This note is intended to be supplementary to the paper, by Mr Muirhead, on “The dissection of any two triangles into mutually similar pairs of triangles.” The constructions given there, for the general case of this problem, yield no real solution if one angle of one triangle be greater than the sum of any two angles of the other triangle. For this particular case, the following constructions supply the necessary requirements; the first leads to a division of the triangles into three parts, the second to a division into four parts.