the  Principle  of  the  Conservation  of  Energy.  139 
according  to  equation  (13), 
a  dr  _  2a?-3 
and  from  this  and  equation  (12), 
-^('JJ!«*+'(«:-2»'J+p''*fi?).  ("i 
or  the  following  equation  for  the  two  variables  r  and  a  : — 
+ 
If  we  now  confine  ourselves  to  small  values  of  a,  for  which  ctr 
is  not,  indeed,  constant,  as  it  is  for  «  =  0,  according  to  section  11, 
but  for  which  it  differs  only  little  from  a  constant  value  «or0  =  7i, 
we  may  put 
e*r=»(l  +  e), .     .     (16) 
where  e  has  always  a  very  small  value.     It  then  follows  from 
this  that 
-  =  (l+2e);3> (17) 
4g  -«* (18) 
dr  dr  v     ' 
Further,  by  (11)  and  (17), 
J 
-=  = =■  COS  V, 
*  If  the  segregating  force  a  vanish,  ecr  must,  according  to  section  11, 
assume  a  constant  value.  But  for  a  constant  value  of  ecr  and  for  a  =  0, 
equation  (15)  reduces  itself  to 
and  this,  divided  by  the  constant  value  «2r2,  gives  the  identical  equation 
iu  accordance  with  section  11. 
