upon the co-ordinate axes. Then the equation of the surface is
In this, and in analogous cases, we shall omit the sign of summation, and understand that the summation is to be carried out for those indices that appear twice. We thus write the equation of the surface
The quantities
determine the surface completely, for a given position of the centre, with respect to the chosen system of Cartesian co-ordinates. From the known law of transformation for the
(3a) for linear orthogonal transformations, we easily find the law of transformation for the