332 On Raiuloni Occur rentts in Space mid Time 
+ + — + 6 
III- 111 
or af- + t- = — ( xxxix). 
m 
Fiuni this we deduce 
in \/ e'" — , + 2 + e'" + + 4+2 
\vi- III J V»i ")ii- III 
<rt= '-rr, . (Xl). 
\iii J 
Lastly we may consider the correlation of length of intervals and number of 
intervals. We have just seen that the regression is not linear in the case of i on n, 
it would thei'efbre be desirable to have 77?, ,i and the two correlation ratios, as 
well as the correlation coefficient t ■ 
To determine the latter we must tirst hnd 
1 1 {n + 2) !| 
V»i"+^ n ! ~ 7H"+' (n + 1) ! rn^'+^'{n+W-. 
X'm 1^' ( e'" - ] 1 - -~ f e'" - 1 - +4 (e'" - 1 
[ill- \ J m \ iiij \ 
ill 2'/i-/ 
/M — + 4' ' ^ 
Thus ,V=^^i!l_^i_^_i^^ (xh). 
1 + e"- ^ 
We must now transfer by aid of (xxxvi) and (xxxviii) this product moment to 
the means. We have 
in \e"' — + 2 + e'" + — + 4 + 2^ 
p,, = - ' , ' , y L 1 . . .(xli)'^^^ 
1 +6"^''^ 
\in 
Accordingly we have, by aid of (xxxvii) and (xl) 
' t, II — 
O-tO-n 
/ 2T 
' e"'{ 
4>T \ 
— + 2 
III 1 
T 
\ + e'" 1 
Km^ iii^ ill ) 
1 + 2 
1^(1 
\iU 
-2) + .ig + 2) 
.(xlii). 
