dOZ METHODS OF INTERPOLATION. 



registration of deaths, it will probably be best to adjust the population 

 for each j'earof age at each census approximately by the second method; 

 that is, by (liO) or some similar formula. The returns of two or more 

 census enumerations thus adjusted will enable us to comijute approxi- 

 mately, by known methods, the mean population living within each year 

 of age during the period embraced by the registry of deaths; and from 

 this series the meannumber of ikmsous who annually attained each year 

 of age during that period can be found by (28) or some similar fornuda. 

 The mean number of deaths annually occurring within each year of age 

 must also be adjusted approximately by the second method, and then we 

 shall only have to divide these annual deaths for each year of age by the 

 mean number of persons annually attaining such age, to obtain an approx- 

 imately adjusted series exi)ressing the probability of dying within a year 

 at each age. The graduation of this series can be completed by either 

 the first or the third method, and from it we can construct the usual 

 series of the numbers who live to attain each year of age out of a gi\en 

 number of persons who are born. 



It should be remarked, however, that in infancy and early childhood 

 the rate of mortality varies so rapidly that the years ought not to be 

 grouped together as in the first and third methods. l>ut these years are 

 unimportant so far as life insurance and annuities are concerned, and 

 for practical purposes it will suffice to have a completely graduated 

 series from the age of ten or fifteen up to the limit of old age, and to 

 adjust the series at the earliest ages by the second method only, or not 

 at all. The latter alternative is perhaps the best, since the ages of 

 young children can be ascertained with greater certainty than those of 

 adults. 



The accuracy of a series obtained by the first or the third method will 

 be greatest at and near the middle, and least at the extremities. If it 

 should be found that the graduated values at either end of a table of 

 mortality thus constructed are sensibly erroneous, they can be rejected, 

 and their places supplied by the original values, and the adjustment 

 of these, and their continuity with the graduated portion, can be 

 approximately secured by the use of some fornuda under the second 

 method. 



METHOD OF CONSTRFCTING A TABLE OF MORTALITY WITHOUT ANY 

 REGISTRATION OF DEATHS. 



It has been proposed to determine the law of mortality for general 

 population throughout a whole country by means of two successive cen- 

 sus enumerations, taken, for instance, at intervals of ten years, as is now 

 the case in the United States and in Great Britain, together with a reg- 

 istry of the immigration and emigration which (;c('urs during the inter- 

 vening ten-year period. If at the first census a certain population, Pu„ 

 is returned as aged m and under m-\-l years, then at the second census 

 the survivors among them will be returned aa. aged w-f 10 and under 



