420 
~ indication of imbecility ; the “ embrace” 
of them by Mr. Morgan, an example of 
the effect of dotage; the “assent” to 
them by Mr. Baily, a manifestation of 
good-natured credulity; and, finally, the 
“conviction of the fallacy of their doc- 
trine, by Mr. Hawes himself, a splendid 
and memorable instance of the efica- 
cious power of nature when properly 
consulted. 
T cannot conclude, Mr. Editor, with-. 
out observing that, in the “ objections” 
of Mr. Hawes, tlie name of Mr. Baily 
holds .a conspicuous place. Why this 
gentleman’s name should. have been so 
frequently mentioned, I cannot con- 
ceive, unless with a view to depreciate 
the value of his works; permit me there- 
fore, Sir, to state, that I have read and 
studied the greater part of Mr. Baily’s 
work, on the Doctrine of Life Annu- 
ities and Assurances,” and that I have 
no hesitation in declaring it to be by far 
the most excellent performance which 
we have on this subject. In the the- 
oretical part of this work, by his great 
skill in analysis, and by a more happy 
notation, the author has demonstrated 
the principles of the doctrine of annu- 
ities, in a manner which delights, no less 
by its elegance, than by its scientific 
accuracy; and in the practical part, the 
very extensive and apprepriate list of 
examples, and the valuable collection of 
tables, while they display the unwearied 
exertion of the author for the perfection 
of his work, render his book of the bighest 
utility, not only to all the Assurance 
Companies in the kingdom, but also to 
every individual who has any interest in 
annuities of every kind, or in the re- 
newal of leases. 
Norwich, 
April 17, 1814, 
R. Saryvt. 
rh 
Zo the Editor of the Monthly Magazine. 
SiR, 
sb your last Number I observe a letter 
signed by Nathaniel Elawes. in which 
he asserts the incorrectness of the 
present mode of determining the pro- 
babilities of life. Your correspondent, 
instead of demonstrating that the emi- 
nent authors whom he names, have pur- 
sued a wrong principle, offers a mode 
of his own invention, and appears to 
conclude that, because the results pro- 
duced by the two methods disagree, 
his own must be correct, and that the 
other must necessarily be founded in 
error. i et 
‘J should hardly think itmecessary to 
attempt to show the fuulity of Mr 
Reply to Mr. Hawes? Objections to the recewed [June 1, 
Hawes’s ‘system, which, to any person 
couversant with the science, must, at 
one view, appear unfounded, if I dic 
not think it essential that there should 
not be two opinions on so important 2 
subject; as you must be aware of the 
great extent of business that is daily 
transacted in this metropolis upon the 
principles that it is Mr. Hawes’s object 
to overturn. , 
Mr. Hawes has very scdulously kept 
us in the dark, as to the foundation 
upon. which his ¢uperstructure is raised; 
and the only effectual mode of showing 
its folly will be, by contrasting it with 
the simplicity and clearness of the doc- 
trine laid down by Dr. Halley, and the 
other authors named. He asserts, (to 
use his own words,)that the subject of 
the present investigation is that of time, 
that is, its component and fractional 
parts:” now it appears to me evident, 
that not “time,” which is made up of 
divisions fixed, and not subject to mu- 
tation, but the probability of a yiven 
event happening, er not happening, in 
any one, or more, of those divisions of 
which time is composed, is the point in 
question; and that given event being 
death, we can only determine the pro- 
bability of its happening, or not, by a 
reference to those tables, that show 
the progression in which given numbers 
have died off, from birth, to the latest 
probable period of human existence. 
‘The fraction that gives the proba- 
bility of a person bemg in existence 
at the end of any term, as expressed 
by every author who has treated on the 
subject, is this, the denominator shews 
the number taken from a table of mores 
tality, living at the aye of the person 
and the numerator, the number living 
at an age older than the given age by 
the term stated: the reason of this may 
be given in few words; in any table of 
mortality the number, therein stated to 
be alive at a given age, shows the num- 
ber of chances for a person of that 
age, both living and dying, in any term 
the number alive at an age older, by 
that term, than the given age, shews 
the number of chances for. living. te 
the end of the term; and the difference 
between those two numbers, shows the 
number of persons that die in the 
term, or the chances for not living so 
loug. This will be made perfectly fa- 
miliar by an example; let it be required 
to find the probability that a person, 
aged 20, shall live 30 years, (asin the 
first example quoted by. Mr, Hawes) 
and, also the probability that he shall 
not 
