Theories ot the Earth's Origin — Upham. 219 
moon grew. In the closing stages of the process it did not vary 
greatlj' on either side of one and one-half miles per second, and 
the phenomena of the present surface may be discussed on the 
basis of that velocity. The energy due to that velocity would 
more than suffice * * * to melt the moonlet if it were com- 
posed of ordinary volcanic rock and provided all of the energy 
were applied to the heating of the moonlet. Practically only a 
portion of it was thus applied; another portion produced heat in 
the contiguous tract of the moon's material; yet another was 
consumed in the deformation of moonlet and moon resulting in 
the crater, and another resulted in modifications of the moon's 
motions, changing its orbit, its orbital velocity, its axis, and its 
rotational velocity. The energy converted into heat might be 
regarded as the remainder after deducting all other effects, and 
the resulting temperatures would be further conditioned by the 
distribution of heat in the colliding masses. 
Since the area of the moon's surface directly struck by the 
moonlet is a function of the square of the diameter of the moon- 
let, while the energy applied to that area, being measured by the 
mass of the moonlet, is a function of the cube of its diameter, 
more energy would be applied to a unit of space in the case of 
large moonlets than in the case of smg-ll, and the temperatures 
caused by large moonlets would therefore be greater. To this 
relation I ascribe the restriction of inner plains, indicative of 
fusion, to the larger craters. * * * 
In the breaking up of the postulated pre-lunar ring there were 
at first many centers of aggregation, — were the moon the only 
center, the scars of impact would all be small. So long as the 
masses were small the process of aggregation developed little 
heat, for the heat of impact depended almost wholly on velocities 
created by mutual attractions. That particular moonlet which 
became the nucleus of the moon may therefore be conceived as 
cold, or at least as sufficiently cool to be solid. As the moon's 
mass grew, the blows it received were progressively harder, and 
for a time their frequency also increased. The rate of heating 
probably reached and passed its maximum while the mass was 
materially less than now. During the whole period of growth 
the surface lost heat by radiation, but the process of growth can- 
not have been slow enough to permit the concurrent dissipation 
of all the impact heat. On the one hand, there should have been 
some storage of heat in the interior, and, on the other hand, the 
stored heat can never have sufficed for the liquefaction of the 
nucleus. Toward the close of the process, when blows were hard 
but rare, liquefaction was a local and temporary surface pheno- 
menon, but the general temperature of the surface was low. 
Impact heat, being evolved simultaneously in the surface and the 
subsurface, was dissipated more rapidly from the surface, so 
that there was a subsurface zone of relatively high temperature. 
