COimECTED WITH HUMAN MOETALITT. 
531 
effect till the age of about 21 in the Carlisle mortality, and then and after, through the 
remainder of life, becomes of total insignificance ; and the third term does not come 
into appreciable effect for calculating the number of living till the age of about 80 ; 
though for anticipating the number of living vrhich -will result from some age to ages 
above 80, for the purpose of calculation, its effect cannot be overlooked when the age 
from which the anticipation is necessary is some years less than 80. And the methods 
of finding those constants which I have adopted will now be explained. Paying atten- 
tion only to the additional function Ars®, the formula will stand 
where M stands as above for and putting AL^+M^--CS*=K^, for the 
sake of brevity, and taking, in order to have two equations, in order to find the two 
constants Jc, s, two values of x, namely x—1, x—2, we shall, from Milne’s Tables having 
aLi, }Ju 2 , and from the knovm values of CS=3-92971, CS^=3-9271, and the values of Mj 
and Mg, have the value Kj and Ka,* and as we have ^a=Ki, we have 
that is, 
£ 
K 
^ and ^= — 
X£=?iKa-XK, =1-79811, and X^=l-16855, £=-62822, ^=-14742. 
These values of Ic and s being now known, we introduce the term and we shall 
have 
and consequently 
— C€ Jc ^ ; 
; 
put this =yK^ for the sake of brevity, and we shall have and in order to 
have two equations for the purpose of finding Jc and ^£, take for x the two ages of x=0, 
that is, the age of birth, and ^=-j^, that is, the age of one month, and we have the two 
equations 
y^=yKo as £®=1, and ^^^£*=^K^, 
and we obtain 
^y=-02266, ?VyyJ:=2-35526, X^£*=l-27720, X^£=9-3264*. 
It now remains to find [m, v of the expression pjf ; which only is of appreciable value 
when Tcz^ become perfectly of inappreciably small consideration ; that is, in the case 
* In deducing the above values of ^Tc^s, there were some slips of the pen: for instance, taking >&= '14042 
for ^='14742, so that Jc was taken too large, namely -02266 by '007, and should he taken therefore =‘01566 ; 
this change will require a change in the value of ^s, which is obtained by making some slight alteration in 
Milne’s date for that is to say, for the age of one month, and that change I have made in my calcula- 
tion to an increase of eight years, making L^=9475 instead of 9467, which is as likely to he correct as the 
other. Some small alteration I thought I found necessary in order not to get into imaginary quantities, and 
my calculation gives 1*43767, Xy£=7-25104, and of course the formula gives XL3^=9475 to he 
adopted, though for the first months of age the last may he retained. 
