284 M. \V. Haidinger on the lodo-quinine Compound, 

 is given by 



HI! - ah (4 +j i)Y-{it +ah («s +4)}" 1 - ' 



or is 



z = <!>(# — A/atf, 7/ — A/a/) -fM' (# + hiat, y + A/«/) • 

 Similarly, the solution of the equation representing vibratory 

 motion in an unlimited gas, namely, 



d*u _ zfd 2 u d*u d*u\ 

 ~dF- a ld^ + ~df *"d?J' 

 is 

 u = <£(# — hiat, y —hjat, z — hkat) + "9 (as + Aw/, y + hjat, z + AAa/) . 



The process of verification of this solution is so simple and 

 obvious, and that of derivation so easy, that they would seem to 

 recommend the form in comparison with that given by Poisson. 

 Again, the following equation occurs in the Theory of the Tides: 

 d*u Jd*u ; d*u ' <Fu\ . . 2tt /7 , , A 



^^ a \aW + aY + a^) =A8m T {Ix + my + nZ ^ vt ^ 

 Its integral is at once 



A 27T 



u= -T—g sin — (Ix + my + nz— W) + <I> -f- ¥. 



It may be observed, that the unit A must obviously be regarded 

 as extra-spatial. In fact, any directive unit, such as 



i cos a +j cos j3 + # cos 7, 

 cannot be commutative with i, j, k. 



Trinity College, Dublin, 

 July 1853. 



XLII. On the lodo-quinine Compound, investigated in its Optical 

 Relations by Dr. Herapath and Professor Stokes. By W. Hai- 

 dinger*. 



THE phenomena of pleochroism of crystals, and those of the 

 occurrence of surface- and substance-colours (Oberflachen- und 

 Korperfarbe) in one and the same individual, have often formed 

 the subject of communications which I have had the honour to 

 lay before the Academy. 



It is crystals possessing both these peculiarities that today's 

 discourse will treat of; but for the greatest part not from inves- 

 tigations which I was the first to make, but according to the 

 results obtained by Dr. W. Bird Herapath in Bristol, and Prof. 

 G. G. Stokes in Cambridge; still I have myself repeated and 

 extended them, in order to show the connexion which exists 

 between them and many of my former observations and views. 

 * From PoggendorfFs Annalen, June 1853. 



