thus also according to the generalised relativity theory it is given by the equation
(73) ds² = gμν dxμ dxν = 0.
If the direction, i.e., the ratio dx₁ : dx₂ : dx₃ is given, the equation (73) gives the magnitudes
dx₁/dx₄, dx₂/dx₄, dx₃/dx₄,
and with it the velocity,
√((dx₁/dx₄)² + (dx₂/dx₄)² + (dx₃/dx₄)²) = γ,
in the sense of the Euclidean Geometry. We can easily see that, with reference to the co-ordinate system, the rays of light must appear curved in case gμν’s are not constants. If n be the direction perpendicular to the direction of propagation, we have, from Huygen’s principle, that light-rays (taken in the plane (γ, n)] must suffer a curvature ∂λ/∂n.
Let us find out the curvature which a light-ray suffers when it goes by a mass M at a distance Δ from it. If we use the co-ordinate system according to the above scheme, then the total bending B of light-rays (reckoned positive when it is concave to the origin) is given as a sufficient approximation by
B = ∫-∞∞ ∂γ/∂[x]₁ dx₂
where (73) and (70) gives