CONNECTED WITH HUMAN MOETALITY. 
52T 
For the selection 40, 60, 80, we have 
^c?=3-75272, -=^=-030345 , 
c_(?=8-6409 , c^^=:-069872 , 
For the selection 60, 70, 90, we have 
-=6Z=3-71469, -^^=-0334825, 
a_(Z=8*55534, e_^=-077096 , 
For the selection 60, 80, 100, we have 
-=(?=3*75272, -^^=-0270605, 
=-(Z=8*74186, =-^=-062309 , 
-=(-^)=3-46094, 
-^(-^)=3-82316, 
_=(-^)=3-18036, 
_^(_'^)=3.54258, 
_=(-^)=2-10984, 
_=(_^)=2-47206. 
-0028903. 
^=-•0066552. 
^=_.0015148. 
0034880. 
^=-•012878. 
7=--029652. 
The selections give, for the analytical expression of corresponding to the several 
values of a below, the expressions below : — 
a 
10 
20 
30 
40 
50 
60 
8-9343-{-160927+-004912^+@75^^+®762^^+®58a;^+@ 35a;^ &c.}. 
8-8127-{-22279+-00662a;+®97995^'^+®9924a;^+®75a?^+@44a;^+@2^®}. 
8-8127- {T7468+-0077443:r+®171678^^+®2537a;^+@2812ar^+ ®24:X^+@2x^}. 
8-6409-{-10888+-007608a?+@2658.2;^+®6191^^+®108a;^+®12a:^+@17^®}. 
8-5534-{-16470+-012696^+@48943^+@1258a;^+®2424^^-f®3738^^+@48.^®}. 
8-74186-{-54134+-033930a^+@1051a;^+®218826a;^+®3396^^-f ®423a?^+@44^5j 
Where observe were a, 10, 20, 30, 40, 60, 60, and were w taken in each case =0, the 
above expression would be respectively the values of cl_L,o, cl-L^o, c-Lgo, ci-Ljo, c^-Lgg, 
which would become 8-9343 — -160927=8-77337 ; 8-9374— -22279=8-71462 ; 8-8127 
—-17468=8-3887; 8-6409— -10888 = 8-5320 ; 8-6534— -16470=8-3887; 8-74186 
— -54134=8-20052: the reader is already informed that the symbol, for instance, 
®3738, signifies, -000000003738. 
Art. 12. And now returning to the assumed formula 
{ef^ .x—h . >>.5'o}, 
of which, in the case of the Carlisle mortality, I have already given the value of C, e, 
and putting C€ — ^L^=M^, we shall have the equation 
and consequently 
.x—k.Kqo=XM.^; 
and using the \ital rule of three, that is to say, selecting three values of x to find the 
three unknown quantities e, h, and say x=m, x=:m+n, x=m-{-2n, we have the 
three equations, 
e'^.{m-h).Xq,=x-M.^, e”^^^(m+n-h).Xq,=xM^^„, e^+^’^{m+2n-h).Xq,=xM^^,„. 
MDCCCLXII. 4 Q 
