196 
The beginning-curve was the circle, inscribed in the square upon 
the amplitudes, the ending-curve was a diagonal of this square. 
A further extension is given by continuing the figure (the diagonal 
being run through), till another circle is described, with smaller 
radius, in consequence of the decrease of amplitudes, due to friction. 
We will call this figure „continued unisson” — it shows a super- 
position of a larger and a smaller unisson and therefore interference- 
curves, which prove to be ellipses with their major axes in coïnci- 
dence with those of both unissons (fig. ITI). 
This set of interference-ellipses is altered in a remarkable way, 
when the resistance of one of the composing movements increases. 
This may be obtained, with the apparatus used, by means of the 
screw-weight at the end of a ruler. 
Successively, the ellipses are transformed into a flame-shaped image 
(fig. IV), then a black cross is formed around the centre (fig. V) 
and at last a set of hyperbolas appears (fig. VI), which is most 
plain, when the angle between the major axes of the beginning- 
and the ending-ellipse is between ; and 5: 
‚Increase of resistance of one of the composing movements induces 
a faster decrease of one of the amplitudes and so, the ellipses are 
no longer inscribed in squares but in rectangles. The major axis of 
each ellipse coincides with the diagonal of the circumscribed rect- 
angle. In this way, a rotation is caused around the centre, joined 
to the alteration in shape, already mentioned. 
When the continued unisson is considered as a superposition of 
two common unissons, the rotations of the latter are in an opposite 
sense. 
The principle of rotation arises immediately from the mathematical 
interpretation of the phenomenon. 
In my first paper is already said, that in a superposition of two 
concentric pencils, the ellipses result from four vibrations. 
Each pencil being given by 
x =rcos(y + a) + r cos (p + ¥) 
y=rsin(p + B) + rsin(p + 9) 
or by 
; ree 
e= 2r cos — f cos G rs 
—ù o 
yer Bel 5 sin (7 + Br ) 
2 
and considering, that generally a—y 4 8—49%, the ellipse with the 
