1892.] of Number of Fellows elected into the Society. 469 



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 pro- 

 longation 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 num- 

 ber was reduced to 422, which is abont 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 1818, the average age in 

 their 17th year was 58'3 years, which is almost exactly the average 

 age of the whole body. Further, it is shown that of the supposed 

 original 15 there remained 10*9 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 3" 7, 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 1*0, which again will not differ 

 materially from 9 per cent, of the original 10'9. 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 addi- 

 tional 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. 



