COraECTED WITH HUMAN MOETALITT. 
533 
which will give an easy means of regularly finding the value of L^, the number of per- 
sons living out of the number L,,, the number taken for the birth, as a base, for every 
year of age to 100, or beyond that if the accuracy can be depended on beyond 100 ; 
und, what will be interesting to the reader in favour of the formula, it will give the 
number agreeing with Miuste’s Table living for the monthly portions of the deaths of 
children below one year of age with a very satisfactory agreement, considering that per- 
fect accuracy in Milne’s Table cannot be expected to exist, owing to the scanty means 
he could have had for that purpose. In a paper I presented for consideration to the 
fourth section of the International Statistical Congress, already referred to, held during 
the week commencing on 16 th July last, “ On the one uniform Law of Human Mortality 
from the age of Birth to extreme old age, and on the Law of Sickness,” which was honoured 
by its publication among its reports, I only offered hints, without the abstruse mathe- 
matical portions being brought forward of this paper which I am venturing to offer to this 
Society; which I felt was partly a duty I had to perform ; namely, to add my small services 
to the Congress; especially in consequence of the insufficient state of my health ever 
since and before I attempted to search into my former published and unpublished papers 
on the interesting subject of Vital Statistics, and useful Application of the Eesults, with 
a view to improve, and add matter of interest to the subject ; which I fiatter myself I 
had treated on with some approbation from the scientific public ; and being doubtful 
if I should be able to offer even the paper I had so far completed for the approbation 
of the Society, I therefore feel satisfied that my having given these slight hints will not 
be a cause to render this attempt to bring these few pages before the Society unaccept- 
able, especially as, since the hints were vrritten, I think I have discovered a greatly 
improved form of the formula of mortality, and a more satisfactory one. The formula 
of mortality which in these hints was given was 
XL^=constant+^e*— P^, being =fl. 
where all the values on the right-hand side of the equation are constant except from 
birth to extreme old age, including fl, w, and u ; and 5 very nearly I said unity, which 
value it was taken ; but I stated I thought it could not be exactly unity, the reason for 
which doubt was that P, having been put for the common logarithm of the number 
whose common logarithm is 6, raised to the power if Q were exactly 1, the 
number whose common logarithm is Q would be exactly 10, and the equation, of which 
the aforesaid equation is the logarithm, would be 
L,=constant X X C"' X D'’- ; 
A, B, C, D being constants, and P,=10^^ \ and it appeared to me that nature 
could not be governed by the conventional notation of the decimal arithmetic. 
Art. 14. In the paper presented to the International Congress, I gave a Table, 
resulting from the above formula, of persons living to the extent of life, from birth to 
the age of 100, and for the age of 1, 2, 3, 6, 9, and 12 months, which appeared to 
