266 
GILBERT. 
In order to determine the angles of incidence correspond¬ 
ing to these ellipticities it was necessary to ascertain the 
general law subsisting between angle of impact and result¬ 
ing ellipticity, and to this end a series of laboratory experi¬ 
ments was instituted. An apparatus was arranged by means 
of which a ball of plastic clay was made to strike a flat target 
of the same material at a measured angle and with deter¬ 
mined velocity. The angle of incidence was systematically 
varied, the velocity of impact was varied, and the softness 
of the clay was varied. A crater similar in appearance to 
the smaller craters of the moon was readily produced, and 
it was found that ellipticity is a function not only of angle 
of incidence, but also of softness of material, and, inversely, 
of velocity of impact. No attempt was made to discover the 
precise character of this complex relation, because it was 
immediately evident that experiment could not be made to 
deal with velocities and strengths of material comparable 
with those associated with the production of the lunar cra¬ 
ters. It was found, how T ever, that ellipticity increases slowly 
with increase of incidence angle up to 30° or 40°, and 
w T ith comparative rapidity for higher angles; and the com¬ 
parison of this relation with observed lunar ellipticities led 
to the conclusion that from 65 to 90 per cent, of the lunar 
craters indicate incidence angles of less than 30°. As the 
theoretic distribution previously derived, on certain assump¬ 
tions, assigns to but 50 per cent, of the moonlets angles 
within that limit, it appeared desirable to look more closely 
into the nature of the orbits of the moonlets as they ap¬ 
proach the moon. This examination required mechanical 
conceptions and mathematic skill I was unable to supply, 
but I was so fortunate as to enlist the interest of our fellow- 
member, Mr. R. S. Woodward, w T ho made an analytic investi¬ 
gation, on which the following paragraphs are based. 
It will be recalled that parallelism of direction was as¬ 
sumed as a means of simplifying the discussion of incidence 
angle in the case of meteors and moonlets. In the case of 
meteors the assumption was fairly warranted, but not in 
