264 ON THE LIGHT OF THE MOON AND OF THE PLANET JUPITER. 
on the very day of inferior conjunction, as a narrow crescent, distant but 5° or 6°, or 
even less, from the Sun, notwithstanding the intense illumination of the sky, is evi- 
dence of a notable deviation from Lambert’s theory; for in this situation, not only is 
the illuminated area exceedingly small, but its light, according to that theory, will be 
intrinsically fainter than in other positions. The reason of this discrepancy is plainly 
because the theory does not take into account the light regularly reflected, which is 
considerable, even for opaque bodies, when the angle of incidence and of reflection is 
small. If the surface of Venus were polished, it would be, when distant 74° from its 
inferior conjunction with the Sun, nearly six times brighter than at'its greatest elonga- 
‘tion; on the other hand, if opaque, by Lambert’s formula, it would be above eighty 
times fainter, which is altogether at variance with observation.* It may be inferred, 
as a consequence of this deviaticn from the theory, supposed to be due to a tendency 
to a regular reflection, that the albedo of Venus, computed from observations about the 
time of greatest brilliancy, and especially as it approached its inferior conjunction, will 
be too large, that is, it will exceed its average value in other positions. 
For the purpose of finding the value of y for the Moon, if we suppose an element 
de presented perpendicularly to its rays, the quantity of moonlight incident upon it 
will be, as in (24), 
The whole quantity incident upon the concave surface of a sphere, having a radius 
^, and circumscribed about the Moon as a centre, will be represented by 
f= A. £s fede 
But if the Moon everywhere shone with its full phase, the total light would be 
JS dil = e B odo 
Since H s and fo, de = 4 v a O,, we have, 
E o 4e 
(40) ¿= a fide 
By means of the table of values of log. H,, given on page 256, we may compute the 
* During the total eclipse of the Sun, July 18, 1861, Venus, being then at its inferior conjunetion, was seen 
by Bruhns with the naked eye, and was considerably brighter than Jupiter. Astr. Nach. 1292, p- us 
