314 Intelligence and Miscellaneous Articles. 



uniform velocity. This cone may always be determined. For the 

 circular sections of the invariable cone coincide with the circular 

 sections of the ellipsoid of moments ; whence the cyclic axes of 

 the ellipsoid, or the diameters perpendicular to the planes of these 

 sections, will be the focal lines of the supplemental cone ; and as 

 the invariable plane is always a tangent plane to this cone, we have 

 sufficient elements given to determine it. 



From these considerations it appears that we may dispense alto- 

 gether with the ellipsoid of moments, and say that if two right lines 

 be drawn through the fixed point of the body in the plane of the 

 greatest and least moments of inertia, making angles with the axis 

 of greatest moment, the cosines of which shall be equal to the 

 square root of the expression 



L(M-N) 

 M(L-N)' 



(L, M, N being the symmetrical moments of inertia round the prin- 

 cipal axes) and a cone be conceived having those lines as focals, and 

 touching moreover the invariable plane, the motion of the body will 

 consist in the rotation of this cone on the invariable plane with a 

 variable velocity, while the plane revolves round its own axis with 

 an uniform velocity. 



Although it is very satisfactory, the author remarks, in this way 

 to be enabled to place before our eyes, so to speak, the actual mo- 

 tion of the revolving body, yet it is not on such grounds that the 

 paper is presented to this Society. It is as a method of investiga- 

 tion that it must rest its claims to the notice of mathematicians ; as 

 a means of giving simple and elegant interpretations of those definite 

 integrals on the evaluation of which the dynamic state of a body at 

 any epoch can alone be ascertained. 



In these applications of the theory of elliptic functions, the au- 

 thor has been led to the remarkable theorem, that the length of the 

 spiral, between two of its successive apsides, described in absolute 

 space on the surface of a fixed concentric sphere, by the instantane- 

 ous axis of rotation, is equal to a quadrant of the spherical ellipse 

 described on an equal sphere moving with the body, by the same 

 instantaneous axis of rotation. 



The last section of the paper is devoted to the discussion of that 

 particular case in which the axis of the invariable plane is equal to 

 the mean semiaxis of tbj ellipsoid of moments. 



XLV. Intelligence and Miscellaiieous Articles. 



ON ANHYDROUS NITRIC ACID. BY M. DEVILLE. 



M DUMAS presented to the Academy in the name of M. De- 

 • ville. Professor at the Faculty of Sciences of Besan^on, the 

 first results of his researches on the action of chlorine on the anhy- 

 drous salts which oxide of silver forms both with organic and inor- 

 ganic acids. 



