Lucy Whitaker 
63 
Now if Dig be the number of deaths, say, occurring in any year and there be 
I years under consideration, then: 
(btandard Deviation)- = ^ ^ , 
or, if we use the form preferred by Bortkewitsch* 
S,' (m, - nqf 
Hence : p = 
l-\ 
(m,, — nq) 
{l-l)nq ■ 
This in other notation is Mortara's Q''\ the only criterion he actually uses 
provided by his equation (liter), p. 18. Thus his Q', which he says must not 
differ much from 1, is only \/p, and it would be better to use j) — which has a 
direct physical meaning — than Mortara's Q' = ^/p. Clearly Mortara's somewhat 
elaborate process of deducing Q', does not amount to more than saying : Fit a point 
binomial and test if p is slightly less than unity. We contend that it is best 
straight off to fit the binomial. 
It is true that Mortara does not reach his Q''\ our j), by the simple process of 
asking whether the binomial is one with a positive probability less tlian unity. 
He endeavours to obtain it by considering whether there is "lumpiness" in the 
observations. But it seems to us clearer and briefer to ask : Are the contributory 
cause-groups independent as in teetotum spinning ? If so, the data will fit a true 
binomial and p will of necessity be a positive quantity less than unity. If they 
are not of this character then p must of necessity be greater than unity. It is of 
interest to see how Mortara's test of dependence of contributory cause groups 
leads to a criterion, but he actually only gets his Q'-, i.e. our binomial p after 
a series of hypotheses which much limit, and that in no very obvious manner, 
* The use of >Jl or sjl-l in the value of the standard deviation when I is small has been several 
times discussed. It may be dealt with as follows : The probable errors of a mean as deduced by the 
two processes are 
and £'= -67449 . alJT^, 
now £'= -67449 (r/Vr(^l + + . 
= -67449— f'^ + -7= ^+ ••• ) ■ 
Now the probable error of a is -67449 — ^ , and is less and often much less than -67449. 
Hence if we only know a from the observations themselves, and this is the usual case, we have: 
i;'= -67449 ~ a', 
where cr' differ from tr by a quantity usually far less than the probable error of a. In other words the 
refinement of using E' for E is idle having regard to the accuracy of our observations; and the form 
used by Bortkewitsch and Mortara with ^/l- 1 for is of no importance. 
