1902.] Correlation of Mental and Physical Characters. 11 1 



Now, it has sometimes been argued that in any investigation of this 

 kind, ' it is desirable to take not absolute weight, but its ratio to 

 stature or some power of stature. Let W = weight, S = stature, and 

 n = any power ; let E rt = W/S 7 *, and v be a coefficient of variation, 

 and r one of correlation, i standing for intelligence. 



Then 



v l = v w + n2v l ~ SnvvrVsFsw (i), 



>;n lt = (ii). 



. ' flu. 



But 



v s = 3-6958, v sw = 0-4860, 



v w = 10-8300, r iW = 0-0459, 



r* s = - 0-0058, 



from results already given for the Cambridge data. Hence, calculating 

 vr u frOm (i) for n = 1, 2, and 3, we deduce 



'Vr, = correlation of intelligence with ratio weight to stature = 0'0540, 

 r;R 2 = „ ,, „ (stature) 2 = 0*0555, 



r/v 3 R = „ „ „ (stature) 3 = 0-0503. 



There is no substantial difference between any of these correlations 

 .and that for intelligence and absolute weight. As they were found 

 indirectly by formulae, it seemed desirable to test at least one of them 

 directly. Accordingly Miss M. Beeton found the ratios of weight per 

 Inch of stature for 1012 Cambridge men. The resulting table was 

 .as follows : — 



(H.) Intelligence and Weight per inch of Stature. 





Honours. 



Pass. 



Totals. 



Over 2 -224 lbs. per in 



Under 2 - 224 ]bs. per inch . . 



258-5 

 265-5 



222 

 266 



480-5 

 531 -5 



Totals 



524 



488 



1012 



j 





The distribution is sensibly the same as that of the table for abso- 

 lute weights, and the correlation comes out 0-0604, i.e., it differs only 

 by 0*0064, or about one-fifth of the probable error from the value of 

 the correlation obtained indirectly. 



We may then, I think, conclude that whether we take absolute 

 weights or the ratio of weight to stature, honours, men are slightly 

 heavier than poll-men. Summing up the whole of our examination 

 thus far of the Cambridge measurements we may say that : 



