There are certain magnitudes which remain constant by any change of axes. In ordinary geometry distance between two points is one such magnitude; so that δ_x²_ + δ_y²_ + δ_z²_ is an invariant. In the restricted theory of light, the principle of constancy of light velocity demands that δ_x²_ + δ_y²_ + δ_z²_ - _c²_δ_t²_ should remain constant. The _separation ds_ of adjacent events is defined by _ds²_ = -_dx²_ - _dy²_ - _dz²_ + _c²dt²_. It is an extension of the notion of distance and this is the new invariant. Now if _x_, _y_, _z_, _t_ are transformed to any set of new variables _x₁_, _x₂_, _x₃_, _x₄_, we shall get a quadratic expression for $$ ds^2 = g_{1\;1}x_{1}^2 + 2g_{1\;2}x_{1}x_{2} + ... = \sum g_{i\;j}x_{i}x_{j} $$ where the _g_’s are functions of _x₁_, _x₂_, _x₃_, _x₄_ depending on the transformation. The special properties of space and time in any region are defined by these _g_’s which are themselves determined by the actual distribution of matter in the locality. Thus from the Newtonian point of view, these _g_’s represent the gravitational effect of matter while from the Relativity stand-point, these merely define the non-Newtonian (and incidentally non-Euclidean) space in the neighbourhood of matter. We have seen that Einstein’s theory requires local curvature of space-time in the neighbourhood of matter. Such altered characteristics of space and time give a satisfactory explanation of an outstanding discrepancy in the observed advance of perihelion of Mercury. The large discordance is almost completely removed by Einstein’s theory. Again, in an intense gravitational field, a beam of light will be affected by the local curvature of space, so that to an observer who is referring all phenomena to a Newtonian system, the beam of light will appear to deviate from its path along an Euclidean straight line. This famous prediction of Einstein about the deflection of a beam of light by the sun’s gravitational field was tested during the total solar eclipse of May, 1919. The observed deflection is decisively in favour of the Generalised Theory of Relativity. It should be noted however that the velocity of light itself would decrease in a gravitational field. This may appear at first sight to be a violation of the principle of constancy of light-velocity. But when we remember that the Special Theory is explicitly _restricted_ to the case of unaccelerated motion, the difficulty vanishes. In the absence of a gravitational field, that is in any unaccelerated system, the velocity of light will always remain constant. Thus the validity of the Special Theory is completely preserved within its own _restricted_ field.