1224 
The “‘isophase” surface of Bertin, by means of which interference 
curves usually are explained, is the locus of points with a constant 
difference of retardations : 
1 1 
2 Wm 
In this formula d means the length of the way in the crystal, 
supposing, with Brrtin'), that the bifurcation of the ray is neglected, 
V the velocity of light in the medium, V, the velocity of the 
ordinary and JV, that of the extra-ordinary ray in the erystal. 
anh d d 
V being constant, we may write ia a aT constant. 
i 2 
The centre of the ellipsoid of polarisation is supposed to be in 
the centre of light in the lower side of the plate. 
Let P be a point of the image of interference curves in the upper 
side of the plate, where d= d,. 
d s 
Suppose Vv =m, then d, =mV,, so P lies on a surface p= m V, 
1 
(m = constant), homothetic with the blade 9 = V, of the surface of 
the wave. 
d 
Suppose — =n, then d‚ =nV, and P lies also on the surface 
Vi 
vy=nV, (n=constant), homothethie with the blade 9 = V, of the 
surface of the wave. 
The surfaces 9 = mV, and 9=nV,, each being cut by the upper 
side of the crystal plate in a pencil of curves C, and C,, when m 
and n are variable, it is evident, that each curve of the image is 
the locus of the points of intersection of those curves of the pencils, 
which correspond to m—n = constant. 
The forms, into which the wave is found to diverge, are a sphere 
and an ellipsoid for uniaxial crystals; so the sections with the upper 
side of a plate, cut parallel to the optic axis, are a circle and an 
ellipse, having the same tangent in the extremities of the minor 
axis of the ellipse (the section in the upper side is an approximate 
form of that in the lower side of the plate). 
For the wave in a biaxial crystal, we find two surfaces, which 
are in fact one continuous surface. A plate, cut perpendicular to 
the first diameter, gives two ellipses, one of which is wholly sur- 
rounded by the other. 
Thus, it may be said generally, that inter ference curves may be considered 
as “watered figures’ of two concentric pencils of ellipses EK, and E,. 
1) Ann. de Chim. et de Phys. (3). 63 pp. 57—92, 1861 en Sér 2. T 63. 1861. 
