Mr. Sylvester on the Optical Theory of Crystals. 461 



a second sponge, and connected with the wire O, a rapid suc- 

 cession of shocks will of course be experienced during the re- 

 volution of the disc A, in consequence of the interruptions 

 which are occasioned in the circuit by the indentations in its 

 circumference. The application of the instrument in various 

 experiments, particularly those on the dead body, will be 

 readily suggested. 



I will not trespass further on your space than to state that 

 the figure is in size one third of that of the instrument, that 

 the copper disc and wires are amalgamated to ensure good 

 contact, and that by a little alteration the apparatus may be 

 employed for the rapid changing of the poles of a battery in 

 electro-magnetic operations. 



Sidmouth, Sept. 27, 1837. 



LXIV. Analytical Development of FresneVs Optical Theory of 

 Crystals. By J. J. Sylvester, Member of St. John's Col- 

 lege, Cambridge. 



T^HE following is, I believe, the first successful attempt to 

 ■*■ obtain the full development of FresnePs Theory of Crystals 

 by direct geometrical methods. Hitherto little has been done 

 beyond finding and investigating the properties of the wave 

 surface, a subject certainly curious and interesting, but not of 

 chief importance for ordinary practical purposes. Mr. Kel- 

 land, in a most valuable contribution to the Cambridge Philo- 

 sophical Transactions *,has incidentally obtained the difference 

 of the squares of the velocities of a plane front in terms of the 

 angles made by it with the optic axes. 1 have obtained each of 

 the velocities separately, and in a form precisely the same for 

 biaxal as for uniaxal crystals. 



I have also assigned in my last proposition the place of the 

 lines of vibration in terms of the like quantities, and that in a 

 shape remarkably convenient for determining the plane of ^ po- 

 larization when the ray is given. For at first sight there ap- 

 pears to be some ambiguity in selecting which of the two lines 

 of vibration is to be chosen when the front is known. If (p) be 

 the perpendicular from the centre of the surface of elasticity 

 let fall upon the front, t t i n the < es made by the front with 

 the optic planes, s t e u the < es between its due line of vibration 

 and the optic axes, I have shown that 



cos,, = / P-J*V «ni, cos .„ = */*!=£!. f«i» 

 s/ a 3 — c* sin i u V a* — c* sin i, 



so that all doubt is completely removed. The equation pre- 

 * See Lond. and Edinb. Phil. Mag., vol. x. p. 336.— Edit. 



