When invited to prepare a paper to the Students' Society I had in mind selecting a topic from each of the various branches to illustrate the types of problems that are inherent in non-life business. However, as my ideas took positive shape, I found myself drawn into a more active study of certain aspects which have received little attention in this country, although some considerable theoretical and a limited amount of practical work has been done on the Continent. Instead, therefore, of giving a general description of various features I have largely limited myself to techniques which could be used in practical application and thus endeavoured to bring into relief some problems which indicate the almost unlimited scope for practical and theoretical investigations.

2. Initially the treatment is simplified; I hope that I have succeeded in picking out the spots where intuition rather than formal proof has been my guide, but if I have not I hope my critics will give me latitude in this exploration into largely unexplored territory.