3G 
PROFESSOR G. H. DARWIR ON THE MECHANICAL CONDITIONS OF 
§ 12. On the Rate of Loss of Kinetic Energy through Imperfect Elasticity, and on the 
Heat Generated. 
In a collision between two meteorites the loss of energy is probably proportional to 
their relative kinetic energy before impact. Therefore, the amount of heat generated 
by a single meteorite per unit time is proportional to the kinetic energy (say h) and to 
the frequency of collision. By (10) the frequency, or reciprocal of T, varies as vws^jm ; 
but ndv is equal to (fhf, and varies as Hence, the frequency of collision 
varies as and the amount of heat generated by a single meteorite per unit 
time varies as }t,hvm~K But, ifp be the quasi-hydrostatic pressure, varies iishiom~^, 
and, therefore, the heat generated by a single meteorite varies as IdpiK. 
Then, to find the total heat generated per unit time and volume, we have to multiply 
this by the number of meteorites per unit volume, that is to say, by imn~^, which is 
equal to dph~^. 
Thus the amount of heat generated per unit time and volume is proportional to 
2 ')'’mdi~^\ Witli meteorites of uniform size, and with uniform kinetic energy of 
agitation, this becomes simply the square of the h 3 ^drostatic pressure. 
The mean temperature of the gases volatilised by collisions must depend on a 
variet v of considerations, but it wot del seem as if tbe temperature would follow, more 
or less closely, the variations of heat generated per unit time and volume. 
^ 13. Oyi the Fringe of a Sirarm of Meteorites. 
The law of distribution of meteorites found above depends on the frequency of 
collisions. But at some distance from the centre collisions must have become so rare 
that the statistical metliod is inapplicable. There must then be a sort of fringe to the 
swmrm, which I attempt to represent by supposing that beyond a certain radius a (not 
the same as the former a) collisions never occur, and each meteorite describes an orbit 
under gravit}'. 
Now, at any point gravity depends on the mass of all the matter lying inside a 
sphere whose radius is equal to the distance of that point from the centre of the 
swarm. Hence, the value of gravity depends on the law of density of distribution of 
the meteorites, which is the thing which we are seeking to discover. 
We suppose, then, that from every point of a sphere of radius a a fountain of 
meteorites is shot iq3, at all inclinations to the vertical, and with velocities grouped 
about a mean velocitj', according to the exponential law appropriate to the case. .As 
many meteorites are supposed to fall back on to the surface as leave it, and this 
inward cannonade against the boundary of the sphere exactly balances the quasi- 
gaseous pressure on the inside of the sphere. Thus, the ideal surface may be annihi¬ 
lated. Since the fallino- half of the orbit of a meteorite is the facsimile of the risino- 
o C? 
half, we need only trace tbe body from projection to apocentre, and then double tlie 
