59 
of Edinburgh , Session 1866-67. 
of the ring; and an attentive examination shows that its curvature 
is much less than that belonging to the projection of the ring to 
the same distance. As the curved wire is farther removed, the 
appearance of the dark line becomes that of an elliptic arc taken 
from near the end of its shorter axis ; and when the ring is taken 
to the distance proper for distinct vision, the dark band becomes 
circular, becomes, in fact, the true image of the ring itself. 
If we continue to remove the ring to a greater distance from the 
eye, the curvature of the dark hand is increased, and presents the 
appearance of a portion of an ellipse taken from near the end of 
the major axis. Its motion across the luminous band is evidently 
greater than that due to the movement of the ring. 
Let us now bring the luminous slit within the distance for dis- 
tinct vision, or, better, let us remove the optical focus to beyond 
the luminous slit, by wearing a pair of deep concave glasses, and 
we shall find that the motion of the dark line is opposite in direc- 
tion to that of the ring, and that the curvature is also turned the 
other way. 
It was this reversion which drew my attention to the phenomena; 
and, not recollecting of having seen it noticed, I thought it worth 
while to bring it before the Eoyal Society. 
4. Note on Determinants of the Third Order. By Professor 
Tait. 
Hamilton long ago showed that if we have 
a — ix + jy + hz , 
ft = ix i + jy i + hz v 
y = ™ 2 + jy 2 + kz 2 , 
then 
S . afty 
x y z 
x i y\ z i 
X 2 2/2 Z 2 
This opens up an exceedingly simple quaternion path to the 
proof of various properties of determinants of the third order. 
Several of those I subjoin have long been known, some, however, 
