In his book "The Meaning of Relativity", Einstein presents an expression for the light deflection $\alpha$ according to the approximate metric $$ds^2=\left(1-\frac{2G}{c^2}\int\frac{\sigma}{r}dV\right)dx_0^2-\left(1+\frac{2G}{c^2}\int\frac{\sigma}{r}dV\right)(dx_1^2+dx_2^2+dx_3^2)$$ He says

"The velocity of light $L$, is therefore expressed in our co-ordinates by" $$L=\frac{\sqrt{dx_1^2+dx_2^2+dx_3^2}}{dx_0}=1-\frac{2G}{c^2}\int\frac{\sigma}{r}dV.$$

So far is ok, but then he says

"We can therefore draw the conclusion from this, that a ray of light passing near a large mass is deflected. If we imagine the sun, of mass M, concentrated at the origin of our system of co-ordinates, then a ray of light, traveling parallel to the x3-axis, in the x1 – x3 plane, at a distance $\Delta$ from the origin, will be deflected, in all, by an amount" $$\alpha=\int_{-\infty}^\infty\frac{1}{L}\frac{\partial L}{\partial x_1}dx_3$$

According to his expression the former equation for $\alpha$ is obvious, however, I was unable to make sense of it. Can someone shed some light on me about this?



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