2^2 Proceedings of Philosophical Socieiics. [March, 



Paris ; the other, by M. Chomereau, tailor at Brie-Comte- 

 Robert. — Committee, Messrs. de Prony and Molard, Secretary. 



The following is the conclusion of the report : 



" It is possible that Messrs. Beck and Chomereau may have 

 been anticipated on some points by those who have treated of 

 the same subject before them, but we are not the less obliged to 

 them for their efforts to submit the art of the tailor to rules that 

 tend to render perfection and economy compatible. We think 

 their zeal and their talents deserve praise from the Academy." 

 • Essai/ upon a general Principle in Mechanics ; by M. Binet. — 

 Committee, Messrs. De Laplace, Poisson, and Fourier, Sec. 



" The author principally considers the proportion between the 

 powers and the areas described by the radii vectores, round a 

 fixed centre. He denominates the fluxion of the area traced by 

 the radius vector the areolar velocity, to distinguish it from the 

 linear velocity, which the moving body actually describes in its 

 trajectory line. He calls the sum of the products of the masses 

 by the squares of these areolar powers the areolar vis viva, and 

 determines the mathematical relation of these quantities. If the 

 power that acts upon a moveable point be represented by a right 

 line given in magnitude and position, and there be drawn upon 

 this line, as on a base, a triangle, whose summit represents the 

 fixed centre, this figure will represent the force of rotation, the 

 plane of the triangle being that in which it exercises its action. 

 If the moveable body passes from the place it occupies into 

 another infinitely near, its radius vector will describe an nifinitely 

 small area, the plane of which may difi^er from that of the rotary 

 power. If on this last plane the area described is projected, the 

 projection will represent the virtual effect of the force of rotation 

 estimated in the very plane of that force. This being done, it 

 may be enunciated as if it were the principal result which the 

 author attained. 



. " If the quantity of each force of rotation be multiplied by its 

 virtual effect, a,nd if all the similar products be added, the sum 

 will represent the instantaneous increase of the whole vis viva, 

 relatively to the areas described, or the sum of the products of 

 each mass by the square of the velocity by which the area was 

 increased. By thus determining the element of the total vis 

 viva for every instant which follows, and by adding those ele- 

 ments together, the integral will express the increase that the 

 vis viva receives during any given time. 



" This proposition is entirely similar to that which expresses 

 the linear vis viva. The same analysis that shows what these 

 propositions have in common, shows also in what manner they 

 differ. Kepler, to whom we owe the discovery of the elliptic 

 motions of the planets, found at the same time, by an assiduous 

 comparison of observations, that the radius vector of a planet 

 described areas proportional to the times. Newton afterwards 

 ascended from the knowledo'e of the mathematical laws deduced 



