F, A. P. Barnard on the Zodiacal Light. 235 
But about 24 hours before midnight, the other branch should 
appear. Its apparent length at midnight should be 72°, and the 
apparent altitude of its summit 21°. At dawn, this arch should 
have attained a length of more than 108°, and an altitude ap- 
proaching 66° at its middle point, its inclination to the horizon 
being about 624°. Its base should be 26° south of the east 
point, and 574° distant in azimuth from the sun. It is evident, 
therefore, that on this supposition, the light would usually be 
very far apparently from the ecliptic. 
Nor will the case be much improved, if we suppose no lateral 
parallax to exist ; for though, by this means, we may reduce the 
apparent place of the phenomenon to that in which it is actually 
observed, by so doing we shall only render the discrepancy be- 
tween theory and observation, in regard to the conspicuousness 
and magnitude of the phases, more striking. To investigate 
this case geometricall y, We must suppose a plane passing through 
the observer's eye, and parallel to the ecliptic, to intersect our 
lmmaginary sphere. ‘The intersection will mark the locus of the 
: light. But, if the ring is to be regarded as a hollow cylinder, 
| J then as, in the new position of the luminosity, it is a small circle 
a of the sphere, we should, if we aimed at extreme accuracy, in- 
ie Crease the radius according to the formula, 
R= 9000? + 3956. sin ZD’, 
in which R is the radius of our imaginary sphere concentric with 
the earth; Z D is the zenith distance of the nonagesimal ; 9000, 
the radius heretofore assumed ; and 3956 the radius of the earth. 
With this new value of R, we should calculate again the arc- 
mit of the luminosity, and, OQ is the line 
Mi its apparent direction from the observer. — 
fom the latitude, the sun’s place in the — 
