probably not a serious risk, but if small the first method is preferable. The first method is also preferable where business is new, as a reversioner is not likely to sell a reversion unless the life-tenant is at least in fairly good health. Consequently the rate of mortality for the first few years is likely to be light, and few reversions will therefore fall in.

(3) Provide for interest by means of annuities set up in the books of the office. The amount available for the annuity fund will be the difference between the sums in reversion and the value of the reversion. The amount of this annuity fund would be entered as a liability in the balance-sheet, and added to the cost of the reversions on the asset side. This is in harmony with our formula 1 - d(1+ a), the 1 forming the sum in reversion and d(1 + a) the annuity fund to provide interest on the 1. The net results of this method are the same as that of (2).

Should the reader desire to pursue the study of reversions further, he will find many valuable papers by different authorities in the Journal of the Institute of Actuaries. A bibliography of such papers is given in the Transactions of the Faculty of Actuaries, vol i. p. 95. N. CAMPBELL.

Royalty. In connection with patents a sum is usually paid to the patentee on every article made or sold, and in the case of the publication of a book it is customary to pay the author a fixed sum on every copy published or sold. These payments are known as royalties. Lessees of mines pay royalties to the lessor or owner of the property, calculated at so much per ton of the mineral raised or a fixed sum per acre worked. In other cases the royalty varies with the price of the mineral. In most cases of mines the lessee is required to pay a minimum rent of a certain amount merging in a royalty no matter whether the output of mineral justifies it If the rent is in excess of the amount of royalty due as calculated on the output, the difference is called "short workings," and the amount is generally recoverable by the lessee out of future royalties which are in excess of the minimum rent. The amount of "short workings" is carried forward as an asset in the lessee's books if it is absolutely certain that the amount will be recovered in future years by the increase of the output.

or not.

Rupee. The standard silver coin of India, weighing 180 grains eleven-twelfths fine. The exchange value of the rupee is about 1s. 4d., but its intrinsic value, in consequence of the fall in the price of silver, is much less. The symbol "Rx" denotes ten rupees. Large sums of rupees are expressed in lacs and crores, the lac being 100,000 and the crore 100 lacs.

END OF VOLUME V.

Printed by R. & R. CLARK, LIMITED, Edinburgh