256 071 a New Metliod of Determining Correlation 
(G) Severity of Attack and Strength of Immunity dm to Vaccination. I look 
first at the data arranged as a two row correlation table. 
Severity of Attack. 
Haemorrhagic 
Confluent 
Abundant 
Sparse 
Very 
Sparse 
1 
Totals 
Since vaccination ^ 
0 to 25 year.s \ 
Over 25 years or ( 
unvaccinated \ 
44 
38 
251 
120 
388 
176 
308 
148 
211 
487 
1202 
Totals 
49 
289 
508 
484 
359 
1689 
xjax = + '5583. 
Here* ^j/<7i = + 1-2700, x.,la, = + V\IM, ^3/^73 = + -7185, 
^4^ = + -3488, x,la; = + -2218. 
From these results we find 7; = -321, a very sensible relationship, and we see 
how the mean vaccination immunity increases as we pass from haemorrhagic to 
very sparse cases. There is very little doubt that we are dealing here with a 
perfectly graduated and continuous cause and effect, remarkably different in its 
character from the alcoholic influences we have just discussed. 
To illustrate this point, I proceed to investigate the same data arranged as a 
three rowed table, using formula (ii). We have : 
Severity of Attack. 
Haemorrhagic 
Confluent 
Abundant 
Sparse 
Very 
Sparse 
Totals 
0—25 years 
5 
38 
120 
176 
148 
487 
25 — J^S years 
29 
155 
299 
268 
181 
932 
Over ^.5 or un- / 
vaccinated ( 
15 
96 
89 
40 
30 
270 
Totals 
49 
289 
508 
484 
359 
1689 
We have-f- : 
:f'/o-^= -9951, 
x'ja^ 
= -5583, 
Jt/a.jc= 1-5533 ; 
a'f(T,= -5069, 
Xi'jaj 
= 1-2700, 
A/<Ti = 1-7769, 
CTija-x = 
-8742 ; 
a;,/o-2= -4329, 
X2 /a-2 
= 1-1194, 
h/a, = 1-5523, 
cr-Jo-x = 
10007 ; 
x,la:,= -9338, 
Xg/a^ 
= -7185, 
Iija, = l-6o2i, 
0-3/0-^. = 
•9401 ; 
x,l(T, = 1-3875, 
x^'/a-i 
= -3488, 
hi a, = 1-7363, 
O-a/o-x = 
-8946; 
^,,/o-5 = 1-3815, 
= -2218, 
/^cTo = 1-6032, 
•9689 ; 
* Reduced 
to a common unit : 
5i/o-^ = 
+ 1-2028, X2I 
cr^= +1-0602, 53/0-^ 
= + -6805, 
Xil<r^= +-3303 
rs/o-^.^: +-2101. 
Reduced to a commou unit : .fi/o-^ = -4431, 32/0-^ = -4332, 5:,/o-^ = -8779, 54/0-^ = 1 -2413, a;6/(r^= 1-3385. 
