The property mentioned by Mr Townsend in his paper in the August No., “On a Property in the Theory of Confocal Quadrics,” may be demonstrated in a form which, it appears to me, better exhibits the foundation and significance of the theorem.

Starting with two given quadric surfaces, the torse circumscribed about these touches each of a singly infinite series of quadric surfaces, any two of which may be used (instead of the two given surfaces) to determine the torse; in the series are included four conics, one of them in each of the planes of the self‐conjugate tetrahedron of the two given surfaces; and if we attend to only two of these conics, the two conics are in fact any two conics whatever, and the torse is the circumscribed torse of the two conics; or, what is the same thing, it is the envelope of the common tangent‐planes of the two conics.

Consider now two conics U, U′, the planes of which intersect in a line I; and let Imeet Uin the points L, M, and meet U′ in the points L′, M′: take Athe pole of Iin regard to the conic U, and A′ the pole of I′ in regard to the conic U′

Take Tany point on I, and draw TPtouching Uin P, and TP′ touching U′ in P′: the points P, P′ may be considered as corresponding points on the two conies respectively.