It is proposed in this paper to examine the forms obtainable for ds2 in Weyl's generalisation of Einstein's Theory of Relativity, when an isolated electron, considered as a spherical entity carrying a uniform surface distribution of electricity, is present. The problem of the electron on Einstein's theory has been discussed by Nordström (Verslag. Ak. Amsterdam, January 1918). W. Van Der Berg (Vraagstukken mit Einstein's gravitatic theorie, Harlem, 1920) has given an approximation to the solution which has been obtained exactly by H. Vanderlinden (Bull. Acad. Roy. de Belgique, May 1921).