AV. I'aijn Eldkuton 205 



who would die at each year of age in a statioiiary coniniunity supported by, say, 

 l^ births, or it iiiay be (•(iiisidcrcd as tiie luiiiibiT of pcisoiis who would die in each 

 year of ago out of /„ persous boiii at the .sanie tiuie. W'heu a nu)itality table 

 is constructed the tirst function obtained is either the prubability of living a year 

 (px) or of dying during a year (q^) at age x, and, sincc d^ is obviou.sly eiiuai to l^ 

 (the number living at the exact age x) x q^ it is easy to see Ikjw the cohunn 

 dj: can bc foruied continuously from q^c- 



In The Chnnces of Death (London, 1.S97)* Professor Pearson gave a de- 

 scription of bis analysis (.)f the " deaths " colunin of the mortality table (English, 

 No. IV. Table) constructed by Dr Ogle froni thr Ivcgistrar-iienend's lleturns 

 for the years l(S71 — ISSO a,nd shewed that the old age part of the deaths curve 

 could be represented accurately by a 'lype III. freipiency curve haviiig its origin 

 at 71-5, that is, at the middle of the </;, group, and whcn this "old age" curve 

 was deducted froin the deaths curve the end of the reuiainder could be fitted by a 

 normal curve having its origin at 4r5. This curve was calied the "Middle lifo" 

 curve and whcn it was deducted a " Yoiith " curve of the normal type with an 

 origin at 225 was fouud. The rest of the deaths curve was fitted by a " Childhood " 

 curve of Type III. with origin at age 3 and an "Infancy" curve which started 

 9 months before birth at infinity and was of the type i/„x-p 6-^". 



Turning from Professur Pearson's work to the table we have graduated we 

 notice at once that from a Statistical point of view there is a great difference 

 between mortality and sickness, for in the case of the former if a persou dies he 

 must, of necessity, pass out of Observation, but a person may be sick, and, especially 

 in the earlier periods of life, recover — that is, he does not cease to be a part 

 of the experience under Observation. For this reason we are obliged to alter 

 our conception of a sickness table in Order to obtain a function analogous to that 

 used in the analysis of the mortality table. The rate of sickness at any age, 

 as it is now used, is the average number of weeks' sickne.ss falling to the lot 

 of each person under Observation at that age and if we divide this rate by .52-167 + 

 we get the average number of years' sickness, or the prohahilitn {r^ sai/) that 

 an individual will bc sick for the whole year under certain hypothetical circum- 

 stances arising from the assumptiou that persons are either sick for a whole 

 year or not at all, and, having been sick for the whole year, pass out of Observation 

 altogether just as if they had died. The assumption is subsequent to the 

 calculation of the sickness rates and it will not affect any results already obtained ; 

 our change of view merely accentuates the fact that we deal with the Community 

 as a whole and not with its individual members. 



If we take /(„ persons at birth, then /(„?•„ (=/„ say) will represent the amount of 

 sickness in years or the number of persons who are sick for the year of age (0 — 1) 



purely hypothetical function tabulated for convenience, and they can only be connected by means of 

 the rates of mortality. The same distinction must be made between the number of wceks' sickness and 

 the / column. 



• See also Phil. Trans. A, Vol. 186, p. 34.S. 



t Number of weeks in the year assumed by Button (see footnote, p. 264). 

 Biometrika ii 3-1 



