490     Prof.  Wilson  and  Mr.  Gold :  Electrical  Conductivity  of 
Hence  Oxk  /  1 
4?r 
(i-i)«<w-°«>i 
so  that  the   change,  in   the  apparent  capacity,   clue   to  the 
introduction  of  the  salt  is  given  by  the  equation 
4         4~U247r\r/o      dj' 
In  the  experiments  we  have  made,  the  self-inductions  of 
the  arms  of  the  bridge  could  be  neglected  in  comparison  with 
the  capacities  without  appreciable  error. 
It  was  found  possible  with  the  bridge  arrangement  de- 
scribed to  obtain  an  approximate  balance.  That  is,  the 
minimum  galvanometer-current  was  always  small  compared 
with  the  currents  when  the  adjustable  condenser-plate  was 
far  from  the  position  which  gave  the  minimum  deflexion. 
This  showed  that  the  arm  of  the  bridge  containing  the  flame 
behaved  like  a  capacity  simply,  or  like  a  capacity  and  self- 
induction  in  series.  If  the  flame  had  behaved  like  a  capacity 
and  resistance  in  parallel,  then  a  balance  could  not  have  been 
obtained.  The  current  through  the  flame  with  a  given 
maximum  P. D.  and  frequency  is  proportional  to  the  apparent 
capacity,  so  that  it  is  reasonable  to  regard  the  apparent 
capacity  as  a  measure  of  the  conductivity  of  the  flame  for  the 
rapidly  alternating  currents  employed. 
To  obtain  relative  values  of  the  apparent  capacities,  it  is 
therefore  sufficient  to  calculate    - —  —  for  each  salt  solution 
cU     dl 
sprayed.  Since  the  absolute  amount  of  salt  in  the  flame 
could  be  only  roughly  estimated,  it  was  useless  to  attempt  to 
obtain  exact  values  for  the  absolute  apparent  capacities  ;  so 
C 
that  it  was  unnecessary  to  know  the  ratio  ^  exactly. 
The  value  of  dx,  the  minimum  position  for  the  flame  free 
from  salt,  was  about  half  the  value  obtained  with  no  flame. 
Consequently    -j   corresponds  to  twice  the   capacity  of  the 
flame-electrodes  with  air  as  dielectric.     The  capacity  in  this 
Q, 
case  was  d'b  cm 
s.,  and  p    was  very  nearly  I  in  most  of  the 
experiments  described  below. 
