146 Proceedings of Philosophical Societies. [Fus. 
reflecting. He then applies the principles to the most important 
questions ef life, which, in general, are nothing else than pro- 
blems of probability. He treats successively of hope, of games, 
of the unknown inequalities which may exist between chances sup- 
posed equal ; of the laws of probability which result from the inde- 
Jinite multiptication of events; of tie calculation of probabilities 
applied to the inquiry into events and their causes; of the means 
which we must choose among the results of a great number of obser- 
vations; of the tables of mortality and the mean length of life; 
of marriages and any kind of associations; of benefices depending 
on the probability of events; of the choice and decisions of assem- 
blies ; of the illusions in the estimate of probabilities ; of the differs 
ent means lo approach to certainty. 
The work is terminated by an historical notice on the calculation 
of probabilities, in which the attempts and discoveries of the ma- 
thematicians who have applied themselves to this subject are stated 
_ and appreciated with great impartiality. Nobody was better en- 
titled than Laplace to draw up this notice, nor more interested that 
it should be well done. 
Theoretical and practical Astronomy, by M. Delambre; three 
vols. 4t0. Paris, Madame Veuve Courcier. 1814.—We have an- 
nounced the abridgement of this work, which appeared in 1813, 
in one volume 8vo. We have said that the plan of the two trea- 
tises is the same. Jt remains to point out what was suppressed in 
the abridgement. What distinguishes the complete treatise is, in 
general, a great variety of questions, of solutions, and formulas, 
more details on the construction, use, and verification of instru- 
ments. Thus, in the article Spherical Trigonometry, will be found 
a number of formulas, expressing the relation between five and six 
parts of the same triangle, the analysis of the different methods in 
use for the resolution of triangles, a more complete and methodical 
collection of differential expressions, and, finally, a proof triangle 
calculated with the greatest detail, and which may serve to_ verify 
all,the formulas imaginable. In the article Gnomonics, besides the 
new formulas for the description of the horary lines and the arcs of 
the signs, the whole gnomonic plan is reduced to a single formula, 
which has only one linear variable quantity, which only affects one 
of the terms of which it iscomposed. In the article Refractions, 
there is a synthetieal solution of the problem of the shortest 
twilight, much more complete, and much easier, than all those 
drawn from the differential calculus. “Ihe chapter on The Diurnal 
Motion offers solutidns, mostly new, of the most useful problems ; 
that of corresponding heights is terminated by tables of correction 
of a new form, followed by useful remarks on the use of logarith- 
mic tables, which we wish to substitute for tables calculated in 
natural numbers. When treating of The Elliptical Motion of the 
Earth, will be found the,comparison of the different hypotheses 
contrived to account for the inequalities of the sun, new solutions 
of the problem of Kepler, a great number of elliptic formulas, and 
