numbers in the fifth column, and therefore indicates the aggregate number of Fellows that will, on the average, be surviving in each successive year of Fellowship, the number elected in each year being always supposed to be 15. It will be seen that the total for the 43rd year is 3970, whereas the actual number surviving, shown in column XI, is 401. This difference is of course due to the number 397, representing what the result would be if the average rates of election and decrease prevailed, instead of the actual rates for the separate years; and it is probably sufficiently accounted for by the fact already pointed out, of the gradually increasing age at election in the later years, which will lead to the lives in the earlier years of the series being somewhat better than the average. Column XI shows the actual results for successive years corresponding to the average results given in column VI. The differences will be seen to be somewhat irregular, but nowhere to be of importance. Column VII gives the aggregate ages of the numbers surviving in successive years, as shown in column V, and from it is deduced the average age of the whole number of Fellows shown in column VI, 397, which is seen to be 57.7 years, a result differing slightly from that obtained from the actual ages of the Fellows surviving in 1891, which was shown to be 584. The cause of this difference has already been indicated. Columns VIII and IX supply the results that would be obtained by applying to an initial number of 15, the rates of mortality in Dr. Farr's tables, for the ages in successive years given in column IV. Column X contains the ratio of column VI to column IX, and indicates that throughout the whole period of 43 years the actual results are somewhat better than the tabular results, or that the lives of the Fellows are better than the ordinary lives, and that this advantage leads in the 43rd year to the actual number of survivors being rather more than 5 per cent. in excess of that which would be given by the life tables, or of about 20 on a total of 400. An examination of this table will show that with the exception of the last six or eight years, in which the number of lives dealt with at last becomes very small, the figures indicate a very regular and consistent progression, and it will practically be quite safe to assume that the series in column VI may be extended on the basis of the ordinary life tables, subject to the addition of 5 per cent. on the total amounts obtained from these last. Hence it will be found that in 10 years after 1891 the aggregate number of Fellows is not at all likely to be increased by more than 15, that the final result may be as little as 410, but is not likely to be more than 420, or at the outside 425. The results of this enquiry are shown graphically in the accom panying diagram, in which the thick line shows the progressive series of actual numbers contained in column VI, and the thin line those in column IX derived from the life tables. The dotted prolongation of the thick line in a direction conformable to that of the thin line, will be seen almost necessarily to fall below the horizontal line indicating a total strength of 420. In an earlier part of this paper I mentioned that the rate of decrease of the Ordinary Fellows elected before 1848 did not appear to differ materially from that which has prevailed subsequently. Taking the number of Ordinary Fellows elected before 1848, and then alive, at 718, it will be found that in 12 years (1860) the number was reduced to 422, which is about 60 per cent. of the original number; after 24 years (1872) the number fell to 206, which is about 30 per cent. of the original; and in 36 years (1884) there remained only 65, which is about 9 per cent. of the first number. Assuming that the average age of the 718 Fellows elected before 1848, and then alive, was not materially different from the average age (58) of the Fellows elected after 1848 and alive in 1891, when it has probably become nearly stationary, it may be inferred that the lapses among a body of Fellows of that age will correspond to the lapses among the Fellows alive in 1848. Now, from Table IV it will be seen that of the Fellows elected after 1848, the average age in their 17th year was 583 years, which is almost exactly the average age of the whole body. Further, it is shown that of the supposed original 15 there remained 109 in the 17th year, of the age above mentioned, 58.3. This number was reduced in 12 years to 6'7, which is nearly 60 per cent. of the number in the 17th year, and again falls after 12 years more to 37, which is not very different from 30 per cent. of the starting number, and after 12 years more the number will be seen to be likely to be less than 10, which again will not differ materially from 9 per cent. of the original 109. These proportions, it will have been observed, are those above shown to hold in the case of the Fellows elected before 1848. On the whole it seems to be established that the present restriction to 15 of the number of Ordinary Fellows elected in any year will lead to an eventual maximum number not exceeding 420; and that the ultimate increase of the total strength of the Society, for each addıtional Fellow elected in excess of 15 may be taken at 28, so that an increase of the annual number of Ordinary Fellows elected to 18 would lead to an ultimate total of 500 such Fellows. |