INTRODUCTION O 



lineating mortals, and 100° in certain of their representations of gods. 

 On the other hand the apes, monkeys, and lower mammals gave angles 

 less than 70°, in a decreasing series, so that this facial angle was roughly a 

 measure of the height of the forehead and hence indicative of the general 

 intelligence. 



As with linear measurements, the Mid-Nineteenth Century, largely 

 under the leadership of Paul Broca, brought into use other angles, for 

 the most part those of the skull, while at the present times important 

 angular measurements have been established for many other bones. 

 Aside from single angles some anthropometrists make use of tri- 

 angles, quadrilaterals, and even higher polygons, mainly in connection 

 with mathematically drawn projections of bones upon a plane surface. 

 With the living body, in spite of the fact that the first angle used, 

 that of Camper, found here its main application, there are now few, if 

 any, angles in common anthropometric use, although certain ones 

 mainly those associated with the arm, leg, or foot, have a pathological 

 or orthopedic significance. 



No International Congress has as yet attempted to establish or define 

 any prescribed angles for either the bones or the living body, and the 

 matter rests at present, as was the case with linear measurements previous 

 to 1906, with the individual investigators; certain obvious angles are 

 commonly employed, and with considerable uniformity in definition, 

 while others are devised by individual authors and used in bringing out 

 relationships the value of which has not as yet been thoroughly tested. 

 A distinct advantage of an angle over a linear measurement lies in the 

 fact that angles may be compared directly in individuals of different 

 size, and need no index; possible disadvantages are found in the uncer- 

 tainty of fixing the lines which describe them, and in the difficulty of 

 reading them accurately. 



Concerning the actual value of anthropometric measurements, of 

 whatever sort, and the extent to which measurement may be profitably 

 carried, both opinion and practice differ widely. As in other forms of 

 biometrics, where mathematics plays an important part in the investiga- 

 tion of a primarily biological problem, certain investigators are bound to 

 be more interested in the mathematical than in the biological side, and 

 there is always danger that, in their hands, the latter cause may suffer, 

 and the work be viewed as a mathematical problem, in which the goal 

 is reached when the new relations involved are expressed in the form of 

 formulae and tables. Others, on the other hand, view Physical Anthro- 

 pology as wholly morphological, and place their reliance upon forms and 

 form-comparisons as revealed to the eye, being very wary about express- 

 ing any character in a mathematical form. 



As an example of the mathematical extreme, of an anthropometrist 

 in whose hands the whole subject becomes an endless series of measure- 

 ments, we may take the Hungarian investigator, Dr. Aurel von Torok. 



