228 
DR. A. LEE AND PROFESSOR K. PEARSON ON 
All the regression equations in the present paper have been worked from the above 
results, the most lengthy being those which depended on the evaluation of the 
numerical magnitude of the above determinant for the correlation of four organs. 
(3.) The special object of this investigation is to apply the theory given in the 
last section to the reconstruction of skull capacity—to determine which of the 
measurements, length, breadth, height, or cephalic index of skull, or which combina¬ 
tion of these measurements, will give the best result. In carrying out this special 
investigation, all the three fundamental problems considered in section (l) naturally 
arise, and will l)e referred to below. Further, certain problems regarding variation 
and correlation in man and woman also occur, and will he considered in their places. 
The problem of the determination of the capacity of the skull has been one which 
has long occupied the attention of craniologists and anthropologists, and a great 
variety of methods have been considered and have found acceptance from one or 
another authority. The ideal method has not, however, been yet discovered, and in 
the well-known ‘ Frankfurter Verstandigung ’ of the German craniologists, the matter 
was reserved for “further consideration,” and has remained for a number of years in 
tljat unsettled state. From a fairly elaborate system of skull capacity measure¬ 
ments made at University College by Miss C. D. Fawcett, B.Sc., it would appear that 
the same experimenter may, with very slight practice, reach surprisingly close results 
for the capacity by very diverse methods ; but that two different experimenters 
may giv^e a mean skull capacity for a series which differs by 15 to 40 cub. centims. 
Tliis of course only denotes about 1 to 3 per cent, of personal equation; hut it 
appears large when read in gross. I cannot think that any conclusions as to relative 
racial differences ought to be based solely on divergencies in skidl capacity of less than 
40 cub. centims. when the two or more series under consideration have been measured 
by different observers. The knowledge of this divergence arising from the personal 
equation of different observers has led certain craniologists to suggest formulre for 
calculating the capacity of the skull without measuring its contents, hiit from 
measurements of its girth, its heiglit, length, or breadth. These formulae seem to 
he unsatisfiictory because they have not been based on a knowledge of the mathe¬ 
matical theory of correlation. It will he shown in the sequel that a formula can 
be found which gives the average capacity of a series of skulls from their mean 
heio'ht, lenoth, and hreadtli with a fair deo-ree of accuracv. In view of this it is a 
matter for consideration whether its use might not effectively replace the laborious 
and unsatisfactory methods of determining capacity by seed, shot, or sand. These 
could always he fallen hack upon should any suspicion arise that the formula in 
question was being ai^plied to a too widely divergent local race. 
(4.) In selecting material for this investigation, I had to hear in mind residts 
already reached by my co-workers at University College, hut only in part at present 
published. In particular, that there was comparatively small correlation between the 
parts of the skull usually measured, and, further, that such correlation as actually 
