ON THE LIGHT OF THE MOON AND OF THE PLANET JUPITER. 933 
@ the ratio between the actual amount of light reflected from s upon ds’ and the 
quantity which the latter would receive if the light ui were dispersed equally in all 
directions from s; we shall then have, for the light incident upon d s', 
(5) dé. eR. 
The coefficient © depends upon the reflective properties of the surface s, as well as 
on the angle between ds’ and I seen from s. Its value in some special cases, we will ` 
now consider. | 
1. A polished sphere, illuminated by parallel rays, reflects them with uniform 
intensity over the whole surface of the surrounding concave,* and we shall have 
(6) posi ditt CP 
2. If s is a flat, opaque disc, it will return back the light incident from I into the 
same hemisphere in which J is situated, and if this be done in equal amounts in 
every direction towards which its bright side is presented, then 
(7) Bet Gum 
3. If, at equal distances, the quantity of light reflected from this disc upon ds’ is 
proportional to its apparent area seen from d s', we have 
(8) 8 — 4 sin. d VE cee LI. aes hs 
7 
where ¢ is the angle which the line joining s and ds’ makes with the plane of 
the disc. > 
The reason for adopting this value of © is not quite as clear as in the previous cases. 
It is evident, however, that the apparent area of the disc represented by s, seen from 
ds, varies as sin. ġ, and that di’ will vary also with sin.. Moreover, the sum of 
all the values of di’ must be equal to the whole of the light reflected from s, so that 
we ought to have | 
(9) J. di pi 
the integral being taken so as to include all positions of d s'. 
* Bouguer, Traité d'Optique, p. 109. 
