1817.] Royal Institute of France. 235 
breathing than organs of smell; and nothing was found resembling 
the internal structure of nostrils. The organs of hearing, without 
and within, were sought for in vain. 
—_—- 
ROYAL INSTITUTE OF FRANCE. 
Account of the Labours of the Class of Mathematical and Physical 
Sciences of the Royal Institute of France during the Year 1815. 
Maruematicat Part.—By M.le Chevalier Delambre, Perpetual 
Secretary. 
MEMOIRS APPROVED BY THE CLASS, 
ANALYSIS. 
(Continued from p. 159.) 
Lectures on Analytical Mechanics given at the Polytechnic 
School, by M. de Prony. Second Part, which treats of the Motions 
of solid Bodies; or, an Elementary Treatise of Dynamics. 
The first part of this work contained Sfaéics, and we announced 
it in our notice for 1810. The second, which treats of motion, is 
divided in quite a similar manner: the laws of motion of a point of 
matter, of a system, or of a body of a form variable according to 
certain conditions, are successively explained in it, the whole being 
preceded by preliminary notions, in which the author has been at 
great care to establish in the most general analytical manner the 
fundamental principles of dynamics. After having explained every 
thing relating to time and its measure, he combines this species of 
quantity with linear extent, considering them as two indeterminate 
quantities, whose relations may be expressed by equations, according 
to which all the possible motions of a material point may be classed. 
The most simple of these relations gives uniform motion, from 
which proceeds velocity; and from this notion generalized he draws 
one of the fundamental equations applicable to every kind of motion, 
The second equation, which is equally general, flows equally from 
purely analytica) considerations ; so that we see an important theory 
established independent of the consideration of moving forces, by 
means of which we can, when certain phenomena are given by the 
fact, discover all those which are not already given, 
The author applies this theory to the vertical motion of heavy 
bodies, whether in a vacuum, or through a resisting medium. 
He analyses successively the phenomena of motion which take 
lace above the surface and in the interior of the earth, and shows 
i these accurate formulas may be deduced from those of Galileo, 
He proceeds to the consideration of force, He distinguishes that 
whose effect is instantaneous from that which is subjected to the law 
of continuity. He demonstrates the laws which result from inertia, 
