312         Prof.  H.  A.  Bumstead  on  the  Heating  Effects 
secondary  rays  from  brass  may  be  obtained  from  Townsend's 
experiments  *,  and  is  6*9  ;  he  did  not  measure  the  absorption 
in  air  of  the  primary  rays,  but  an  estimate  of  its  value  may 
be  got  from  the  statement  that  the  number  of  ions  produced 
by  the  primary  rays  when  they  traverse  a  layer  of  air  1  cm. 
thick  is  about  half  as  great  as  the  number^  produced  by 
complete  absorption  of  the  secondary  rays.  Combining  this 
with  Allen's  result  that  complete  absorption  of  the  primary 
rajs  produced  1900  times  as  many  ions  as  complete  absorption 
of  the  secondary  rays,  we  get,  for  the  coefficient  of  absorption 
in  air  of  the  primary  rays  used  by  Townsend,  approximately 
3x10" K  Assuming  that  the  ratio  of  the  coefficients  of 
absorption  in  the  metal  is  of  the  same  order  as  that  of  the 
coefficients  in  air,  we  have  roughly 
VJ-XJ    =    2      x  1()4   . 
and  as  J  1 
|^  =  2000' 
we  get  a  =10. 
Now  if  the  conclusion,  toward  which  the  present  experi- 
ments point,  be  accepted,  it  is  not  surprising  that  the 
ee fraction"  a,  should  be  greater  than  unity;  for  if  atomic 
energy  is  set  free  it  is  not  unlikely  that  it  is  through  the 
mechanism  of  these  easily  absorbed  secondary  rays.  Of 
course,  the  data  from  which  the  above  calculation  has  been 
made  are  not  sufficiently  accurate  to  give  any  weight  to  the 
actual  number  obtained  for  a.  ;  but  it  is  sufficiently  clear  that 
a  considerable  number  of  these  easily  absorbed  secondary 
rays  must  be  generated,  of  which  only  a  very  small  fraction 
can  escape  from  the  metal. 
This  conclusion  in  itself  makes  it  somewhat  improbable 
that  a  large  part  of  the  energy  could  be  transformed  into  the 
more  penetrating  secondary  rays  and  so  carried  away  ;  but  it 
is  desirable  to  consider  the  question  of  this  type  of  rays  inde- 
pendently. Sagnac,  who  has  made  an  extensive  series  of 
experiments  upon  secondary  rays  t,  finds  that  heavier  metals 
in  general  give  out  more  intense,  and  more  easily  absorbed, 
rays  (of  the  type  now  under  consideration)  than  lighter 
metals;  and,  in  particular,  that  this  is  true  of  lead  as  compared 
with  zinc.  On  the  other  hand,  Townsend  (he.  cit.~)  finds  that 
lead  is  an  exception  among  the  heavier  metals  and,  as  a 
matter  of  fact,  gives  out  less  intense  and  more  penetrating 
rays  (of    this  type)  than  zinc,  and  this  result  has  recently 
*  Carnb.  Phil.  Soc.  Proc.  x.  p.  217  (1899). 
t  Ann.  Chim.  Plnjs.  xxii.  p.  493  (1901). 
