June 1, 1899.] 



KNOWLEDGE. 



127 



do with all these figures when we have got them. For 

 purposes of comparison between different races, it is essential 

 that WG should reduce them to a common standard, and 

 this has been done by many anthropologists with much 

 advantage and proiit. The average proportions of different 

 races may be thug numerically expressed, and by careful 

 study and comparison of these figures, results of much 

 value may be arrived at. But, as a matter of experience, 

 we are bound to confess, elaborate tables of measurements 

 convey little to our minds. We content ourselves, as a 

 rule, with reading" the summary, which the author may by 

 chance have been good enough to supply ; the tables are 

 glanced at, to see if there is anything very striking about 

 them, and then, unless our interest happens to be directed to 

 some particular point, they are set aside, unstudied, and 



parts which makes it so difficult to realise the true relation 

 of each part to the other when expressed in figures. It 

 seems to us that the only satisfactory method to adopt is 

 to reduce the data to graphic form and so represent them. 

 The advantage of such a system is that the eye is 

 quick to pick out the characteristics of each type, and it is 

 only necessary to run the eye along such a series of types 

 to recognise what are the main features on which their 

 differences depend. 



In the diagram here given an attempt has been made to 

 put these views into practice, with what success the reader 

 must be left to judge. 



As previously stated, the matter is not quite so easy as 

 might be imagined, the diificulty being due to lack of 

 uniformity in the measurements employed and the omission 



Fig. 4. 



517 Iroquois 



Indians. 



Graphic REPEESExiATioy of the Peopobtions of some Races 



little appreciated. Now, there must be something wrong 

 in all this. Considering the vast amount of time and 

 trouble spent in securing these data, there should be some 

 more profitable way of demonstrating the results than that 

 usually adopted. 



For statistical purposes curves have long been employed, 

 and are extremely useful to express the variations which 

 occur when dealing with one class of measurements (height, 

 for instance), but when we have more than two factors to 

 consider, curves become unmanageable, or, at least, so 

 complicated as to be beyond the reach of all but expert 

 mathematicians. In studying such a question as racial 

 proportion, the reader will recognise that we have to deal 

 with variations in the proportions of trunk to limbs, 

 hmbs to Umbs, segments of limbs to each other, &c. ; it 

 is this complication in the inter-relation of the various 



of certain measurements which are necessary to the 

 scheme. 



Each figure represents the proportion of the limbs, 

 trunk and head in terms of one thousand. The first, second 

 and fourth figures are constructed from data obtained from 

 Topinard's work on Anthropology, the Australian type is 

 based upon measurements given in Spencer and Gillens' 

 " Tribes of Central Australia," whilst Figs. 5, 6, and 7 are 

 derived from the data furnished by Dr. Hagen in his atlas of 

 " Ostasiatischer and Melanesischer Volker" (1898). Apart 

 from the racial characters which are here displayed in 

 graphic form, the figures strikingly illustrate many of the 

 points to which attention has been already directed. In 

 no case have I been able to determine satisfactorily the 

 point from which to draw the length of the upper limb 

 {i.e., the acromion process). In four cases I have assumed 



