N f* * ro-' ,
~ 2<r XttX
N f _ - r2
v2ir cr J h
1 __ ; L
= a-' x 0'156,975.
Now let us find the proportion of the population which has a head as large as the mean head of the exceptionally able people. We have if n be their number :
.,,/N = JL f e-W*dy'.
V/27T 0-156.975
We easily find from the tables 7i/N = 0*438. Thus 44 per cent, of the population have heads as large or larger than the mean head of the exceptionally able 2 per cent. Conversely, 44 per cent, of the population are as able or abler than the 2 per cent, of the population with exceptionally big heads. When we recollect that 50 per cent, of the population would be abler or larger headed than the mean of the population, it will be recognised how small is the basis upon which we can argue from ability to largeness of head or from largeness of head to ability.
In dealing with this problem we have dealt with a normal distribu- tion of ability in the general population. There is nothing thus far to prove a clow relationship between ability and either shape or size of the head. If phrenology were not a discredited branch of knowledge it would be easy to investigate its claims by a like statistical method. But phrenology has not met with the same widespread acceptance among men of science as the belief that ability brain power is corre- lated with the size of the head has done. Of course if abnormal ability genius and abnormal dulness crass stupidity were both associated with large-headedness, our method of investigation would fail to exhibit this result. We have no means of isolating crass stupidity from the mass of poll men. But we are able to pick out from the honours men unfortunately only 524 in number the grades of ability corresponding to first, second, and third classes under com- petitive examination. I found the following distributions :
