Adams. — On Mortality in Neio Zealand. 63 



It will be observed that the average deaths and average 

 population in Table A are given in groups of five years. The 

 next step in the construction of the final tables is to ascertain 

 the population and deaths at each year of age. The method 

 now generally adopted is that known as Milne's Graphic 

 Method. After a very careful consideration of this method it 

 was decided not to adopt it, but to use instead a mathematical 

 process of distribution based on the method employed by 

 G. W. Berridge ("Journal of the Institute of Actuaries," xiii., 

 220, and xiv., 244; " Text-book of the Institute of Actuaries," 

 Part ii., p. 465). The results of the distribution are given in 

 Table B. As a test of the smoothness of the distribution, the- 

 results were drawn to scale on large diagrams, of which Plates 

 I. and II. are reduced copies. 



The population and deaths from 5 to 75 were treated in 

 this way, the figures relating to the first five years of life re- 

 quiring special treatment. 



From Table B the ratio of deaths to population at each 

 age {m^ is at once obtained, and these ratios are given in 

 Table C. 



The probability of living a year at each age {lo^ is derived 



immediately from m^ by means of the relation ^j^ = nr — -- The 



columns headed p^ in Table E, from 5 to 75, were calculated 

 by means of this formula. 



The ages to 5 now require consideration. Table D gives 

 the annual births and deaths of children under five years of 

 age for each of the years 1880-92. From these figures, by 

 means of a modification of the method used by Dr. Farr 

 ("Journal of the Institute of Actuaries," ix., p. 134), the pro- 

 babilities of living a year at each age were determined. The 

 results, after a slight adjustment to make them join smoothly 

 on to the rest of the table, are given in column ])^, ages 0-5, 

 in Table E. 



The probability of dying in the year at each age [q^ is 

 obtained from y^ by subtracting j;^ from unity : thus, g'x = 1 — i?x' 



The next column in the order of formation is the /^ column. 

 Starting with an assumed 10,000 births (/q), the number sur- 

 viving the year (Zj) is obtained from the relation /i = ZgX^o- 

 Similarly the number who reach the age of two alive, out of 

 10,000 born alive, is l2 = li'X2h> or generally for any year ic, 



The difference between the number born, Iq, and the 

 number surviving the first year, Zj, gives the number who die 

 in the first year, dg, or do=lo — li. Similarly for the number 

 who die in the second year, di, di = li — l2, and generally for 

 the number dying in the a;th year d^.i = l^^i— l^. In this 

 manner the column d^ was formed. 



