The following notes were put together in order to collect into a convenient form for reference a few ideas as to what may have been the procedure adopted in the Graduation of the Annuitants' Experience.

The Student is greatly indebted to Mr. Hardy for the information given both in the volume, “Account of the Principles and Methods, &c,” and for affording subsequently, in his Lectures on Graduation, the opportunity to follow his work, and is again fortunate in having, for purposes of reference, the stores of information to be found in Mr. Ackland's paper to the Faculty, and Mr. Todhunter's Reviews in Vols. 38 and 43 of the Journal.

In considering Indian Railway Securities as investments it is advisable to have a knowledge of the history of the railways. The first lines to be built in India were constructed by Companies on land supplied free by the East India Company, who also guaranteed that a certain rate of interest should be paid each year on the capital expended with their approval. This arrangement was made with the idea of attracting Companies to build lines, and in return the East India Company had the right to exercise a certain amount of supervision and control and also had certain options of purchase. When in a position to do so, the Companies repaid each year, to the extent of one half the excess net earnings in that year, any amounts paid by the East India Company under the guarantee arrangements.

The principle of book-keeping by double entry is the complete recording of every transaction as it occurs in a. System which is composed of a number of accounts. An Account is simply a statement of a set of monetary transactions, classified in a convenient form to show the effect of each transaction, and of the transactions as a whole, on the business. The usual form of Account is as follows:–The left-hand side is called the Debit side, and the right-hand side the Credit side. All monetary transactions, involving as they do an exchange of one kind of property for another, can only be completely recorded by two entries in the Accounts, the one debiting the Account which receives the benefit, and the other crediting the Account which imparts the benefit.