586  Mr.  A.  S.  Eve  on  the  Absorption  of 
Then  comparing   corresponding    terms    in    the   expansion 
of  (11), 
1  f 
dT~  (2s+Z)\2s  +  V  AT     "'     "     (32) 
The  particular  cases  .9  =  1  and  2  were  given  in  M.  p.  443 
without  proof.  Making  a  similar  application  to  the  angular 
integral  (3),  the  type  of  an  individual  term  is 
J^  P  b>xmviiv'zd(o  _  Vj_  V2  \v%  f  *  K(i/„  v2,  v3  5  a)  dfi  ,„^ 
2ttJ  up[ujL+pvp)'+i        ~\2s.Asa    'J?  "  VA<>)  '  ^  * 
The  special  cases  5=1  and  2  were  also  given  in  M.  p.  445 
and  p.  459. 
The  calculation  of  the  coefficients  K  is  facilitated  by  the  use 
of  sequence  equations,  obtained  by  differentiation  of  (31). 
Thus  differentiation  with  regard  to  x  gives  the  first  of 
ViK(vl9  v.,,  vz;  a)  =  (v1  +  v2  +  v3)[aK{vl  —  2,  v2,  vz)  +  c/K(v1  — 1,  v3  —  1.  i/3) 
+  &,K(i/1-l,v3,v3-l)] 
^2K(i/1?  v,,  p3  ;  «)  =  (vi  +  v2  +  v3)  [c'K^—l,  v2-  1,  v3)  +^K(v1?  v2-2,  v3) 
+  a'K(v„  v3-l,v3-l)] 
v3K(v1?  v2,  vo  ;  a)  =  (v1  +  v2  +  v3)[//K(j/1  —  1,  v2,  v3—l)  +a'K(vu  v2  —  l,v3—M 
+  cK(Vl,  v2,  v3-2)]. 
If  in  K(v1?  j>2,  i/3)  one  of  the  indices  is  negative  K  =  0. 
There  is  a  second  group  of  relations  of  which  the  type  is 
Afa  +  lJKfa  +  l,  v2}  v3;  a)  +  (y(va  +  l)K(vl9v9  +  l,v9;  a) 
+  B'(v3  +  l)K(i/„  f„  vg  +  l;  a) 
=  (vi+.vg  +  i'3  +  l).K(v1-- 1,  v2,  1/3  ;  a), 
got  either  by  inverting  the  first  group,  or  independently  by 
the  use  of 
(Ai+c'i+B'i)<=2^:-r1- 
XLIX.  The  Absorption  of  the  7  Rays  of  Radioactive  Substances. 
By  A.  S.  Eve,  M.A.,  Lecturer  in  Mathematics,  McGill 
University ,  Montreal  *. 
rT^HE  following  investigations  were  made  in  order  to 
1  ascertain  whether  the  7  rays  could  be  taken  as  an 
accurate  measure  of  the  total  amount  of  radioactive  matter 
present  in  a  given  substance.  It  was,  therefore,  necessary 
to  ascertain  whether  the  7  rays  of  various  substances  were 
absorbed  to  an  equal  degree  under  the  same  conditions. 
*  Communicated  by  Prof.  E.  Rutherford,  F.E.S. 
