350 



" This new ellipsoid touches the old one at the ends of the 

 given mean axis ; but it also cuts the same old or given ellip- 

 soid, in a system of two ellipses, contained in planes perpen- 

 dicular to the asymptotes of the focal hyperbola. 



" If the semiaxes of the given ellipsoid be a, b, c, the 

 common distance of the i^o foci of the new or derived ellip- 

 soid (of revolution) from the common centre of the two ellip- 

 soids, is expressed by the formula 



V(a^-&^) V(6^-c^) 

 ^ ^{a?-b^ + c^) ■ ^^> 



" And I venture, although with diffidence, to propose the 

 name of the two medial foci, for the two points thus deter- 

 mined on the mean axis 26 of the ellipsoid a, b, c. If their 

 vectors be denoted by + 6, the equation of that original ellip- 

 soid may be thus written : 



T(Xi + £) + T(Ai-£) = 26; (2) 



or thus, 



T(Xi-£) = i + Z.-i S.eXi; (3) 



where 





11, 0, p, having the same significations as in notes recently 

 read ; while e may perhaps be called the medial excen- 

 TRiciTY of the ellipsoid aba. 



" In a future communication I may be induced to return 

 on the quaternion analysis employed, and to submit to the 

 Academy some account of it." 



Mr. M. Donovan concluded his paper on the Universal 

 Vitality of Matter. 



He remarked, that the title of his paper on the Universal 

 Vitality of Matter had led some persons to imagine that he 

 believed every kind of matter to be endued with life, under- 

 stood in the common acceptation of the word, than which 



