Page:The Meaning of Relativity - Albert Einstein (1922).djvu/107

Rh transform (96). We multiply (96) by $$g^{\mu\nu}$$ summed over the $$\mu$$ and $$\nu$$; observing the relation which follows from the definition of the $$g^{\mu\nu}$$,

we obtain the equation

If we put this value of $$R$$ in (96) we obtain

When the approximation which has been mentioned is carried out, we obtain for the left-hand side,

or

in which has been put

We must now note that equation (96) is valid for any system of co-ordinates. We have already specialized the system of co-ordinates in that we have chosen it so that within the region considered the $$g_{\mu\nu}$$ differ infinitely little from the constant values $$-\delta_{\mu\nu}$$. But this condition remains satisfied in any infinitesimal change of co-ordinates, so that there are still four conditions to which the $$\gamma_{\mu\nu}$$ may be subjected, provided these conditions do not conflict with the conditions for the order of magnitude