Solutions of the Einstein equations involving functions of only one variable

are satisfied. The results are given in (14), (20), and (17) below. They involve only elementary functions, and the corresponding four-dimensional manifolds can be represented as imbedded in flat space of seven dimensions. Making use of the formulas for Rik calculated in a previous papert we find that, of the ten equations (2), the six with unlike subscript vanish identically, while the four with like subscripts become