314         Prof.  H,  A.  Buuastead  on  the  Heating  Effects 
tlie  fraction  is  seen  to  be  of  the  form 
l-e~x 
x      ' 
which   (for  positive  values  of  x)   increases  as  x  diminishes. 
Hence 
I2<JaI1(l-C-401)- 
The  primary  rays  absorbed  in  the  zinc  strip 
hence 
A, 
=  1 
,(1- 
-e~ 
-^')>X 
(1- 
e   - 
'0; 
r2 
< 
i.1- 
—  £""" 
40  ? 
_i 
~4 
*(!  +  «- 
-"") 
;  or 
i; 
a; 
<o 
ou 
A1 
4*L. 
—  cv_ 
20/  = 
in  which,  of  course,  if  there  is  to  be  no  generation  of  fresh 
energy,  a  must  be  less  than  unity. 
We  may  make  a  similar  calculation  for  the  rear  surface, 
but  it  is  sufficient  to  observe  that  even  if  all  the  effect 
observed  behind  the  metal  is  due  to  secondary  rays,  the 
ratio  of  these  to  the  primary  rays  absorbed  cannot  be  greater 
than  0'2.  So  that  by  considerably  exaggerating  all  possibi- 
lities in  favour  of  the  production  and  escape  of  secondary 
rays,  we  are  unable  to  give  to  the  secondary  rays  which 
escape  an  intensity  one-half  as  great  as  that  of  the  primary 
rays  absorbed.  Now  in  order  to  account  in  this  way  for  the 
observed  difference  in  the  heating  of  the  lead  and  the  zinc, 
we  must  assume  that  at  least  half  of  the  energy  of  the  primary 
rays  absorbed  in  the  zinc  escapes  in  the  form  of  secondary 
rays  :  this  is  on  the  supposition  that  none  so  escapes  from  the 
lead  ;  if  the  lead  loses  any  energy  in  this  manner,  then  the 
fraction  for  the  zinc  must  be  greater  than  one-half.  It 
appears  therefore  that  the  experimental  results  cannot  be 
accounted  for  in  this  way. 
Numerical  Results. 
The  measurements  of  the  absorptions  of  lead  and  zinc  ran 
so  nearly  parallel  throughout  the  course  of  the  experiments, 
with  rays  differing  considerably  in  penetration,  that  it  was 
eventually  considered  unnecessary  tojnake  a_separate  correc- 
tion to  each  measurement  with  the  radiometer.  The  absorptions 
were  measured  from  time  to  time  during  the  investigation, 
and  the  results  are  given  in  the  following  table  ;  the  numbers 
give  the  fractions  of  the  primary  rays  absorbed  by  aluminium 
of  the  same  thickness  as  the  window,  and  by  lead  and  zinc  of 
the  same  thickness  as  the  strips,  the  latter  being  behind  the 
aluminium  except  in   the  first  three  experiments  when  no 
