474. JS. *W«. Gibbs— Double Refraction and Circular 
Since this factor varies but slowly with 4, it may be neglected, 
if its omission is compensated in the values of K and KY. The. 
formula being only approximative, such a simplification will 
not i aia render it less accurate. 
without any such assumption as that contained in 
the finer paraire , we may easily obtain formule for the ex- 
perimental determination of @ and @’ for the optic axis of an 
uniaxial crystal. Considerations analogous to those of § 13. 
of the former paper (page 271 of this volume), show that in 
differentiating equation (89) we may regar and @ as con- 
stant, although they may actually vary with 4) This equation 
may ‘be written 
OM @. : Bx O' pe 
cai Seeley (41). 
Therefore, 
6 2 
a) 
=—27'°9'” (42). 
a(ys) 
When @ has been determined by this equation, @ may be 
aoe from the preceding. 
. If we wish to represent g geometrically, = U, and U,,. 
we Aa construct the surfaces 
Aw’ + By’? + 02? + ny2+F2e+Gry=+1, (43): 
the coéfficients * B, ete., being the same by which ¢ is ex- 
pressed in terms 0 L , M*, ete. The numerical value of g, for 
any direction of the wave- ‘normal, will thus be represented by 
the square of the reciprocal o the radius vector of the surface: 
drawn in ee: same direction. The positive or negative charac- 
ter of g must be separately indicated. There are here two 
eases to be Saeed If the sign of g is the same in all. - 
directions, the surface will be an ellipse, and we have only to 
know whether all the values of ¢ are to be taken positively or 
all negatively. But if g is positive for some directions and 
negative for others, the surface will consist of two conjugate 
hyperboloids, to one of which the positive, and to the other the 
negative values 
39, The manner in which the ellipsoid (24) may be par- 
tially determined i the relations of symmetry which the 
medium may possess, has been sufficiently discussed in the for- 
mer 
With m reupest to the quantity g, and the surfaces which 
determine it, the following principle is of fundamental import- 
ance. If one y is identical in its internal structure with 
the image by reflection of another, the values of gin corres- __ 
