1616.] Royal Institute of France. 145 
eastern part of the mountains of New Granada; finally, a geolo- 
gical picture of the singular volcano of Jorullo, which sprung out 
of the earth in the month of September 1759, surrounded with 
several thousands of volcanic cones of 100 toises in height. 
Tables of the Divisors for all the Numbers of the 2d Million. 
By M. Burckhardt.—We have already spoken of this work, which 
appeared on the first of January, 1814. We take the opportunity 
of announcing that the third and fourth millions are in the press. 
Treatise on the Differential and Integral Calculus, by M. Lacroix; 
2d Edition, revised and augmented, volume second. About 850 
pages. Paris, Madame Veuve Courcier—The author, in a short 
advertisement, gives the motives which led him to deviate in some 
points from the plan pointed out in the preliminary discourse to the 
first volume. In his opinion the general theory of the conditions 
of integration ought to follow immediately the methods relative to 
the integration of functions, with a single variable quantity ; be= 
eause it is to this integration that is reduced that of any differential 
functions whatever, when they satisfy the conditions of integra- 
bility. In what concerns partial differential equations, he has 
made some considerable transpositions, in order to prevent repeti- 
tion, and to show more clearly the properties and the connexion 
of the different processes proposed by the great mathematicians of 
our time, to treat this kind of equations. By this new arrange- 
ment, by his remarks on the integrals to which this new edition 
gives new developements, he has endeavoured to throw light on a 
subject which had not yet been sufficiently elucidated. He is at 
pains to point out the difficulty. 
The calculus of variations is treated with all the details which 
the importance and singularity of the method required. To make 
its nature sufficiently understood, it beeame necessary to point out 
the principal attempts that have been made to unite it with the 
principles of the differential calculus. This the author has exe- 
euted in his last chapter, where the method of variations is pre- 
sented in all the generality and simplicity which the first symbols 
employed by M. Lagrange, and the consideration of infinitely 
small quantities, give it. 
Philosophical Essay on Probabilities, ly M.le Compte Laplace. 
A Volume in 4to. of 96 pages, Paris, Madame Veuve Courcier.— 
M. Laplace, after having in a first work treated this interesting and 
difficult subject like a consummate mathematician, and having singu- 
larly enriched it by new methods, more general and fruitful than those 
of the great mathematicians who had made it the subject of their 
meditations, examines it here in a point of view purely philoso- 
phical. Without the assistance of analysis, without supposing the 
feader acquainted with any thing more than arithmetic and the first 
elements of algebra, he explains the principles and the general 
results of that theory. He makes it eriginate from suppositions 
the most simple, combined so as only to require the degree of 
attention of which every man is capable, who has the habit of 
