304 
Anthropometrji of Scottish Insane 
criminals. One long series is available for L and B, viz. Macdonell's criminals. 
In the case of the 25,878 American recruits there is a very distinct positive 
asymmetry (•038 + •004) accompanied by mesokurtosis. The New South Wales 
males show quite significant negative asymmetry for the age groups 25 — 30 and 
60 and over, perhaps significant negative asymmetry for the 40 — 50 and 50 — 60 
groups, while the 20 — 25 and 30 — 40 groups are not significant although still 
negative. Mr Powys while noting that, for each group, it/(.<ilf„, observes that 
the skewness in all cases is small, but relatively this is not so, for at least the 
25^ — 30 and 60 upwards groups. The Italian conscripts and recruits both show very 
significant negative asymmetry, agreeing with the New South Wales males and 
the Scottish "general insane" population. The conscripts show very marked 
leptokurtosis, and the recruits significant platykurtosis. For four long series, then, 
viz. New South Wales males, Italian conscripts, Italian recruits and the Scottish 
general insane population, there is agreement as to asymmetry — in all four 
cases it is significantly negative ; in one case, the American recruits, there is 
quite significant positive asymmetry. In two cases of very long series there is 
relative symmetry, viz. 15,117 N. S. W. males (30 — 40), and 5442 N. S. W. males 
(20 — 25) group. Macdonell's 3000 English criminals show slight negative asym- 
metry. Thus it is seen that in these long series of stature distributions, considered 
without reference to the ages of the adults in the populations measured, there is 
significant a.symmetry in all cases except one; in three cases it is negative, in one 
only is it positive. It falls finally to be noted therefore that the negative 
asymmetry in stature of the "general insane" population is not specially 
characteristic of the insane ; it is also a characteristic of some sane populations. 
As already stated, no very long series of head measurements are available for 
comparison with the exception of the 3000 English criminals, the skew curve 
of B for the series being given by Macdonell*. Here again negative asymmetry 
is found, and since the ratio = 3^34, the deviation from symmetry is probably 
significant. The L distribution of the same series also shows distinct negative 
asymmetiy, the ratio = 3'40 being found by the writer from the figures kindly 
supplied by Dr Macdonell. Thus in L and B,just as in stature, wJien long series are 
■pitted against long series, there is agreement as to the nature of the distribution, 
wJtich seems to he in the direction of negative asymmetry. The rule, therefore, as 
stated by Fawcett'\', Macdonell]. and Pearl^ for short series of distributions of 
a ntlirojw metric characters does not appear to hold for long series. 
For L and H, except the abo\ e case for L, only short series are at present 
available, and since there is no definite deviation in one direction more than 
another for these (Macdonell's English Crania, Favvcett's Naqada Crania, etc.), and 
since the probable erroi's are large, no comparison can profitably be instituted 
between them and the long Scottish series. 
* Macdonell: Biometrika, Vol. i. p. 183. t Fawcett : Biometrika, Vol. i. p. 443. 
1^ Macdonell : Biometrika, Vol. iii. p. 2"27, § Pearl : Biometrika, Vol. iv. p. 40, 
