75 
1910-11.] Relative Positions of certain Biological Types. 
large probable errors due to random sampling. Wherever possible, there are 
needed more extended observations of the various measurements and indices 
on many of the crania, so that the probable errors of the average values in 
Table I. may be reduced as far as possible, and the absent measurements 
supplied. Where the main object is an attempt at placing various crania of 
extinct type in their correct evolutionary positions between the anthropoid 
apes on the one hand, and modern man on the other, this is necessarily in 
many cases impossible. Attempts should, however, be made to determine 
as accurately as possible certain standard positions in the evolutionary 
scale. Anthropoid apes and certain highly and lowly developed races of 
modern man could have their various average measurements determined 
to a considerable degree of accuracy. Any individual prehistoric cranium 
would, of course, take its position on the strength of its own individual 
characteristics. It might or might not be a representative specimen of the 
race to which it belonged. 
It should be pointed out that, were new determinations of the relative 
positions and the relative values of the measurements and indices as 
criteria at any time undertaken with data completed as above indicated, 
and dependent on a much greater amount of material, such determinations 
would be no more laborious than are the present. In fact, were the empty 
spaces in Table I. filled in, the calculations of all the resultant values 
would be lightened, the necessity for Tables III. and V. would vanish, the 
coefficients of correlation in Tables IV. and VI. being determined by 
reference in each case to a single standard series, and so on. The values 
obtained in the present work are those deduced from the available data. 
They are correct as far, and only as far, as are the available data. More 
accurate initial average values of the various cranial measurements would, 
following the same methods of analysis, lead to more accurate final values. 
Turning to the relative values of the various cranial measurements 
and indices as criteria of position in the evolutionary scale, we find the 
calvarial height to be the most reliable single measurement by which to 
place various types of crania in their proper evolutionary positions. At 
the top of the scale, where several types are near one another, minor 
alterations of positions are only to be expected ; but, taken as a whole, the 
close agreement between the evolutionary order as given by this measure- 
ment and the composite order will be seen by comparing, say, the first line 
of Table II. with the corresponding series of Table Y. 
Following the calvarial height (> = 0-9777) are, in order (see fig. 2), 
the frontal curvature (> = 0*9579), the calvarial height-breadth index 
