PROCEEDINGS OF SECTION G. 519 



1 should say tliat the above values agree with those used by 

 ilie actuarial sub-committee in investigating the superannuation 

 scheme for the New South Wales Public Service. They differ, 

 however, slightly from the values used by the Commonwealth 

 Statistician in his investigations, as he put forward the age half 

 a year. 



As I have said, the children at each age were related to the 

 total males of the ages concerned, married and unmarried, as 

 distinct from fathers. The number of children, of each age from 



to 15, bom to males at each age was multiplied by the 

 respective temporary annuity values shown above. The sum 

 of the products gave what may be termed the " total annuity 

 value " for males of each age, and this value divided by the num- 

 ber of males, gave for males of each age, at time of death, the 

 average value of an annuity of 1 to each surviving child up 

 to age 16. 



This process was applied to each of the experiences of New 

 South Wales in 1903 and 1911, and to the experience of New 

 Zealand in 1906-10. The moi'tality tables used may not suit 

 altogether the latter experience, but they were the most suitable 

 available, and the annuity values deduced for New Zealand will 

 probably not be so far from the truth as to affect the comparisons 



1 wish to make. 



The results obtained in this manner were, of course, the un- 

 adjusted values, and exhibited considerable inequalities from age 

 to age. Before they could be considered properly it was neces- 

 sary to subject them to a process of graduation which would re- 

 duce the whole series to a smooth curve without modifying to any 

 great extent the inherent characteristics of the function. 



To graduate the original annuity values I adopted the graphic 

 method described first in Messrs. Moors' and Day's publication, 

 and later in the report of the New South Wales Actuarial Sub- 

 Committee, and called the " pins and thread " method. This 

 is a great improvement on the old method of graphic graduation, 

 as it can be applied readily and rapidly to any series requiring 

 adjustment. The "tools of trade" are a' table of fair size, hav- 

 ing the top accurately ruled into squares, a reel of thread, and 

 some pins with coloured heads. In my own case I had at my 

 disposal the same table that was used by the actuarial sub- 

 committee. 



The annuity values in regard to the males of each age, as 

 ascertained from the deaths among the general population in 

 New South Wales in 1903 and 1911, and in New Zealand in 

 1906-10, were computed by me. The annuity values as ascer- 

 tained from the experience of the New South Wales and Common- 

 wealth Public Services were extracted from the reports thereon 

 previously cited. 



