A SWARM OF METEORITES, AND ON THEORIES OP COSMOGONY. 
Also, if P be small, the approximate result is 
m 
= 1 4- 
Before proceeding to give numerical values for the fall of mean mass as we proceed 
outwards from the centre of the isothermal sphere, we must consider 
The Adiahatic Layer. 
In this case we assume, as before, that the ratio of the two specific heats is if, and 
we therefore have for the relationship between Zp and at radius r, 
Hence, 
1 dhp 
hw dr 
Sp 
hPo 
— 6 
SlV \"3 
hio. 
'SSp^ 
BWr, 
d / Bto Y 
dr \8 wqJ ’ 
But, since Sp^, Swq apply to the radius a where h = a constant, 
3Sy, 
8v: 
0 
Thus, in the adiabatic layer the equation of hydrostatic equilibrium is 
whence. 
or 
Jl,d^/Sw\i dx_r. 
X dr \8wf^) dr ’ 
Sw = SlUq 1 
5/C_ ■ 
(60) 
The investigation now follows a line parallel to that taken before. 
We have Sti/Swg = Sip/Swq, and Sn^ = f{x) dx, so that 
=('■ - 
This is the law of frequency of masses lying between x and a: + Sa; at radius r. 
As Sw can never be negative, we see that there can be no mass greater than ■f/^'o/x ’ 
and, if M be the greatest positive value of the expression f{x), there can be no mass 
greater than the smaller of f hJx 
