the  a,  Rays  emitted  by  Radium.  725 
parabolic  arc  whose  radius  o£  curvature  varies  sufficiently 
slowly  within  the  given  limits  to  render  it  indistinguishable 
from  a  circle. 
Let  y  =  hn  be  the  height  of  a  point  above  the  plane 
against  which  rests  the  photographic  plate,  he  the  distance  of 
the  slit  below  this  plane,  kn0  =  a  the  distance  of  the  source 
below  the  same  plane.  Then  the  equation  of  a  parabola 
whose  axis  is  parallel  to  the  .I'-axis,  and  which  passes  through 
the  source,  the  slit,  and  the  point  (x,  y),  may  be  written 
2Ra?=(y  +  a)(y  +  ie)* 
or 
2Rx  =  k2(n  +  n0)(n-\-e). 
The   values  of  z  = 
— ,    which    are    nearly    coincident 
n  +  n0  J 
with  the  straight  line  z=(n  +  e)8,  were  calculated  in  -g-J0ths 
of  a  mm.,  so  that 
R  =  |2  x  600, 
a   value    which    is    practically  identical  with  the   radius  of 
curvature  of  the  parabola 
^r,        1  f        a  +  ke\2~]^ 
p  =  B[i+i?(y+^-)J  • 
The  following  tables  show  the  extent  of  the  agreement 
between  the  observations  and  the  mode  of  interpretation 
explained  above. 
Experiment  C.  19/10/1905.— a  =  25'15  mm.  ;  £  =  0-920  ; 
11  =  10,809.     Trajectory  through  air  only. 
n= 
1 
o 
3 
4 
5 
6 
7 
8 
9 
10 
11 
5=1-5646;  2#(obs.)  = 
57-5 
105-2 
157-4 
210-S 
272-5 
333-0 
391-4 
458-5 
529-8 
602-7 
681-3 
6^=0-43  f   observed = 
2-01 
3-55 
5-14 
6-65 
8-35 
9-91 
11-31 
12-87 
14-47 
16  02 
17-64 
(n-\-e)d    [  calculated  = 
1-98 
3-54 
5-09 
6-65 
8-20 
9-76 
11-31 
12-87 
14-42 
15-97 
17'53 
n= 
12 
13 
14 
15 
16 
17 
18 
19 
20 
2x  (obs.)  = 
7550 
829  6 
9250 
1018-7 
10961 
11930 
1297-0 
1397 
1493-7 
C    observed  = 
(n-\-e)oi 
I  calculated  = 
1906 
1908 
20-42 
2064 
22-23 
22-19 
23-90 
23-75 
2511 
25-30 
26-74 
26-86 
28-43 
28-41 
2i 
21 
•97 
•97 
31-39 
31-52 
*  In  this  form  will  be  recognized  the  principal  term  of  the  expression 
which  gives  the  radius  of  a  circle  passing  through  the  three  points, 
K  -  L  ±v +  2  J   +       I ' 
