554 
ME. B. GOMPEETZ ON THE SCIENCE 
This Table was not given in the paper written for the (late) International Congress, but 
was calculated for the present, from the formula — being 
put for all the qualities except w being constant from birth. 
Art. 28. It remains now slightly to touch on the law of sickness, though the subject is 
already mentioned in the paper I presented to the Congress, in consequence of a simi- 
larity, as far as I have had data to discover, with the law of mortality. I gave the formula, 
but not the investigation of that formula ; but I gave Tables of comparison with the 
sickness stated to have occurred in different societies and in different places, which appear 
to be extremely satisfactory as to the approximate agreement with the stated results. The 
formula I gave is as follows : — If S'*' be the number of weeks of sickness due to a person 
of .r in the Society, the log of S^=A-fBC*, where A, B, C are apparent constants for a 
long period, to be found by the vital rule of three, from the stated sickness prevailing 
at three selected ages ; and here the apparent constants are evidently not truly constant, 
as their values will slightly change with the selection. The formula S^,=A.Bj‘^"' has the 
— \q^ 
same form as L,r=D.^|" , the theorem of mortality, and, as in that theorem, the elements 
A, B, C, though apparently constant for a less time, depend on three selected ages for 
the determining their values, and are only apparently constant, but afford for a long 
time near approximations to the amount of sickness which occurs in different societies. 
The values of A, B, C of the formula, as determined from statements of societies, I gave 
in my paper presented to the International Congress, with Tables showing the near agree- 
ment with the statements of those societies. I quote from that paper as follows : — 
Selected ages, 25, 45, 65, from Mr. Axsell, all England. 
Selected ages, 25, 45, 65, Town : 
XA=T-72778; aB= 2*6772 ; xC=-020433. 
Selected ages, 25, 45, 65, Scotland ; 
xA=l-66237 ; xB=2-4I35I ; xC=-02433. 
Selected ages, 25, 45, 65, Ansell, Town : 
XA=I-65112; xB=l-04297; xC.-=-02818. 
Selected ages, 35, 50, 65, Ansell, Town ; 
?.A=l-92937; XB=I'70942; xC= -0165265 
Selected ages, 25, 45, 65, City district: 
XA=1-84121; XB=2-47741; xC=-009206. 
Selected ages, 25, 45, 65, City : 
XA=1-84121 ; XB=1-1553 ; XC=-0301685. 
Selected ages, 30, 40, 50, Eural: 
kA=:l-85616; aB= 2-02951; kC= -0301685. 
