A very large proportion of the life assurance policies in force in the British Isles give the assured the right to participate in the profits of the issuing office. Where a policy has been effected in recent years, it is almost certainly the case that the assured at the time of making his proposal, was given some indication of the bonuses which he might expect to be allotted to his policy. Sometimes an intending assured merely learns the latest rate of bonus declared, or the rate of interim bonus for the time being in force, by reading the prospectus of the issuing office, while on other occasions figures given verbally by an agent, or in a leaflet or letter describing the proposed policy, contain an allowance for future bonuses. It is almost invariably the case that some information along these lines is given and, no matter how guardedly it is done, the assured regards the figures which he has received as the office's estimate of the bonuses which will in due course be allotted to his policy.

Prior to 1915 profits arising from monies invested by Life Offices in the purchase of Reversionary Securities were untaxed. Rapidly increasing expenditure forced the Chancellor of the Exchequer to break new ground and the Life Offices were invited to show cause why this apparent anomaly of an untaxed source of revenue should be allowed to continue. In due course there remained only to be determined the basis of taxation of these profits.

Mr. Geoffrey Marks, who represented the Life Offices in the negotiations with the Revenue Authorities, was instrumental in obtaining a valuable concession in respect of contracts completed prior to 5th April 1915.

The student approaching the subject of summation formulae is constrained to follow the historical order in which it develops in the Journals of the Institute and the Students' Society. Not only is his path made harder by the difficulty of finding a suitable starting point, but the development he must follow is not always the logical one.

The purpose of the present note is primarily to provide the student with a starting point. If a few of the more important conclusions of the subsequent reading are anticipated herein the author feels that the student's appreciation of the original papers by Hardy and Lidstone will be none the less keen for having already navigated some of the wider channels.

It should be added that except in the method of preparation no originality is claimed for this note.