INTRODUCTION 7 



the best advantage, and during this investigation, endeavoring con- 

 stantly to bring out real morphological differences, has established 

 certain measurements which now rank among the most important and 

 universally employed of anthropometric data. 



Aside from Schwalbe, who was very conservative in his use of measure- 

 ments, there is a large school of anthropologists of moderate ideas, who 

 seek to describe the bones of representatives of the various races, and 

 their bodies as well, by making a reasonable number of measurements, 

 and at present in the special measurements selected there is in general a 

 close agreement. Actual conditions may be represented by a comparison 

 of the work of several of the leading investigators in regard to craniometry, 

 or the application of measurements to the description of the skull. In 

 1906 Frederic, an associate of Schwalbe, described certain individual 

 skulls by the help of 53 separate data, of which 26 are linear measure- 

 ments; 17, indices; 5, angles; and 3, girths. Adachi, in 1904, in a paper 

 specially devoted to the examination of the orbital region of Japanese 

 skulls, employs 56 separate data, of which the greater number refer to 

 the orbit proper. E. Fischer (University of Freiburg, 1913) presents 

 in his laboratory outlines, for skull mensuration, which he furnishes to 

 his students, a list of 77 separate data, 43 of which are linear measure- 

 ments, 3 are angles, 8 are girths, and 22 are indices; and Schlaginhaufen 

 (University of Zurich, 1913) uses for the same purpose 82, for the most 

 part identical with the former. Even v. Torok, with his extreme views 

 regarding possible craniometrical measures, is yet willing to print a list 

 of what he calls the "most important" data, which he considers sufficient 

 for purposes of general description, and which include only 26 linear 

 measures, 8 indices, 3 girths, and a few other data, 39 in all. Duckworth 

 (University of Cambridge, England, 1910) employs in a descriptive 

 paper on Sardinian crania no more than 11 measurements and 5 indices, 

 although he recommends in practical laboratory work (1904) 15 linear 

 measurements, 7 indices, 3 angles, and the cranial capacity. Finally 

 the Prescription of 1906, which obtained the unanimous approval of 

 the International Anthropological Congress, comprises 38 separate data ; 

 viz., 32 linear measurements, 3 arcs, 1 angle, and the cranial capacity. 



A real danger that besets the anthropometrist along the mathematical 

 side, and one to which a student may be naturally brought by seeking 

 to be accurate, is the temptation to treat with too great respect the actual 

 figures obtained from the individual measurements, to regard the decimal 

 places as of equal importance in all cases, and to feel that a series of 

 measurements carried out to the third place, for instance, is much more 

 accurate and reliable than one carried out only a single place beyond 

 the point. 



As a matter of fact, the accuracy of a result depends essentially upon 

 the method of making the measurement, and here not only must the 

 personal equation, as involved in the operator, be taken into considera- 

 tion, but also the condition of the material measured, for where the 



