NOTICES AND ABSTRACTS 
OF 
MISCELLANEOUS COMMUNICATIONS TO THE SECTIONS. 
MATHEMATICS AND PHYSICS. 
On a MeOiod of definite Iniegralton, B}f George Boole, M.A. 
Sur k Principe du dernier Mttltiplicateur dans les Prohlemcs de Mcamque. 
By M. Bobchardt. 
On a new 7'hewy of the Polarization of Light. 
By the Rev. Professor Challis, M.A., F.H.A.S,. 
In this theory the ather is regarded as a continuous fluid substance, and is treated 
on hydrudyuamical iirincipice. By means of a new general equa ion 
‘ I'ydTodynamics. which ihu autJinr has discovered, he shows that • filament ot me 
Tajuwrse vibrations. In n ray of common light the transverse muu.;.. .= .*• 
JJ^ pasBing through the axis of the rav, and is alike in all directions from me 
i m a idaoc.polarii^cd ray the tninsverse motion is in planes not passmg iroug 
^ Mil j Mil i,j an clliiiticallv nolarir-cd ray the transverse vibrations are elliimcai. 
•'‘■Iwior Challis hn* extended his theory to the pbfDnomena of doub ft 
2 ! rapthod which involves a new llieory of the dUpvrsion of light Ho the 
of elasticity to be that of an cllinsoid, which is nut in accordance with l res- 
* ditory of double refraction. The equation of the wave-surface is, however, me 
>n Freind’s theory. __ 
On the Thmrif of Ju/i/ilibriu/n of Floating Bodies. 
By M. Davihow \roinmuiiicated by Prof. Brasclimauii). 
theory gives all positions of equilibrium for any floating 
the geueml theory of stability of equiUbnum, with then 
^ to floating bodies The detemination of all 
to analysU. Dupin resolved this problem 
O^om^trie et dr Micanique,’ but M . Davidow baa giv g 
I tile problem with numerous apiilicationa. j.nmcrzed 
h-9uilihrium-porition$ of Floating Ihdtes. A y amoved 
Hid U ‘‘nown. in equilibrium when the Sara- 
H anij“ with that of the immerged volume is perpendicular to the 
”l”^‘t‘o*»8 suffer some little change if we it 
Hre»xift, '®to one fluid and partly into another the air, fimfl a mutual 
ft' particle, of tl.e floMlns tody and ft”'”'a 
■'^Pdlary action, &c. The investigation of the equihbnum-p^ 
