1892.] of Number of Fellows elected into the Society. 467 



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 397"0, 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 58*4. 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 indi- 

 cates 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 con- 

 sistent 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- 



