Kathleen V. Ryley and Julia Bell 
433 
It appears therefore reasonable to assume that racially, where the nasal portion 
is large, so also is the maxillary portion of the nose. Notwithstanding this and the 
positive correlation of the simotic and maxillary nasal angles, as well as of the 
subtenses, the projections of the nasal and maxillary portions on the base of the 
nasal bridge are negatively correlated. The algebraic explanation of this paradox 
is given below *, but it seems probable that its physiological explanation lies in the 
relative constancy of the mesodacryal chord. If the reader will examine Table XIV 
he will see that the variability of the simotic chord relative to its size is almost 
twice that of the mesodacryal chord, and although some of this may be due to the 
relatively greater difficulty of accurate measurement the bulk of it is not. The 
following results will indicate the relative stability of the mesodacryal chord. 
They are deduced from Tables VIII and XIII, males. 
Mesodacryal 
Chord' 
Simotic 
Chord 
Interracial Mean 
21-6 
8-47 
Mean racial s. d. 
2-44 
1-97 
Interracial s. D. 
1-37 
1-20 
Mean racial s. d. 
100 x =—- 
Interracial Mean 
11-3 
233 
Interracial s. D. 
100 x^— 
Interracial Mean 
6-34 
14-13 
Racial Rans;e 
100 X . . -° — 
Interracial Mean 
235 
58-9 
Whichever method we take to measure the variation we see that the meso- 
dacryal chord is far less variable than the simotic chord. The breadth of the base 
of the nasal bridge is relatively constant. The nasal bridge has to span the nasal 
base, and whether we deal with the problem from the interracial or intraracial 
standpoint we realise that the nasal structure has to be considered as a whole, and 
that its anatomical units are very far from being necessarily evolutionary units, or in 
* The problem is algebraically of the following kind: given two right angled triangles ABC and 
A'B'C with C and C" for right angles, then with the usual notation c 2 = a 2 + b 2 , c' 2 = a' 2 + b" 2 , is it 
possible for c and c', a and a' and A and A' to be positively correlated together and yet b and b' to be 
negatively correlated ? Clearly if the means be denoted in the usual manner, we have approximately : 
bSb = c5e-a8a, b' 8b' = c' Sc' - a' 8a' . 
Hence multiplying together, summing for all possible pairs and dividing by their number, we have 
bb' <r b H' r bh' = CC' <r c <V 'V + 55 ' a a< T a' r aa' ~ ck ' °c a a' r ca' ~ °V a a r c'a- 
Hence if ?' cc < and r aa , are positive as the hypothesis supposes, and at least one or both r ca , and r c i a are 
positive also, the negative term or terms on the right may exceed the positive and r bb > be negative. In 
the case of the simotic and maxillary nasal triangles both r ca - and r c , a are positive, and the last pair of 
terms on the right is wholly negative and in excess of the first pair. The above result depends of course 
on c 2 = a' 2 + b' 2 and c" 2 = a' 2 + b' 2 being nearly true. These give c 2 = 84-83 against actual 84-64 and c" 2 = 29-68 
against 29-16. These are close enough to justify the use of the above formula, which on putting in the 
actual numbers gave r w the correlation of the projections negative, as the direct investigation gave it. 
Thus the origin of the negative value for the projections' correlation lies in the negative terms 
involving the cross-correlations of nasal bone with maxillary height and simotic subtense with maxillary 
wall, which are themselves positive. 
