^ Frejick Nalionul Instiiiite. 355 



M, Des5aerts, extending this latter observation to the 

 bladders to which naturahsts liavc given the name of luj- 

 datides, and which they consider as real animals, thence 

 concludes that this opinion of naturalists is very doubtful; 

 and he announces that he proposes to combat it in a memoir 

 whicli he will soon present : he flatters himself that he shall 

 be able to show, from powerful authority, that the melan- 

 choly decision of the hydatides being an incurable disease, 

 is void of foundation. 



A great and important work in medicine has appeared 

 this vear. It is the medical anatomy of M. Portal, in 

 • which, besides a new and detailed description of the human 

 body, he has given an account of every thing he hai- ac- 

 quired by long and extensive practice in regard to licsions 

 of the organs, and their relation to the apparent symptoms 

 of diflerent aflections. 



MATHEMATICAL PART, 



Bij M. Delamkrk, perpetual Secretanj. 



GEOMETUV. 



Huygens has given in his treatise De Horolngio Oscllla- 

 torio the two following thetnems, which may be applied to 

 all solid bodies : The ctntrc of oscillation and thai <if .^/isptn- 

 sio» arc alivaijs reciprocal one with the other ; the same body 

 is always isochronous lo it-idf when it oscillates around pa- 

 rallel axes taken at equal distances from the centres of gra- 

 vity. M. liiot has given to these theorems a remarkable 

 extension. 



All these parallel axes form the surface of a right cyhn- 

 der, the axis of which passes through the centre of gravity. 

 But the analytical expressi.ni under which M. Eiot presents 

 the theoix-m'of Huvgens sliowed him that an arbitrary in- 

 clination might be given to this axis, provided that the radius 

 of the cylinder shoidd be also changed in a proper manner. 

 J3v these means there will be oht'aiued, acctnding to the 

 di'H'erent values of the inclination, an inliuile number oi 

 cylinders the edges of which have the same properties as 

 those of the jjrimitive cylinder, liut tins i-^ not all : the 

 axis, without changing its incliiiation, may de.-.enbe a coni- 

 cal surface arouJul"its']>ri!niti\e position, which still multi- 

 , plies the number ot the cvlinders already found, as many 

 times as there mav he conceived ridgie- on the biu'tace ot 

 tlic cone. ' 



The same analvtical expression being oF the second degree 



in regard lo the radius of the evliuder, or, what amounts to 



Z 1 llu* 



