In the Presidential Address delivered to the Institute in December 1918, Mr. Geoffrey Marks attempted a comprehensive description of the actuary, and indicated some directions in which his usefulness might be enlarged. It was this portion of the address which attracted the particular attention of the present author, chiefly because at the time the address was delivered he was engaged by a number of large engineering firms upon a statistical problem which had arisen in connection with certain repairing contracts involving payments totalling over one million pounds, a problem incapable of correct solution without the use of knowledge possessed exclusively by the actuary, and presenting, indeed, an almost exact analogy to a valuation for the purpose of amalgamation of a number of Sickness Insurance Societies.