368 Measurement of Internal Capacity of Skull 
Now it will be seen at once from these results that to say a skull has a certain 
capacity does not fix the product of the circumferences, and to say that it has a 
certain product of circumferences by no means fixes its capacity. The only thing 
that is possible for us to assert is that Theban skulls with a capacity of 1380 — 90 
will cluster round the value 58,208 of the circumference product, and skulls with 
a circumference product between 58,600 and 59,100 will cluster round the capacity 
value 1389. If these clusters follow — and they do follow — the usual distribution 
of characters in man, then these mean values are the " most probable values " for 
product or capacity when deduced from a knowledge of capacity or product re- 
spectively. Tables can now be dressed giving these "most probable values" for each 
small range of capacity or product. Such tables are only another form of the corre- 
lation table and the regression curve, which Dr Beddoe seems to find so mysterious ; 
they are the only scientific way in 1904 of approaching these questions. Such 
" most probable values " in the case of most characters in man are found— allowing 
for the errors of random sampling — to increase uniformly with the uniform 
increase of the known character, in other words the regression curve is usually a 
straight line. The equation to this straight line is found by perfectly easy 
mathematical work and is what Dr Lee gave in her paper for the product of the 
three diameters, and what we give in this paper for the product of the three 
circumferences. If such a linear formula is to be used at all this is the only 
scientific way of approaching the probleni. Dr Beddoe himself uses such a linear 
relation, ; yet how does he write of the only method of scientifically dealing with 
a perfectly elementary statistical problem ? 
" Je me reconnais incompt^tent pour decider si I'idee de correlation pent tromper 
quand il s'agit de la forme cranienne et de sa capacity, et si I'idee de compensation, 
moins distinctement appreciable, il est vrai, merite d'etre etudiee*." 
We assert, with a distinct appreciation of the seriousness of the statement, 
that a writer who cannot realise what correlation is and how it is used in a simple 
problem of this kind has no right nowadays to deal with craniometric problems at 
all. It is only by frankly asserting on every occasion this truth that we can hope 
to render anthropometry in all its branches a real science. The day for the old 
methods is once and for ever gone. Correlation is simply the mathematical process 
of finding the best linear relation between the known value of one character and 
the most probable value of a second. It determines in the special case A and B 
in the relation : 
Probable C^A^Bx Known P (i). 
Dr Beddoe also wants to find a linear relation between Probable G and a 
Known P. How does he proceed ? In no case does he go through the laborious 
and necessary work of tabling the mean G for a given small range of P. He 
simply puts : 
Probable G^Bx Known P (ii), 
* Loe. cit. p. 278. 
