} & + \frac{\delta e_3}{\delta x_3} = \rho \end{align} \right\} $$}}

{{MathForm2|(20)| $$ \left. \begin{align} \frac{\delta e_3}{\delta x_2} - \frac{\delta e_2}{\delta x_3} & = - \frac{1}{c}\frac{\delta h_1}{\delta t} \\ \frac{\delta e_1}{\delta x_3} - \frac{\delta e_3}{\delta x_1} & = - \frac{1}{c}\frac{\delta h_2}{\delta t} \\ & \cdots \\ \frac{\delta h_1}{\delta x_1} + \frac{\delta h_2}{\delta x_2} & + \frac{\delta h_3}{\delta x_3} = 0 \end{align} \right\} $$}}