2GÜ Graduotion and Ancdi/sis of a SicAness Table 



ou the assumptions iiivulvcd in uiir altered arraugement of the table. If we 

 continue the calculations remembering that hx=hx-.i—fx-\ andyx = /'x'* we shall 

 form an "/" column for sickness equivalent to the " d " column for death. 



An "/"" column was fornicd from the graduated rates of sickness and, as it 

 appeared to shew sonie similarities to the "d" column, I proceeded to split it up 

 into component parts beginning, of couree, with the old age end of the curve. 

 The equations found for the various curves and the corrcsponding uuinbcrs are 

 given in Table II. and the curves drawn out (Fig. 2) but it would be \mwise to 

 place much reliance on the " Childhood " curve as the figures on which it is ba.sed 

 are derived from comparatively few cases. Taking the curves in order, be- 

 ginning at old age, we notice that the old age sickness curve is much steeper and 

 lias its origin some nine years earlier than the death curve relating to the same 

 period of life. The normal curves representing the sickness in " Middle Age" and 

 " Youth " have thcir origins a little earlier than the correspoiiding death curves 

 for tlie Eiiglish N«. IV. table, but die difference is slight. In other words on tlie 

 average, death, if it comes, follows quickly on sickness in early life, but in old age 

 it may follow the modal age of sickness by even nine yeai-s. A uotioeable character 

 in the analy.sis of the sickness curve is that the proportion of sickness ascribed to 

 the "Youth" and "Childhood" groups is iinich larger than the proportion of 

 deaths which Pi-ofessor Pearson found related to the e([uivalent death groups. 



We have referred above to the fact that the old age sickness curve precedes 

 the death curve and that tho distance between them iucreases with the age ; 

 this is, of course, natural at the end of the table for sickness must come before 

 death, and the curve for the latter will therefore become in.significant at a later 

 age than the curve for the former. \Vhen we get nearer birth however it is 

 not necessary for the origins of the sickness curves to be earlier than those of the 

 deaths curves, for, if tho rate of mortality is low (most obviously wlicn it is 

 decreasing) the fact of the sickness origin Coming after tho deaths origin would 

 onl\ indicate that the incideuce of the sickness in the particular period of life was 

 such tiiat the sickness rate was increasing at a relatively greater rate than the 

 death rates. The only thing that secms necessary is that the sickness curve 

 for any group should not start later than the death curve. 



I may here digress to refer to an auxiliary table which I found useful in 

 Splitting up the/ column wlien the component part required a curve of Type III. 

 The equation of a curve of this type may be expressed as 



logioy* = log,o2/o + 7 logio (1 + a;) - 7a; log,, e, 



where the ränge on the side of the origin where the curve does not c.xtend to 

 infinity, is taken as the unit for x. Now since 1/0 can be taken as unity the right- 

 hand side of this equation may be written 7[log]o(l + a;) — a; log,,, e] and a table 

 of the function in square brackets was formed to si.x places of decimals for values 

 of X from — 1 to iö with intervals of '05. The use of such a table for findinff 

 7 and a is obvious and as it is also a help in calculating the actual curve when 



