590 Analysis of Books, #c. 



1. That the phenomena of capillary attraction are due to mole- 

 cular action, modified not only by the form of the surfaces, according 

 to the theory of Laplace, but also by a peculiar state of compression 

 existing in the superficial stratum of the fluid. 



2. That a sphere is the only figure of equilibrium of a fluid 

 uninfluenced by any external force. 



Note on the Roots of Transcendental Equations, by M. Poisson. 



IN this paper the author shews that a rule given by M. Fourier*, 

 for ascertaining the existence of impossible roots in any equation, is 

 not generally applicable to transcendental equations. He then 

 explains the connexion between the roots of an equation of n 

 dimensions, X=0, and the parabolic curves represented by the 

 series of equations 



' 



in which m has successively all values from m==0, to m=n 1. 



In conclusion, the author corrects an opinion he had previously 

 entertained f, viz., that transcendental equations consisting of as- 

 cending powers of a;, with increasing numerical denominators, might 

 be assimilated to algebraical equations, by neglecting the terms in- 

 volving high powers of <r, but with very large denominators. 



Extract from a paper on the integration of partial differential 

 Equations, by M. A. L. Cauchy. 



THE author of this paper explains a method by which he considers 

 that some formulae which he has given in the 19th Number of the 

 Journal de. VEcole Poly technique, may be extended to the integra- 

 tion of linear partial differential equations, with variable coefficients. 



Extract from a Memoir on some series analogous to that of La- 

 grange, on symmetrical functions, and on the direct formation of 

 the equations which result from the elimination of unknown 

 quantities between given algebraical equations; by the same 

 Author. 



IN this extract a method is given for finding the sum of the m th 

 power of the roots of an equation of n dimensions, and for ex- 

 pressing the products of all the roots in terms of the sums of their 

 different powers. 



* Thlorie Analytique de la Chaleur, p. 373. 

 t Memoires de TAcadSmie, torn. viii. p. 367. 



