A Riemannian geometry is completely determined by defining over a space a quadratic differential form ds2 = gabdx'dX , called the metric form. Let {PI and {Q} denote two Riemannian spaces, of dimensions p and q, with metric forms whose coefficients are gab and gii . Then the product { P } X { Q } is a welldefined space { R } of dimension r = p + q. A metric may be assigned to I R I at will, but, in order that the geometry of { R may be accessible through the geometries of { P } and { Q }, a metric is suggested which depends on the given metrics of { P } and { Q }. If the metric of { R } has coefficients