expressive of the law of human mortality, ^c. 5^3 
Logarithm of w = 2,6020600 
Log. of/? = 0,0703997 
therefore w/? =,047039 
Log. 'of »!/?=: 2,6724597 m/>* =,055317 
Log. of mp^zz 2,7428594 mp ^ = ,065051 
Log. of 772 /?*= 2,8128591 
These logarithms of the approximate number of living at 
the ages 15, 25, 35, 45 and 55, are extremely near those 
proposed, and the numbers corresponding to these give the 
number of living at the ages 15, 25, 35, 45 and 55, respect- 
ively, 848; 773,4; 694; 612,3; and 526; differing very 
little from the table in Mr. Baily^s life annuities ; namely, 
848 ; 774; 694; 622 and 526. And we have a = 15, r=io, 
w = ,04; x(w)= 2,60206; 1—^ = — ,176; {p)= 
— a —a 
,00703997; Hg)= , and is negative; 
^ ^ (g) = X(. 04 ) — 15 X, 00704 — X ( ,176) = 1,35095 ; 
k{d) = X(L^) — ^=3,9284 +,22727=3,1557;.-. X(LJ = 
S,i 557 — number whose log. is (1,25095 + ,00704 x), for 
the logarithm of living in Deparcieux' table in Mr. Daily's 
annuities, between the limits of age 15 and 55. The table 
which we shall insert will afford an opportunity of appre- 
ciating the proximity of this formula to the table. 
Art. 9. To interpolate the Swedish mortality among males 
between the ages of 10 and 50, from the table in Mr. Daily's 
annuities : 
3 Y 
A ^Lj^) =2,92840 
— 77 * = ,04 
77?/? = — ,04704 
2,84136 
— 77 ?/?* = —,05532 
2,78604 
— 77 ?/?* = — ,06505 
2,72099 
MDCCCXXV. 
