50 ON PROBABILITY. 
with a measure of probability; and the superior probability of head falling 
the first time, as compared with either of the other two combinations men- 
tioned by him, can be accurately allowed for only by taking the sum of all 
the ways in which one of two couflicting events may occur in two experi- 
ments. As to D’Alembert’s farther observations on the possible difference i 
in the law of facility of sequence of any set of events, the only answer that can gr 
be given is, that when any such difference is observed, it ought undoubtedly 
to form an element of the calculation of probabilities ; but to suppose, as he lo 
seems to have done, that until such law is determined we are nnable to esti= at § 
mate them, is to misapprehend entirely the meaning of the results we pro- ject 
fess to deduce from it. 0f 
83. Laplace inserted several memoirs on the subject of probabilities in the slg 
Memoirs of the French Academy, which he afterwards embodied iu his splen- Was 
did work, “Théorie Analytique des Probabilités,” in which he also gave pure] 
the calculus of generating functions. The principal application which 1s the 
he there makes of it, is to the solution of the equations of differences but 
to which he reduces the questions of probability, by considering how the as L 
chances vary at each succeeding step. This is, in fact, the method, of which term; 
one of the simplest instances may be seen in Pascal's solution of the problem with 
of points, although it is there put in rather a different form. Laplace's work Ther 
contains the application of the theory to a variety of most intricate and inter- freat 
esting questions ; and independently of the results he has obtained, this book per ¢ 
is in the last degree valuable, from the specimens of refined and beautiful ana- rates 
lysis it affords. Besides the authors here mentioned, a great number have vean 
composed works on the subject of probability, not very remarkable for the Sines 
introduction of new principles or methods. The principal attention of more 
English writers has been directed to compilations on the subject of annui- for {] 
ties; and it is very much to be regretted that, with a few exceptions, a Sug? 
wanton and barbarous scheme of notation should conceal whatever may be Tesi 
valuable in their writings, nearly as much as if they were written in an then 
unknown language. used 
84.'The first complete tables of life annuities constructed in this country from foun; 
Halley’s and Demoivre’s theory were by John Richards, of which the edition in in the 
the British Museum is dated 1730.* It contains the following short but curious Nica 
historical sketch of the erroneous methods it was intended to supersede. “In n 
valuing three lives absolute in copyhold estates, the general rule was, formerly, the re 
to reckon it as a lease of twenty-one years certain, which, by the tables for that Rov: 
purpose, at 5 per cent., is worth, in ready money, 12°82 years value and no subid 
more for three lives, the first of which they esteemed worth 6 years, the enlitl 
second 4, and the third 2-82 ; so that to renew two lives in reversion of one Ey 
would cost 7 years, or oue in reversion of two, three years’ value. And this bo 
was the constant expectation, what age soever the life or lives in esse were of. Vom 
at the time of renewing. Whether this estimation of the value of leases arose ro 
from the Act of 32 Henry VIII., or was in use before, I know not; but it is Loot 
there enacted, that a lease for more than twenty-one years, or three lives, is Hs 
void: by which it seems as though three lives and twenty-one years were hand 
reckoned an equal duration, the contrary of which was very evident even wi 
before any experiments were made concerning the duration of life, and there- o 
fore this way of computing was corrected by another, which is likewise in Du 
several respects erroneous. By this other method (which is still in practice) oe 
a lease for one life may be reckoned equivalent to one of 9, 10, 11, or 12 b 
* Gentleman's Steward Instructed. London, 1930. enue 
T Lt seems more likely that the framers of the Act were guided by the pre-existing popular prejudice, than 01 We 
that they gave rise to it. fs vy