58 
PROFESSOR G. H. DARWIN ON THE MECHANICAL CONDITIONS OF 
X (M — ic) —^dx= 2/3^ 
Therefore, 
or 
9 9 
0 . i 
'M 
13 
4 
9 
m 
=--W 
M 
/3 
i 1 
J\I 
/3 
771 
AI 
4 
9 
?«' 
M 
vn 
_6_ 
1 1 
9 
( 66 ) 
In order to compute from the formulae, (59), (64), (66), it is necessary to make an 
assumption as to the value of m the mass of the meteorites of uniform size whose 
arrangement of density is supposed to be the same as that of the heterogeneous 
meteorites. 
We have supposed that the law of frequency of masses is known at radius a, and 
that the mean mass is there equal to ^M. Now, inside of that radius the larger 
masses are more frequent, and outside of it the smaller masses. I suppose, then, that 
throughout the isothermal S23here m lies half way between niQ or |-M and the 
maximum mass M, and in the adiabatic layer that it lies half way between niQ or -gM 
and the minimum mass 0. 
Thus, inside I take m = |M, and outside m = ^M. 
As we only want to consider the general nature of the sorting process, these 
assumjDtions will suffice. It may also be remarked that a large variation of m is 
required to make any considerable difference in the numerical results. 
We now have— 
In the isothermal sphere (where Wq = ^p), 
^=4 
m' ’ 
P = log,, , 
w 
In the adiabatic layer, 
M 
= 4 
m 
m 
Tl'.us, our formulae are :— 
In the isothermal sphere, from (59), 
IM = mo; 
3 . 
m 
W'o 
2 6)-2(P+ 3) 
p /w\^ 
j (P _ 2) + (P + 2) 
(67) 
