W. R. Macdonell 
183 
We will next attempt to fit a curve to the observed frequencies of Head 
Breadth and Height in the case of the 3000 criminals in accordance with Professor 
Pearson's method (see Phil. Trans. Vol. 186, A. pp. 343—414). 
(i) Head Breadth. 
The moments are : 
fji^= 25-14526 y8i= -010385 
/i3= 12-84962 /32 = 3-032609 
/i4 = 1917-47151. 
Therefore the criterion 2/32 — 3/3i — 6 = + -03406 ; the curve is therefore of 
Type IV., and the remaining constants are : 
d^- -253365 Skewness = - -050526 
r= 356-203035 m =179-101518 
v=- 194-9783 a = 82-900557 
log y, = 20-3543484. 
The equation to the curve is : 
a; = 82-900557 tan 6, 
log y = 20-3543484 + 358-203035 log cos 6 + 1-477904 6. 
The maximum ordinate or mode is 239-39 and occurs at « = 45-124714, cor- 
responding to a head breadth of 15-0188; the mean or centroid occurs at 
a; = 45-378079, its value being 15-0442. 
The curve obviously approximates very closely to the normal curve. 
(ii) Height. 
fi^= 6-45660 /?!= -002578 
fi^= -83300 /S2 = 3-175076 
/A4 = 132-36172. 
2^,- 3/8,-6 = + -342418. 
The curve is again of Type IV., and the remaining constants are : 
d = - -058071 Skewness = - -022853 
■r= 38-067473 m = 20033736 
v = - 2-870793 a = 15-42649 
y, = 433-647. 
The equation to the curve is : 
«= 15-42649 tan^, 
y = 433-647 (cos ^)«-<»"'« gT«,mze_ 
