1. A proof of Dupin's theorem with some simple illustrations of the method employed. 2. Two methods of obtaining Cayley's condition that a family of surfaces may form one of an orthogonal triad. 3. An extension of Dupin's theorem to the case in which a family of surfaces is cut orthogonally by two other families which intersect at a constant angle, with the condition that a family may be capable of being cut in this manner
Proceedings of the Edinburgh Mathematical Society