ON PROBABILITY. 45 
1 Wey they paper published in the Philosophical Transactions in 1693. In this cele- 
8] ang brated paper, from which we must date the commencement of real knowledge 
UF 0 mak on the subject of life annuities and insurances in this.country, Dr. Halley 
0 aye has made choice of a register of deaths which had been kept at Breslau, in 
We quanti Silesia, and which had been then recently communicated by Neumann (pro- 
Agen ght bably at Halleys request,) through Justell, to the Royal Society, in whose 
uch Prop. archives it is supposed that copies of the original registers are still preserved. 
Wager (hat Before continuing our notice of this very interesting branch of the subject, 
though yt we shall mention some other important works which appeared about the 
if 1 out of same time, 
74. James Bernoulli had shown that he was not inattentive to the progress 
Kepler hag of this science by a problem which, according to the fashion of that time, he 
1 is here had published in the Journal des Scavans for 1685, in the form of a chal- 
eared i lenge to his contemporaries, This problem was to determine the chances of 
hanes. gn A and B, who are each to score a certain number of points thrown on the dice, 
NW nite A beginning with one throw, B following also with one; A then being 
¢ 0 them allowed two, and B two ; A three, and B three, and so on till the conclusion 
Ve in the of the game. ILeibnitz answered the question, and undertook to divine the 
$28 enfire analysis which had conducted Bernoulli to the solution given by him, without 
in aoher demonstration, in the Journal de Leipsic for May, 1690. 
de. shut 75. There is also a treatise by Leibnitz, on Complexions, or, as we now 
of Decase more commonly call them, Combinations, but which was not written with 
part of the any reference to the science of chances, in which this theory is so pre-emi- 
tis. if nently useful. 
The distinctive names which Leibnitz adopts, of combinations, conterna-= 
re Topi tions, conquaternations, &c., to express what we now call combinations two 
ath Tithe by two, three by three, &c., are no longer in use, except among German wri- 
ud 1603, ters, where we still meet with the terms binions, ternions, quaternions, &c. 
ott frst Leibnitz mentions Clavius as having been the first who gave, in 1583, a clear 
is et view of this theory, “not being able to find any traces of it in the Arithmetic 
i. 80m. of Cardan, to whom Schwenter refers it.” Schwenter probably alluded to 
sits of Cardan’s book, ¢ De Proportionibus,” in which the figurate numbers are 
bert Bl mentioned, and their use shown in the extraction of roots, as employed by 
ith Stifel, a German algebraist, who_wrote in the early part of the sixteenth 
1 50 asthey century. : ” " 
und witha, 76. It is not necessary to do more than mention an essay, by Craig, on the 
othe sch probability of testimony, which appeared in 1699, under the title of “Theolo- 
Lo Hl gize Christiana Principia Mathematica. This attempt to introduce mathe- 
Rn matical language and reasoning into moral subjects can scarcely be read 
a with seriousness ; it has the appearance of an insane parody of Newtons 
a Principia, which then engrossed the attention of the mathematical world. 
et ia "The author begins by stating that he considers the mind as a movable, and 
fh arguments as so many moving forces, by which a certain velocity of suspicion 
or is produced, &c. He proves gravely, that suspicions of any history, trans- 
vei mitted through the given time (ceteris paribus), vary in the duplicate ratio of 
Ll the times taken from the beginning of the history, with much more of the same 
Ni kind with respect to the estimation of equable pleasure, uniformly accele- 
# a rated pleasure, pleasure varying as any power of the time, &e. &e. 
77. An anonymous essay in the Philosophical Transactions of the same 
IGE year, and of not much greater value, may perhaps be attributed to the same 
author. The theory there laid down is, that a fraction of the doubt which 
always remains as to the truth of a narrated fact, after any number of con- 
current witnesses, is always removed by an additional testimony. This 
obviously false theory was taken up at a much later period, by Bicquilley, in