io Records of the Indian Museum. [Voi,. XXIII, 



ciation ; that it is not one resulting from coincidence, but that it 

 represents an inseparable connection between natural phenomena.' 



"The attributes and conditions of living things are so widely 

 variable, are so delicately graduated in different individuals that 

 their correlation can seldom be legitimately postulated, and can 

 never be precisely estimated, without aid from a correlation 

 calculus : that is to say, social science almost entirely, and biolo- 

 gical and medical sciences to great extent, can only be built up 

 after preliminaiy mathematical analysis of large series of carefully 

 collected data ". This is the reason why we asserl that statistical 

 methods are indispensable for our present enquiry. 



We have, got Anthropometric measurements of 200 Anglo- 

 Indians as our material in the present case. We know that this 

 constitutes only a very small sample of the whole Anglo-Indian 

 population. We wish to investigate the Anthropometric charac- 

 teristics of the whole population but we are constrained to do so 

 from a stud} 7 of the sample alone. If the sample exhibits certain 

 typical features, we shall be justified in inferring the presence of 

 these typical features in the general population. Thus our first 

 statistical task is to find out the typical features of our sample. 

 In order to do so, it is necessary to describe the given sample by 

 means of a suitable typical curve, that is, to graduate the given 

 sample suitably. 



This very process of graduation itself will " smooth out " the 

 irregularities peculiar to the particular sample considered. Hence 

 when a typical formula is once obtained we get rid of the special 

 individual peculiarities of the given sample and can replace the 

 given sample by our graduated curve in all subsequent discussions. 

 This graduated curve is, by logical induction, assumed to be typical 

 of the whole population. 



This typical frequency curve is defined by certain statistical 

 constants ' calculated from the measurements actually given in the 

 sample. The reliability of each constant is determined by the 

 internal consistency or uniformity of the particular set of measure- 

 ments from which it is derived (and the total number of measure- 

 ments). The reliability (measured by the probable error) can be 

 precisely calculated with the help of the statistical calculus based 

 on the theoiy of probabilities. 



Thus in any statistical enquiry the first part of the work con- 

 sists in the determining of the appropriate frequency constants 

 and their probable errors. This is done in section II of the pre- 

 sent paper, which also 0011 tains an elaborate technical discussion 

 of the effect of grouping. 



The next part of our work consists in constructing a type 

 which is assumed to be true for the general population, within the 

 limits of the probable error of the type. This is the problem dis- 

 cussed in section IV. 



' I havi given ;i shorl account <»t some oi these constants in non-technical 



language in Appendix I. pp. UO — Q4. 



