238 Proceedings of Philosophical Societies. | [Marcn, 
The fourth section treats of the motion of bodies and systems of 
bodies whose form is variable. 
This part of mechanics, notwithstanding the efforts of the 
greatest mathematicians, is far from possessing all the resources 
necessary for the solution of problems relative to systems, whether 
solid or fluid. From these considerations, and the impossibility of 
establishing a close connexion between the questions to be treated 
of in succession, M. de Prony formed the resolution of making 
this section consist of problems gradually increasing in difficulty, 
and connected with each other as much as the nature of the subject 
will permit. 
The object of the first is the variation of the duration of the 
oscillations of a compound pendulum, when we displace a part of 
the mass of the pendulum. The author demonstrates the formulas 
which he had given in the Connaissance de Temps. He takes for 
one of his examples a problem which had occupied Euler and the 
Bernoulli. He examines the case of the oscillations of a heavy 
body obliged to move in a curve, and fixed to an immoveable body. 
He determines in this case the curve which possesses the property of 
tautochronism, and obtains a curious result relative to the cycloid. 
It is impossible for us to give to these details an extent proportional 
to their importance. We will satisfy ourselves with saying that the 
volume is terminated by an exposition which includes the demon- 
strations of all the great principles of mechanics. ‘These different 
principles had been mentioned and verified several times in the 
body of the work ; but had only been considered under particular 
points of view. ‘The author thought proper to reserve the general 
demonstration till his readers were sufficiently prepared for it by 
anterior studies. 
M. Charles Dupin, an officer of Maritime Engineers, Foreign 
Associate of the Institute of Naples, and Correspondent of the 
Class, presented the following works :— 
PRINTED WORKS. 
Memoir on the Re-establishment of the Marine Academy.—M. 
Dupin, who in the Ionian Isles exerted all his efforts in the organi-~ 
zation of the first academy ever founded in these celebrated coun- 
tries, endeavours in this new publication to hasten the revival of an 
institution of this kind applied to one of the most important 
branches of the public power and prosperity. He endeavours to 
prepare for this edifice more secure foundations, and better com- 
bined than those of the first creation. He points out and explains 
the means of spreading through the practice of our ports the theo- 
retic perfections which originate in the capital, and to furnish in 
return to the scientific men who reside in this centre of civilization 
the maritime data to be procured only at sea and in the arsenals. 
He points out the investigations necessary for completing the mari- 
6 
