306 
Atithroponietr}/ of /Scottish Insane 
The removal of medically defined " exceptionals " tends to improve the goodness 
of a normal distribution, but it is far from making it essentially good. 
On the other hand the only test made of the goodness of fit of skew curves for 
the "general insane" population is in the case of L (</), and this gives P = 'SS, 
a splendid fit as compared with the P = '14 of the corresponding normal fit, or the 
practical impossibility of fit at all for the "entire insane" population before the 
" exceptionals " are removed. It seems likely therefore that the skew curves 
would describe the " general insane " population satisfactorily in these cases where 
the normal curve fails. This is a case again of close approximation to symmetry, 
differing to some extent from normality. But until long series of sane populations 
are measured it cannot be said that in the " general insane " population there is a 
wider deviation from the normal curve than occurs in samples of the " general 
sane " population. 
It seems desirable to notice more specially the H distributions, the physical 
constants of which indicate a wider deviation from the normal curve than exists in 
either of the two characters L and B. Dealing firstly with HJ', we find that, 
while the values of /S, , /S.,, «•] and /c, are less than for the whole series (k.2 still 
indicating Type IV.) significant leptokurtosis is associated with significant asym- 
metry, and that, owing to the emphasis on the positive side of the range between 
2"30 to 3"73 on the relative scale, the normal curve fails to fit the distribution. 
The distribution of shows a different tj'pe of curve from the one deduced , for 
the "entire insane" population. The value of k.. being > 1 (TSIS) a curve of 
Type VI. is indicated. A 5 mm. grouping however gives k., = "8, indicating Type IV. 
Mesokurtosis occurs with significant asymmetry, and, compared with the normal 
curve, there is emphasis on both sides of the range. The emphasis occurs at the 
points 2-49 and 3'23 on the negative, and 2"68 and 3"42 on the positive side of the 
relative scale. Since the skewness in the character H is certainly significant, 
both in males and females, since a relatively greater proportion affects the good- 
ness of fit of the normal curve, and since H shows greater relative variability it is 
evident that this character differs somewhat from L and B in the nature of its 
distribution. Here, however, the character head height, as defined in the first part 
of this memoir, must be considered. 
It should be noted that the character H in the living head, as measured from 
the mid points of the ear passages to the vertex, cannot properly be compared with 
any of the three similar measurements on the skull, even after due allowance is 
made for scalp-depth. These three measurements are as follows: 
(1) Basi-vertical height, i.e. height of skull, from the basion to the point on 
the top of the skull vertically above it, perpendicular to the horizontal plane of 
the Frankfurt Concordat — the German horizontal plane. This plane is determined 
by three points, the two highest points on the upper rims of the auricular passages 
and the lowest point on the under rim of the left eye socket. 
(2) Auricular height, i.e. the vertical height of the skull measured perpen- 
dicular to the German horizontal plane, in a line perpendicular to the auricular 
