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. Theory of Fresne. New formule, founded on that theory, for the velocities and polarisations of 
a plane wave or wave-element. New method of deducing the equation of FresneL’s curved 
wave, propagated from a point in a uniform medium with three unequal elasticities. Lines of 
single ray-velocity, and of single normal-velocity, discovered by FrEsNEL...... is/dtetniciatetelatote 128 
. New properties of Fresneu’s wave. This wave has four conoidal cusps, at the ends of the 
lines of single ray-velocity ; it has also four circles of contact, of which each is contained on a 
touching plane of single normal-velocity. The lines of single ray-velocity may therefore be 
called cusp-rays; and the lines of single normal-velocity may be called normals of circular 
CONTACE occ cccislsiniewecddeiesicicccveccscccecuacccaseessedes Mis vateietusela's ste avelnereraters dite 6192 
. New consequences of FresNeEv's principles. It follows from those principles that crystals of suffi- 
cient biaxal energy ought to exhibit two kinds of conical refraction, an external and an internal ; 
a cusp-ray giving an external cone of rays, and a normal of circular contact being connected 
WILLMAN LC PNARGCONE s\sieiaiatelo(a(elslsrt=/e/elaisslaisieis\sslais.c c'e'sicleiei= =/<isa'e's sipiareleinlelsievetelsiatets pelo aie 's 134 
. Theory of conical polarisation. Lines of vibration. These lines, on FresnEL’s wave, are the in- 
tersections of a certain series of concentric and co-axal ellipsoids .........22eeeeeeeeeeeeeee 138 
. In any uniform medium, the curved wave propagated from a point is connected with a certain 
other surface, which may be called the surface of components, by relations discovered by M. 
Caucuy, and by some new relations connected with a general theorem of reciprocity. This new 
theorem of reciprocity gives a new construction for the wave in any undulatory theory of light : 
and it connects the conoidal cusps and circles of contact on FRESNEL’s wave, with circles and 
cusps of the same kind upon the surface of components ....+.seeeeeeeeseseeeseeeetes 
