ON THE LIGHT OF THE MOON AND OF THE PLANET JUPITER. 249 
illuminating aperture, near the axis of the pencil, we may proceed with the reductions 
as though this were actually the case. 
From (12) we have for the moonlight, incident at right angles upon d e, 
(24) di = LB 
p being the Moon's radius, r and 4 its distance from the Sun and Earth. The quan- 
tity incident upon the bulb, denoted by 7’, will be obtained by substituting for d e the 
area of its section, by a plane perpendicular to 4, or d e — 7 E, whence 
| pz ORE FE 
d, ; deet ` Se 
By the equalization of the images of the Moon and lamp upon the bulb, we have 
i = 1, and from (23), 
l 
e go 4 av 
The light of the Moon for any particular value, v,, of v, and at the distances 4, and 
r, from the Earth and Sun, gives 
l down Op 1 p! E 
ed | WX. Har 
1 
O, and d, being the puer values of O and d. Comparing (26) and (27), we 
find, by making H = 2, 
1 
(28) En. 
The values of H, must be derived from observation at different ages of the Moon ; 
we shall then have from (24), for the quantity of moonlight at any phase, and for 
given values of r and 4 compared with the assumed standard, 
