197 
ic ae 
2 
variable difference of phase is inscribed in a variable 
and therefore will 
a = 4 
rectangle with sides 4r cos a and 4r ard 
rotate around the centre. 
This rotation of the singular ellipses may not be confounded with 
the rotation of the whole unisson around the centre. 
In this case, interference curves are also seen by superposing a 
unisson and the same figure after rotation, — the image shows 
however slightly curved, parallel lines, cutting orthogonally the 
bisectrix of the angle between the axes, when the latier is about 15°. 
At last, it is evident, that a sufficient result will be obtained in 
combining all the conditions, above mentioned, that is: The image 
of the hyperbolas proceeds from the superposition of two concentric 
pencils of ellipses (each ellipse resulting from four vibrations). The 
beginning-curves of these pencils are an ellipse and a circle, having 
common tangents in the extremities of the minor axis of the ellipse; 
the ending-curves are short, coincident, straight lines. The curves 
between show both a regular alteration in shape and a rotation. 
The latter has an opposite sense for both pencils, but good results 
were also obtained in the case of rotation of one of the pencils only. 
When these conditions are not observed, great differences become 
immediately visible. 
So, the figure of the hyperbolas degenerates into a Maltese cross, 
when there is but a small angle between the ending-ellipses. The 
four arms of the cross point to the extremities of the major axes. 
Such a cross is also formed, when these ellipses (straight lines) are 
coincident, but differ to much in magnitude. . - 
The rotation of the ellipses being too fast, the ‘‘asymptotes” of 
the hyperbolas are curved in the same sense; when the two pencils 
have but a slight difference besides, the figure shows a pencil of 
curved radii. 
If both ending-ellipses are coincident, but too large, the figure 
of the hyperbolas is exactly formed, but the upper and the lower 
part are translated in opposite sense. 
The same remarks are applicable to the black cross around the 
centre in the image of the lemniscates. 
The here described method of moiré figures to explain interference 
curves needs not to suppose (as is done with the commonly used 
method of isophase-surfaces of Bertin), that both broken normals to 
„tbe wave-fronts follow the same way in the crystal. 
