Page:The Meaning of Relativity - Albert Einstein (1922).djvu/110

98 Then we get for $$T^{\mu\nu}$$ and $$T_{\mu\nu}$$ the values {{MathForm2|(104)| $$ \left. \begin{matrix} 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & -\sigma \end{matrix} \right\}. $$}} For $$T$$ we get the value $$\sigma$$, and, finally, for $$T_{\mu\nu}^*$$ the values, {{MathForm2|(104a)| $$ \left. \begin{matrix} \frac{\sigma}{2} & 0 & 0 & 0 \\ 0 & \frac{\sigma}{2} & 0 & 0 \\ 0 & 0 & \frac{\sigma}{2} & 0 \\ 0 & 0 & 0 & -\frac{\sigma}{2} \end{matrix} \right\}. $$}} We thus get, from (101), {{MathForm2|(101a)| $$ \left. \begin{align} \gamma_{11} = \gamma_{22} = \gamma_{33} & = -\frac{\kappa}{4\pi}\int\frac{\sigma dV_0}{r} \\ \gamma_{44} & = +\frac{\kappa}{4\pi}\int\frac{\sigma dV_0}{r} \end{align} \right\} $$}} while all the other $$\gamma_{\mu\nu}$$ vanish. The least of these equations, in connexion with equation (90a), contains Newton's theory of gravitation. If we replace $$l$$ by $$ct$$ we get

We see that the Newtonian gravitation constant $$K$$, is connected with the constant $$\kappa$$ that enters into our field equations by the relation