ON THE LIGHT OF THE MOON AND OF THE PLANET JUPITER. 251 
With the exception of the last, which depends, as has already been remarked, upon 
an isolated observation, made with the sky partially clouded, there is a satisfactory 
agreement between the two series. It will be interesting to compare with the above 
results from observation the following values furnished by the formule of Lambert 
and Euler, and the empirical formula (22), which, as we have seen, represents the 
changes from the half to full Moon with tolerable precision. 
LAMBERT. EULER. 
Obs'd log. Hp. Log. ree Log. BIER Log. sin. } v. 
£e = 0 — 0 — o — 00) iced OD 
20 7.224 7.653 8.749 5.488 
40 8.049 8.536 9.068 7.204 
60 8.574 9.037 9.398 8.194 
80 8.974 9.374 9.616 8.848 
100 9.291 9.613 9.768 9.305 
120 9.551 9.785 9.875 9.625 ' 
140 9.769 9.908 9.946 9.838 
160 9.951 9,975 - 9.987 9-960 
180 0.000 : 0.000 0.000 0.000 
It is plain that neither of the theoretical expressions accords with the observations, 
though the last is barely tolerable between v — 90° and v = 180°. Lamberts, which 
succeeds better in the whole range from new Moon to full, still makes the half-Moon 
from two to three times too bright. And if his theory is true for most opaque sub- 
stances, it would seem, as has been already remarked, that, in the disposition of the 
asperities which reflect the sunlight from its surface, the Moon has a peculiar con- 
stitution. "This, too, is indicated in the fact, that the borders of the full Moon are 
disproportionately bright, contrasted with the centre. It deserves attention, in con- 
nection with the subject, that Secchi* has noticed a peculiarity in the polarization of 
moonlight, which he compares to that observed in reflection from glass-paper. It may 
be worth while to notice, too, that the Moon is little if at all exposed to the disinte- 
grating action of water or of an atmosphere; hence it is not unlikely that its surface, 
instead of presenting the dull, weather-worn aspect of the Earth, may rather resemble 
that of bright, fresh-fractured rocks, with their usual crystalline lustre, and that this 
condition may contribute to the appearances in question. 
The quantity of light received from Venus, when at the distance — 1.000 from the 
-.* Monthly Notices Astr. Soc., Vol. XX. p. 70. 
