206 Objections to Doctrines adopted by Mr. Baily, [April 1, 
given term,” is a doctrine that was sug- 
gested by Dr. Halley, adopted by Mr... 
De Moivre, adhered to by Mr. Simpson, 
confided in by Mr. Dodson, espoused by 
Dr. Price, embraced by Mr. Morgan, 
and assented to by a recent writer, Mr. 
Barty. The purport of this letter 
is, to represent the fallacy of such a 
doctrine. The definition of a fraction 1 
take to be this: the numerator denotes 
the number or quantity, and the deno. 
minator the distinguishing name of what 
is numbered. The subject of the present 
investigation, being that of time, thats, 
its component and fractional parts, it, 
follows, that the measure of the proba. 
bility of the dyration of baman life must 
he expressed by. a fraction, whose deno- 
minator is a. period of time, composed of. 
a specific number of years, and, whose 
numerator is a portion of such period, 
composed of a less number of years, and 
@ fractional part of a year. 
In the first example of Mr. Batty’s 
fiyst practical question, chapter xi. 
he asserts: ‘ the probability that a. per- 
son, whose age 1s 20, shall attain to 
the age of 50, or live 30 years, is, 
according the observations, of M. De 
Parcieux, as given in table 3, equal to 
581 
—re 
314 
whose age is 40, shall attain to the age 
of 70, or live SO years, is, accord~ 
ing to the same observations, equal 
And the probability that a person, 
to But the probability, that both 
those persons shall live to the end of 
} 531 ae 
30 years, is equal to aie multiplied by 
310 ! 180110, 
——: that is, equal to —-——, 
O57 5547 98 
By consulting Nature; in preference to 
my Own imagination, or to-any received 
doctrine, I find the probability that: a 
person, whose-age is 20, shiall attainto the 
age of 50, or live 30-yeers, is, according 
to the observations.of M. De Parcieux,. 
as given in Mr. Baily’s third: table, 
25.6689 
<a instead of 
30.0000 
581 
equal to 
21.3882 oot 
30; 0000, 814, 
And the probability that a person, whose 
years, 
years, as per fraction 
3 
' ble 14th, equal’ to se) 
age is 4Q, shall attain to the age of 70,, 
or liye 3Q yeaus, is, according’ to. the same.. 
, , 23.4056, 
observations, equal to Sy oopg Sls 
4 
tion . T hus ever y ste : 
657 : Ps m true 
knowledge, affording a glimpse of whag 
lies next beyond it, in the gcale of nae 
ture, the same unerring law evinces, the 
probability that both those persons shall 
live to the end of 30 years, is equal to 
24.6580 ; 10.1034 
———_ years, instead of ——— 
30.0000 80.0000 
; 581X310 
years, as per fractions heeabalne 
aaa 814K 65T 
= "534798" 
It appears to me, that the most es- 
sential point of consideration attached to 
this subject has been wholly overlooked 
by every author whose name I have 
mentioned ; namely; to keep within the 
verge of probability, Had this been ate 
tended to, that anomalous mode of pro» 
cedure of multiplying causes without 
necessity, as evidenced in Dr, Halley’s 
sixth and seventh uses of his Breslau 
Table, could never have been introduced 
into the science; nor the fallacy of sup- 
posing that a year (instead of being come 
posed of certain portions of time) was 
made up of a continually fluctuating 
number of human beings, as taught b 
the same author, in the second use of 
the same table, and relicd on, as well as 
amplified, by every celebrated author.om 
the subject since. , 
In his second example, page 356, Mr, 
Baily aflirms: ‘‘ The probability thata man, 
aged 46, shall attain to the age of 56, or live 
10 years, is, according to the observatia 
ons made in Sweden, as given: in tae 
And' the pro. 
5991 
bability that a woman, aged 40, shall: 
attain to the age of 50, or.live 10 yearsy. 
ig, according ta the same observations, 
4027 ha 
¢ 4 Buti t ili 
rr ut the probability, 
that both those’ persons shall’ live 10! 
8096 Hy 
ears, i to ——- multiplied, by: 
years, is) equal Pesce aatulaaaiae by 
12467592 5 
18889408 
Now the probability that a: man, aged. 
46, shall attain to the age: of 56, er lives 
40. years, (asin the aforesaid), exampley: 
9219 
T,find equal to 70,0000 
equal to 
4027 
that is, equal to 
years, instead of 
Be es 
we 
