274 
Pecmvimus ! 
Again : 
and If ^^^r i' 
+ 50^j' 
+ 
|3 
which after reduction gives 
. f {- 4 4.) 4) - (- 4) ^4 - (i - ^1 
(L). 
Clearly if ^/Sj were as large as 0"5, pB^ for an array of 30 would be of the 
order "02 and thus the array means have an approximately symmetrical distribution. 
We now turn to the value oi pB.,, and find with the same value of f as before 
2 2 \ , /, () 
Furth... (,jf,r' = f = 4 4 4) ^ - (i 4) ^ - *f ' 
Multiplying the previous result by this we have 
^.--4^1-(-l4)(i4)-(--^)(i4)' 
-44^)1 
-Ki4)44r=-('4-)(4^444^)l 
For example, in an array of 25 in a sample of 1000, if p0.2 were as high as 3"8, we 
should have pB., slightly less than 3'2. Accordingly the constant pB.2 of an array is 
not as approximately normal as pB^, or, we have the material thrown out further 
towards the tails than in the normal distribution. 
It is probably, however, adequate to speak of the means of an array of variable 
size as roughly following a Gaussian curve and give the usual meaning to the 
" probable error " of the mean of such an array. Its value however is more accurately 
