372 Measurement of Internal Capacity of Skull 
(4) We now turn to Dr Bed doe's rule ^3, which up to the date of wiiting this 
he considers his best formula *. 
If we put Dr Beddoe's rule into a formula it is, if C be the capacity in cubic 
centimetres : 
where / is the cephalic index, U is the horizontal circumference, Q' is the 
auricular circumference from the centre of one auricular passage to that of the 
other, and S' the sagittal arc from nasion to inion, all in millimetres. 
It may be written in the form : 
where the product U x S' x Q' is to be read in cubic centimetres and not cubic 
millimetres. 
Now let Pi stand for U x S' x Q' and p2 for I x U x 8' x Q', and let o-„ be 
the standard deviation of the character or quantity v and ?•„,„ the correlation of 
* Dr Beddoe gives three formula in his paper Bj, B„, B.j, and calculates some of the results by one 
and some by another of these rules. He tells us that he has another rule in preparation, and 
that he has been gradually feeling his way. It is against any such process as this that we wish 
emphatically to protest. Every one of Dr Beddoe's formulae is a mere guess. In no case does he 
adopt a certain type of formula and determine by recognised statistical methods the best values to be 
given to the constants of that formula. If he finds it gives him somewhat too high a series of values 
he merely reduces it by cutting off a series of percentages from the result. As he tells us B^ is his best 
formula at present we have used B^. This is designed to give what Dr Beddoe terms Flower's values, 
or what we should simply term the capacities properly measured, e.g. not the recognised erroneous 
values of Barnard Davis. It is obtained in the following manner : he measured his sagittal arc, S', 
from the nasion to the inion instead of to the opisthion — of this later more — and since the sagittal arc, 
S", is usually measured to the opisthion, he subtracts 50 mm. from it to find S'. Next he takes the 
vertical circumference, Q\ which he measures from the centre of one auricular passage to that of the 
other. This is really not our Q. Our transverse circumference is measured from top of one auricular 
passage to the top of the other and " vertical," i.e. perpendicular to the Frankfurt " horizontal plane." 
He ought not accordingly to have interchanged as he has done our Q with his own Q'. Probably 9 or 
10 mm. ought to be subtracted to get Q from Q', even if we could possibly accept his " passant par le 
bregma ou pas loin en arri^re " as giving even an approximation to the "vertical plane." But as 
Dr Beddoe appears content to use our Q for his Q', we have made no attempt to modify it in order to 
reach an arc so vaguely described as " passing through the bregma or not far behind it." As a matter 
of fact the "vertical plane" may easily fall 10, 20, or even 30mm. behind it. Lastly, to get the 
capacity Dr Beddoe multiplies -J of the horizontal circumference (U) by J of the nasio-iniac arc S' by | 
of his auricular arc. He then divides this product by -j^jVu' ^-nd deducts J per cent, of the result for 
each unit of the cephalic index below 80, and adds a third per cent, for each unit above 80. This is 
the rule which we have represented by the formula in the text. It will be observed that it is by no 
means so simple as the product formulae we have used, besides being obtained by a theoretically 
unjustifiable process. B^ takes 4.5 mm., not 50 mm., ofi S to get S' and neglects the cephalic index 
correction. B„ takes 50 mm. off like B^, but takes A instead of i per cent, for cephalic index correction. 
It will be seen that the constants are pure guesswork changeable at will. 
C = 0000926 Ix UxS'xQ'+ -020374 U x S' x Q', 
