230 F. A. P. Barnard on the Zodiacal Light. 
hundred miles; or as, under a favorable supposition, we have de- 
termined it, 186 miles above the earth’s surface. The arc-radius 
of the circle of the horizon would in this case be 179 14’; and 
that of the limiting circle 72° 46’. Now, as the zodiacal light is 
always most conspicuous just after twilight, 5. 
or just before the dawn, let us assume the 
depression of the sun to be 18° below the 
horizon. The centre of the shadow, which 
isthe pole of the limiting circle, will be [—-=s=5 
equally elevated. In the figure, AOB is “——*—— 
the earth, O being the place of the observer. 
HR is the rational, and H’R’, the sensible horizon. HZR is the 
imaginary concentric sphere, generated by the revolution of the 
ring, and P is the pole of diurnal rotation. S$ is the point opposite 
the sun,.or the pole of the limiting circle, which must always be © 
somewhere in the circumference of a small circle, DE, parallel 
to the horizon, HR, and distant from it by an arc equal to the 
sun’s depression. Now if Q be taken as the extremity of the 
light, any where upon the circumference of the limiting circle 
(not drawn) of which S is the pole, the four points involved in 
our discussion are P,Q, S, and Z. ZS is the complement of the 
depression of the sun; PS is the co-declination ; ZP, the co-lat- 
itude ; and SQ, the arc-radius of the limiting circle. be- 
ing in the plane of the ecliptic, the sun’s place in longitude will 
furnish the means of determining the angle PSQ ; and the de- 
pression will enable us to find PSZ: consequently, ZSQ, or the 
angle made by the ecliptic with the vertical passing through the 
sun will become known. Consequently ZQ, which is the zenith 
distance of the cusp, as seen from the centre, C, will be ascer- 
tained. By reduction to the surface, O, we shall obtain the ap- 
parent direction of the light. 
we now assume the point Q to be somewhere upon the cit- 
cumference of the small circle, H’/R’, we shall be able to find 
what is the maximum angle, ZSQ, made by the ring with the ver- 
tical, at which the cusp can be seen by the observer at O. And 
comparing this with the angle made, at different seasons, by the 
ecliptic with the vertical, at the assumed depression of the sun, 
we can determine the various aspects which the light ought to 
assume. Taking, for example, the latitude of Oxford, Missis- 
sippi, which may be roughly stated at 34° 30’, it will appear that 
the summit of the light ought to be in the horizon, when the an- 
gle between the ecliptic and the vertical passing through the sun, 
at the close of twilight, is 18° 4’ ; and also that the point where 
the summit is last seen, is distant from the sun, in azimuth, more 
than 90°. The ecliptic will at this time have an apparent 10- 
ion Of 7° 9’ to the vertical drawn to its setting point, an 
int will differ from the sun in azimuth less than six de- 
