264 
GILBERT. 
In the case of moonlets reaching the moon from the plane 
of the postulated flat ring, all 
points of incidence would lie ap¬ 
proximately in one plane, which 
plane would intersect the center 
of the moon. Postulating, as be¬ 
fore, that the distribution of moon- 
lets in this plane is equable, and 
that they move in parallel courses, 
and ignoring the attraction of the 
moon, we have the geometric rela¬ 
tions shown in Fig. 11, and obtain 
sin i as an expression of the pro¬ 
portionate number of moonlets 
whose incidence angle is less than 
i. This differs from the expression obtained in the case of 
Fig. 11.—Diagram illustrating inci¬ 
dence angle of moonlets. 
cosmic meteors, in that it 
involves the first power of 
the sine of the angle instead 
of the second, and there re¬ 
sults a very different law of 
distribution, which is ex¬ 
pressed by curve B of Fig- 
12. In this distribution law 
the number of bodies inci¬ 
dent at 90° is a vanishing 
quantity, but the] number 
incident at 0° instead of be¬ 
ing a vanishing quantity is 
a maximum, and one-half 
of all the moonlets have in¬ 
cidence angles less than 30°. 
The law of incidence an¬ 
gle for ring-derived moon¬ 
lets agrees with the law sug¬ 
gested by the round ness of 
the impact scars in that it 
Fig. 12. —Distribution curves. Abscissas = 
angular deviation from verticality of bodies 
colliding with the moon. Ordinates = rela¬ 
tive numbers of colliding bodies. A = curve 
for meteors. B = curve for bodies in a 
single plane. C= curve for moonlets, ac¬ 
count being taken of the moon’s attraction 
but not of the earth’s. D = type of curve 
deduced from ellipticities of craters. 
