to Age, and the "English Life Table." 29 



similar exception, the English Life Table for males is in close 

 agreement, at the same nine intervals of age, with the Table 

 constructed according to the true law and formula of 1866. In 

 the two excepted cases the apparent defects are the same, and 

 consist in the observed rates of mortality in the first month from 

 birth being just three times as great as they ought to be accord- 

 ing to either of the two theoretical Tables. This apparent defect 

 will vanish if it be assumed, as is probably true, that two out 

 of three of the deaths in the first month after birth would have 

 been uterine deaths, in the eighth and ninth months of pregnancy, 

 if approaching death had not induced premature birth. 



The errors of construction in the " English Life Table " at ages 

 above 75 years (as exhibited in Table IV. hereunto annexed) have 

 their origin in a novel principle adopted for the determination of 

 the annual rates of mortality at the precise ages 20, 30, . . . 80, 

 and 90 years. The constructor of that Table (Dr. Farr) has made 

 the gratuitous assumption that the above annual rates are identical 

 with the annual ratios of the dying to the living according to 

 observation for the decennial intervals of age, 15-25, 25-35, .... 

 75-85, and 85-95 respectively. This assumption, unsupported 

 by any evidence, although near the truth at ages under 55 years, 

 is probably more or less erroneous at every age. At ages above 

 75 years there is no appearance of truth in the above assumption, 

 as may be seen on inspection of any ordinary Table of mortality. 

 For example, according to my Table of " Mean Mortality," the 

 annual ratio of the dying to the living for the decennial interval 

 from 75 to 85 years of age is identical with the annual rate of 

 mortality at the precise age 79*1 years instead of 80 years. Also 

 the annual ratio of the dying to the living in the decennial in- 

 terval from 85 to 95 years of age is identical with the annual 

 rate of mortality at the precise age 87*9 years, instead of 90 

 years, as assumed by Dr. Farr. These differences in age corre- 

 spond to errors of 7 per cent, and 13 per cent, in understate- 

 ment of the rates of mortality observed and truly belonging to 

 the ages 80 and 90 years respectively. 



The constructor of the English Life Table does not proceed 

 directly to the interpolation of the values of m at annual inter- 

 vals from the erroneous values of m at decennial intervals assumed 

 as above, but commences by deducing for each of the decennial 

 values of m the corresponding value of the probability of living 



k q ot 

 one year by the use of my formula com. log? t = - — (1— p*), 



and making t = unity. The probabilities of living one year at 

 the precise ages 20, 30, .... 80, and 90 years having been thus 

 erroneously obtained, the corresponding probabilities of living 

 one year for all intermediate years of age have been interpolated 

 by the method of finite differences. 



