1811.] 
not live 30 years;—the number living 
- at the age of 20, in Mr. Baily’s third 
table is 814, and at the age of fifty 581— 
the fraction $84, therefore, expresses 
the probability chat the person in ques- 
tion will be alive at the end of that 
term, and the fraction 223 shews the 
probability of dying in that time: both 
those fractions added together or $24 
$ig¢ will be equal to unity, as itis cer- 
tain that the party will be either alive 
or dead at the end of the term. 
I should have been at a loss to dis- 
cover in what way Mr. Hawes obtains 
his numerators, if I had not observed 
that in those examples, where he makes 
the term for which the probability is 
to be found, equal to the.difference be- 
tween the age given and the oldest age 
in the table of mortality, from which the 
calculation is to be made, the nume- 
rator is the same number that is given 
in the table of expectations deduced 
from the same table of mortality; as, 
for example, he makes the ‘probability 
that a person, aged fifteen, shall live 
eighty years, 42°5924 the numerator of 
which fraction is the number given in 
Mr. Baily’s third Table, as the expecta- 
tion of a life of fifteen; and from hence 
I conclude, that the mode which he so 
confidently offers as a substitution for 
the present, is nothing more, than in 
the case of single lives, the making the 
number of years, for which the pro- 
bability is to be calculated, the denomi- 
nator, and the expectation of life. for 
that term the numerator. By tle expec- 
tation of life, I mean the share of life, 
which, according to any table of ob- 
servation, belongs to any individual of 
e given age, or in other words the ave- 
rage number of years which they will, 
one with another, enjoy. 
Mr. Hawes has forgotten, that by at- 
tempting to overturn the present mode 
of estimating the probabilities of life, 
he tries to overturn the way by which 
his own numerators are calculated, 
which are nothing more than the sums 
‘of the fractions expressing the chances 
of living one, two, three, &c. years, 
to the end of the term named. In the 
case of joint lives, I need not under- 
take any investigation, but shall con- 
tent myself with observing that he has 
been guilty of a palpable error, which 
at once shews his whole system tw be 
founded in absurdity, and maintained 
by ignorance. I mean, his making the 
probability that two lives shall continue 
together in existence to the end of a 
égyui, greater than the probability thac 
Doctrines of the Probabilities of Life, 
421 
one of them shall live to the end of 
the same term, In his first example 
of his own method, he makes the chance 
of a person, aged twenty. being alive at 
the end of thirty years 23:8988 years; 
that a person, aged forty, shall be alive 
at the end of thirty years, 23,4058 years, 
and the probability that both snail con- 
tinue in being together to the end of 
the same term 24:85281!!_The same 
result is produced in every example he 
has given. 
It is now almost time for me to leave 
Mr. Hawes, ‘whose futile attempts will 
avail little, in opposition to the doc- 
trine laid down by such men as Halley, 
De Moivre, Simpson, and other emi- 
nent authors, and so ably treated by 
Mr. Hawes’s contemporary Mr. Baily, 
who has certainly combined in his va. 
luable treatise on the subject nearly 
all the information to be found in pre- 
ceding authors, in addition to his own 
improvements, althought it is to be wish- 
ed that he had blended with his talent 
some greater portion of liberality, 
would however, before I close, inquire 
of Mr, Hawes in what way writers on 
this branch of science, have overstep- 
ped the bounds of probability; and 
why, their principles are not correct. 
Mr. Hawes scems by his sneers, at 
what he calls the “mathematical faith. 
ful,” to suppose that the science may 
be made independent of the mathemas 
tics; to that [ shall observe, that had> 
he been able to investigate the sub- 
ject mathematically, five of your cos 
lumns would not have been occupied 
with the tissue of absurdities, we have 
seen from his pen; nor would he have 
ssked so many unmeaning questious, 
which have no other tendency than to 
perplex his readers and to involve the 
question in obscurity. By what imae 
ginary law of Nature does Mr. Hawes 
make kis deductions from registers of 
life and death? Can he suppose that 
a system laid down by the authors he_ 
has mentioned, will yield to his insig- 
nificant attack, which is unsupported 
by either reason or argument? Had 
your correspondent stated his objec- 
tions, with becoming modesty, and de- 
ference to acknowledged talent; and 
offered his system in a manner free 
from arrogance, he might have been 
considered ingenious, or at the worst 
have passed unnoticed; but his style 
is such as cannot fail of exciting emo- 
tions of contempt for his vanity, and 
pity for his ignorance. 
Puito abate tot 
fe) 
