1908-9.] On Energy Accelerations and Partition of Energy. 371 
-02y- 
For stability A + 
0S 2 
must be positive. Now, in order that energy 
equilibrium may be possible, it is necessary that 
[f)’] 
1 1 
+ 
~0 2 V~ 
_ ds* _ 
} 
should be positive ; for it has been shown that this expression is equal 
"0 2 V - 
to [g 2 + r 2 ], which is obviously positive; that is to say, A + 
0S 2 . 
must 
be positive in order that energy equilibrium may be possible ; so that 
the stability condition which we have just obtained is consistent with 
this. As in the general case, a consideration of the translational mean 
-0 2 V' 
energy shows that 
dx 2 . 
must be positive ; and this is consistent with 
our hypotheses. 
(18) Let us now consider the case where the attraction between the 
particles offers very great (in limit infinite) resistance to any variation of the 
distance AB from a mean value a. 
Let r = <x + £ where £ is small, and let us assume for the law of force 
f(r) = ?(r* — a) 2 , where K is a very large constant which may be supposed 
A 
infinite. 
Let us suppose that 
^ = K (r -a) = Kf . 
dr 
Lt. K(r-a) = A, a constant. 
r-a 
It is clear that r 2 is an infinitesimal, so that Maxwell’s Law cannot hold 
good in this case. 
Now 
df A , f , 
= — + powers ot £ 
rdr a 
S- K 
= A 2 in the limit, 
and r 2 is of the same order as £ 
Let r 2 = B£ when g is very small ; then 
dr 2 _ 
becomes AB in the 
limit, where B is a finite constant. 
