44 ON PROBABILITY. 
not capable of being reduced to a mathematical reasoning ; and when they ir 
cannot, it is a sign our knowledge of them is very small and confused ; and 03 
where a mathematical reasoning can be had, it is as great folly to make S 
use of any other, as to grope for a thing in the dark when you have a x 
candle standing by you.”— There is likewise a calculation of the quantity, | 
of probability founded on experience, to be made use of in wagers about 7 
any thing. The yearly bills of mortality are observed to bear such propor- ly 
tion to the live people as 1 to 30 or 26; therefore it js an even wager that 
one of thirteen dies within a year (which may be a good reason, though not 
the true, of that foolish piece of superstition,) because at this rate if 1 out of; 
26 dies, you are no loser.” 
71. Long before mathematics had been applied to this science, Kepler had 
formed the same accurate notion of the real meaning of chance as is here 
expressed by Motte. In his dissertation on the new star which appeared in 
1604, after mentioning that some were of opinion it came by chance, and 
illustrated their meaning by supposing a set of dice to be thrown an infinite 
number of times, in which it would necessarily happen (according to them) 
that any required number would at Jast be thrown, he says that, even in the 
case adduced, those are very unthinking who look upon the events as entirely 
without a canse. “ Why does six fall in one throw and ace in another ? 
Because this last time the player took up the die by a different side, shut his 
hand upon it differently, shook it, threw it in a different manner, or because . 
the wind was blowing differently upon it, or it fell on a different part of the . 
board. There is nothing in all this, which is without its proper cause, if 
any one could investigate such niceties.”* 
72. The bills of mortality, mentioned in Motte’s book, are registers 
which began to be kept in 1592, of the annual number of deaths in the 
city of London, which, with some intermission between 1594 and 1603, 
have been regularly returned to the present time. They were first 
intended to make known the progress of the plague; and it was not 
till 1662 that Captain Graunt, a most acute and intelligent man, con- 
ceived the idea of rendering them subservient to the ulterior objects of 
determining the population and growth of the metropolis; as before his 
time, to use his own words, “ most of them who constantly took in the 
weekly bills of mortality, made little or no other use of them than so as they 
might take the same as a text to talk upon in the next company; and withal, 
in the plague time, how the sickness increased or decreased, that so the rich 
might guess of the necessity of their removal, and tradesmen ‘might con- 
jecture what doings they were like to have in their respective dealings.” 
Graunt was careful to publish with his deductions the actual returns from 
which they were obtained, comparing himself, when so doing, to * a silly, 
schoolboy, coming to say his lesson to the world (that peevish and tetchie 
master,) who brings a bundle of rods, wherewith to be whipped for every 
mistake he has committed.” Many subsequent writers have betrayed more 
fear of the punishment they might be liable to on making similar disclosures, 
and have kept entirely out of sight the sources of their conclusions. The 
immunity they have thus purchased from contradiction could not be obtained 
but at the expense of confidence in their results, 
73. These researches procured for Graunt the honour of being chosen a fel- 
low of the Royal Society, and, to pass over Sir Win. Petty’s «“ Observations,” 
as bearing less directly on our subject, were undoubtedly the cause which led 
Halley to consider the duration of human life. as he himself owns. in the 
* De Stella novi. - Prag, 1606,