French National Injlitute. \%^ 



propofed by d'Alembert: by C. F. Nieuport. The object of 

 this problem- is to determine the direction of the force which 

 would keep in equilibrium and immoveable a body of anv 

 figure whatever, traverfed by a (lack and flexible thread 

 having its extremities attached to two fixed points. 



The analyfis of Nieuport conduces to a refult of which 

 d'Alembert had only a faint idea; that is to fay, he con- 

 cludes that in all cafes the direction of the force divides into 

 two equal parts the angle formed by the direction of the two 

 parts of the thread which are without the body. 



It rcfults alfo from this analyfis, that if the groove which 

 affords a paffage to the thread be of a curvilineal figure, the 

 folution will not be more complex, and the equation will al- 

 ways retain the fame form. This d'Alembert did not ven- 

 ture to affert. 



Demonjhation of a geometrical theorem on eflimating the 

 folidity of the hemifpherical arch of Viviani : by C. Tedenat, 

 profejfbr of mathematics in the Central School of Aviyron. — 

 On reading the Integral Calculus of Lacroix, publifhed a few 

 years ago, he conceived the idea of determining algebraically, 

 by a method of Euler, the folidity of that part of a hemi- 

 fpherical arch of which Viviani determined only the furface. 



In the fecond volume of the Memoirs of the Inftitute for 

 the year 6, it is feen that C. Boffut had announced to the 

 Oafs the folution of the fame problem, of which he gave 

 merely the refult, promifing to give the calculation on fome 

 other occafion. This he indeed did fome time after, at the 

 end of the fecond volume of his Integral Calculus: two folu- 

 tions of the problem may be feen there; the fecond of which 

 is exceedingly fimple. 



C. Tedenat, having read in the above memoir this extenfion, 

 which may be given to Viviani's problem ; a circumftance 

 not before mentioned by any geometrician, was defirous of 

 proving that he himfelf had made the fame remark, and with 

 that view fent to the Inftitute the folution here announced, 

 and which, in regard to the definitive refult, is agreeable to 

 that of Boffut. 



Longitude of Florence. — C. Lalande read a memoir on the 

 longitude of Florence, the pofition of which was very uncer- 

 tain. He has learned from new obfervations received from 

 Ciccolini, and which he has calculated, that the difference 

 between the meridians of Paris and Florence is oh. 35' 40 J . 



Secular motion of Venus. — This memoir was alfo by La- 

 lande, who has found by the laft inferior conjunction of this 

 planet, that the epoch of the longitude is exact as well as 

 the equation of the orbit, and that there is no change to be 



M 4 made 



