228 F. A. P. Barnard on the Zodiacal Light. 
or R/T”, that of the circle of the shadow, it is plain that the 
extremities of the illuminated arch will always be found in 
the circumference RT, or R’T”’; but the question of the visi- 
bility of either of these extremities will depend on the relation 
of the plane of the ring to that of the horizon. For conven- 
ience, let the circle R'l’ be called the limit of illumination, or 
more briefly, the limiting circle; and in order as much as pos- 
sible to simplify the illustration, let the sun be supposed to 
be in the equinox, and the observer at the equator. At the mo-. 
ment of sunset, the limiting circle will be in contact with the 
other by its upper or preceding limb. As the sun sinks, the cir- 
cles will intersect; and in what follows, we may distinguish 
three cases, according as the limiting circle is equal to, less, or 
greater than, the circle of the horizon. If the two circles are 
equal, the intersection will continue until the sun’s depression 
becomes 90°, when the planes of the circles will coincide. Dur- 
ing all this time it is possible that one of the illuminated cusps 
of the ring may be above the observer’s horizon, and therefore in 
a situation to be seen. There is, in fact, but one position which 
can possibly be given to the ring, by which it may be kept 
wholly invisible ; and that is, a position at right angles to the 
equator, which in the case in hand is exeluded by the condition 
that the plane of the ring shall coincide with the ecliptic. Onl 
one cusp, however can, in this case, ever be seen at a time; but 
as the first cusp disappears at midnight, the second one will im- 
mediately make its appearance, and continue to be visible until 
dawn. At the moment of sunrise, the limiting circle will touch 
the horizon again, but will make the contact, this time, by Its 
following limb. 
If the limiting eircle be less than the circle of the horizon, 
then the sun descending as before may bring into view one of the 
cusps immediately ; and in a right sphere it would do so, though 
not necessarily in an oblique one. When the centre of the lim- 
iting circle, however, reaches the horizon, one of the cusps must 
appear, whatever be the observer’s latitude ; and both of them 
may do so. But the appearance of the second is not a matter © 
hecessity until the limiting circle touches the horizon by 1ts fol- 
lowing limb. At the depression of 90°, the planes of the two 
circles will be parallel, and the two cusps will be equal; after 
which the preceding one will diminish and the following one will 
increase; the phenomena preceding the dawn corresponding 19 
inverted order to those which followed the twilight. The ob- 
servations made by Mr. Jones of the two luminous columns 
simultanec isible at midnight would indicate that, if they 
were sps of an interrupted ring, the case which actually 
-hature is that which is here described. : 
~The third case supposes the limit of illumination to be greater 
than the horizontal circle. In this case, the intersection of the 
ELS ey Ee eae ere ee Ce ee 
