256 ON THE LIGHT OF THE MOON AND OF THE PLANET JUPITER. 
A graphical projection of the values of log. E gives d, = 0°.9705 for the distance 
from the disc Z at which its illumination is equal to that received from the mean full 
Moon. Substituting d,, we may derive from the above, normal values of log. H, or 
the logarithms of the quantity of light received from the various phases of the Moon 
at its mean distance from the Earth and Sun, taking the light of the mean full Moon 
as the unit. 
peg Log. H, = — © 
20 e 7.224 
40 x 8.049 
60 - 8.574 
80 e 8.974 
100 x 9.291 
120 E 9.551 
140 » 9.769 
160 = 9.931 
180 sE 0.000 
In order to compare these with the results derived from Herschel's observations, we 
must subtract from the logarithms of the Moon's apparent brightness the constant 
3.543, representing the light of the mean full Moon according to his scale, and apply 
the proper corrections for reducing the amount of moonlight on each date to the mean 
distances of the Moon from the Earth and from the Sun. There are not sufficient data, 
precisely at the opposition, among the Cape observations, for a direct calculation of 
this constant, but it may be inferred from the whole series of their differences * from 
log. H. 
The comparisons which may be used for this purpose are as follows: — 
Log. Hp. . Cape Obs. Diff. Wt. 
e 1099 9.324 9.368 —0.044 7 
121.7 9.574 9.560 -]- 0.014 8 
131.8 9.681 9.711 + 0.030 9 
135.7 9.724 9.725 = 0.001 9 
143.7 9.805 9.778 -- 0.027 10 
158.7 9.990 —— 9.868 - -+ 0.052 18 
167.0 9.964 9.991 — 0.027 6 
179.8 0.000 0.157 — 0.157 2 
* Results of Astronomical Observations, Cape of Good Hope, p. 367. 
