Flames  containing  Salt  Vapours  for  Alternating  Currents.    503 
In  the  paper  on  the  conductivity  of  flames  for  steady 
currents,  referred  to  above,  numbers  are  given  which  are 
proportional  to  the  molecular  conductivity  of  all  the  salts 
tried,  so  that  it  is  not  necessary  here  to  discuss  further  the 
variation  of  the  conductivity  with  the  nature  and  concen- 
tration of  the  salt  vapour. 
Let  q  be  the  number  of  ions  produced  per  c.c.  per  sec.  in  the 
flame  and  n  the  number  present  per  c.c.  Then  g  =  un2,  where 
a  is  a  constant  which  has  been  shown  by  Langevin  to  be  equal 
to  f  .4:7re(k1-hk2),  where  /is  a  proper  fraction,  and  ku  h2  are 
the  ionic  velocities   due  to  unit  electric  intensity.     For  the 
flame   we   have   &2  =  1000-— ■    for    one    volt   per    cm.,    or 
sec 
cms. 
oX  10~J  -  —for  one  E.S.  unit  of  electric  intensity.     Hence 
sec. 
a  =  47r ./ .  3  X  10-10  x  3  x  10'  =  l'l  x  10-3/. 
Xow  for  the  strongest  K2C03  solution  sprayed  »  =  1'8  x  1013, 
hence 
q  =  f  l-l  x  10-3  x  1'82  x  1020  =  4  x  1023/'. 
The  number  of  salt  molecules  per  c.c.  is  about  5x  1014;  so 
that  it  appears  that  each  salt  molecule  is  ionized  and  re- 
combines  about  109/  times  per  second.  The  value  of/  under 
ordinary  conditions  is  about  0*2.  Probably  in  the  flame  it  is 
less,  say  O'l.  Taking  the  temperature  of  the  flame-gases  to 
be  2000°  C,  we  get  for  the  number  of  collisions  made  by  a 
salt  molecule  per  second  in  the  flame  rather  less  than  5  x  10s. 
So  it  appears  that  the  K2C03  molecules  are  ionized  once  for 
every  5  collisions  with  another  molecule.  It  is  therefore 
probable  that  the  cause  of  the  ionization  of  salt  vapours  in 
flames  is  the  shock  of  molecular  collision. 
The  current  which  could  be  carried  by  the  5  x  1014  ions 
produced  per  c.  c.  is  about  60  amperes,  which  is  enormously 
greater  than  the  observed  currents  per  c.  c.  of  flame  between 
the  electrodes.  This  result  agrees  with  the  conclusion  *  that 
the  observed  steady  currents  through  flames  containing  salt 
vapours  are  very  far  from  the  saturation  value.  Since  each 
salt  molecule  is  ionized  many  times  per  second,  the  salt  would 
all  be  carried  to  the  electrodes  as  ions  if  the  current  were 
sufficiently  great.  If  we  suppose  that  the  electrodes  absorb 
the  ions  which  reach  them,  then  the  maximum  possible 
current  would  be  equal  to  that  required  to  electrolyse  the 
same  amount  of  salt  in  a  solution.  This  has  been  previouslv 
found  to  be  the  case  for  alkali  salts  vaporised  in  a  current 
of  air  t. 
*  IT.  A.  Wilson,  Phil.  Mag.  October  L905. 
f  H.  A.  Wilson,  Phil.  Mas.  August  1902. 
