Mathematics. — “Explanation of some Interference-Curves of Uni- 
avial and Bi-axial Crystals by Superposition of Elliptic Pencils.” 
(Second paper). By J. W. N. Le Hevx. (Communicated by 
Prof. Henprik pr Vries). 
(Communicated at the meeting of October 29, 1921). 
In a former paper *), it is shown, that the interference-curves of 
some crystals — without regard to the isogyres — may be considered 
as the ‘“moiré’-images of two concentric elliptic pencils, each eon- 
taining the curves of intersection of the two parts of the successive 
wave-surfaces with the upper side of the crystal plate. 
These wave-surfaces were supposed to be homothetie and so, the 
velocities in directions, normal to the wave-fronts, were uniform. 
From experimental results it is seen, that this supposition explains 
the phenominae, observed in a polarisation-microscope, only at some 
distance from the centre, not immediately around it (fig. 1 and 2). 
For the caracteristic black cross, which appears around the centre 
with uni-axial and bi-axial crystals, is in those figures indistinetly 
to be seen. 
It is proposed in this paper to give an account of some further 
experiments, which enable us to obtain the black cross in the centre 
with a fair accurancy and so to find some further conditions as to 
the elliptic pencils. 
Consider first the figure of the hyperbolas (fig. 1). If the inner 
curves were not little circles, but ellipses, ending in short, coincident, 
straight lines, this image would become much better. For in this 
way, a nearly sufficient effect was obtained by superposing two 
excentric sets of ellipses, as is shown in my first paper. 
By causing two of the four pendulums of the former described 
apparatus to begin a very short time after the two others, the 
ending-curves of both unissons are short, coincident, straight lines 
and the results are indeed more satisfying, but not yet wholly right. 
There is another condition to be fulfilled, as was remarked with 
the following experiment. 
The name of unisson was given — according to Lissasous — to 
the figure, described by two equal pendulums, with this extension, 
that the whole family of ellipses, described by altering the phase- 
JT 
difference from 5 to 0, was also called unisson. 
1) Proc. Royal Acad. XXIX, p. 1114—1117. 
