Xolices respecting New Boohs. 235 
" Sulle Cubiche ternarie sizigetiche," G-. Battaglini : discusses 
several properties relating to a cubic and its Cayleyan, and gene- 
ralizes some theorems of Clebsch on polar conies and poloconics. 
" On the Complexes generated by two Correlative Planes,'' T. A. 
Hirst: this is connected with Dr. Hirst's paper '•'■ On the Correla- 
tion of two Planes'" (Proc. Lond. Math. Soe. vol. v.). "Nota 
sopra alcuni Iperboloidi annessi alia cubica gobba," E. D'Ovidio : 
commences with a resume of results got in the author's " Studio 
sulle cubiche gobbe," and then, amongst other matters, specially 
treats of the properties of hyperboloids through three chords of a 
cubic. " Constructions planes des Elements de Courbure de la sur- 
face de l'onde," A. Mannheim : starts from MacCullagh's generation 
of the wave-surface and construction for the normal at any point, 
and then determines the elements of curvature of the surface* (in 
this we find the author's definition of normalie, a term he employs 
elspvrhere without defining it). "Sulla integrazione delle equazioni 
a derivate parziali del primo ordine," E. Padova : is an extension of 
a method of Ampere's to any number of Variables, and shows how 
it leads (avoiding a difficulty indicated by Bertrand) to the method 
given bv Cauchv. " De fractionibus quibusdam continuis," H. J. S. 
Smith : discusses the equations P^— 2R 2 = ±1, P 1 P 2 -3E 2 = ±1 
(adopting a lemma due to Sylvester), and gives certain developments 
of square roots in the form of continued fractions. " Sopra i sistemi 
lineari triplamente infiniti di curve algebriche piane," E. Caporali : 
the object of this memoir is the solution of the principal problems 
of numerical (enumerativa) geometry which present themselves in 
the study of the triply infinite linear systems of plane curves. The 
investigation is founded on stereometric considerations ; and the 
properties obtained are got from the study of a surface represented 
point by point on the plane of the linear systems, so that the plane 
sections have for images the curves of the linear system. "Lntorno 
ad una generalizzazione di alcuni teoremi di Meceanica," V. Cer- 
ruti ; " Sugli assi di Equilibrio," Or. Bardelli ; " Sur Fequation 
de Biceati," Cr. Darbouxt : want of space forbids our noticing 
these three papers as we could wish; we must then pass on. 
" Sur deux Algorithmes analogues a celui de la moyenne Arith- 
metico-geometrique de deux Elements," C. W. Borchardt : this 
friendly letter, written on a sick-bed, applies an elegant analysis to 
what is sometimes called Schwab's series [discussed in Hansen's 
' Theory of Perturbations,' by Ctlaisher (" Solutions of Cambridge 
Senate-House Problems, 1878"), M. J. Tannery, and others]. " Sopra 
* The author says his solutions " reposent sur la representation geome- 
trique d'un element de surface reglee au moyen d'une droite auxiliaire et 
sur la representation d'un pinceau de droites au moyen d'une circome- 
rence et d'un point." 
t The author applies a covariantive property to the solution of an 
equation studied bv Prof. Cayley (' Messenger of Mathematics/ 1874, 
p. 69). 
