24 Size of Articular Surfaces of Long Bones 



in each division, the transfer being 1.25 per cent. In the smaller 200 

 there were 30 male (15 per cent), and 170 female (85 per cent). In the 

 larger 200 these figures were reversed. 



Surely these results are very convincing, and the manipulation by which 

 two even halves are obtained quite justifiable. 



Let us now inspect the curves. It stands to reason that there must 

 be some overlapping. It is self-evident that the joints of all males 

 cannot be larger than those of all females, even of the same race. I have 

 already given the figures which show how surprisingly few of either sex 

 pass beyond the average of the other sex; that is, how few male bones 

 are below the female average and how few female bones above the male 

 average. Now these curves show that if we suppress a small percentage 

 composed of erratic individuals, the overlapping is remarkably small and 

 restricted to a very narrow debatable ground. The curve of the vertical 

 diameter of the humerus (Plate I) shows that the smallest male measure- 

 ment is 41 mm. and the largest female 50 mm. Thus there is an over- 

 lapping extending through half the breadth of the two curves. There 

 are 313 individual measurements overlapping (78.25 per cent). But 

 the chart shows clearly that this wide spread of overlapping is due to a 

 few aberrant specimens. If we take away only 9 male and 10 female 

 (4.75 per cent);, the number of overlapping bones is reduced to 64, or 

 16.80 per cent of the remaining 381. What is most remarkable is that 

 after this elimination of extreme formations, the overlapping is limited 

 to diameters of 45 and 46 mm.^ 



The curve of the transverse diameter of the head of the humerus 

 (Plate II) is very similar; 303 overlap (75.75 per cent), but if 7 male 

 and 9 female (4 per cent) are thrown out only 68 bones (17.71 per cent) 

 of the remainder overlap; and the overlapping is limited to bones meas- 

 uring 41 and 42 mm. 



The curve of the head of the femur (Plate III) is interesting inas- 

 much as there are fewer aberrant bones to remove and yet greater ulti- 

 mate overlapping. Originally 313 bones (78.25 per cent), (precisely the 

 same as in the vertical diameter of the humerus) overlap, but of these 

 only 6 male and 3 female (2.25 per cent) are sufficiently isolated to 

 justify their removal, after which 113 (28.90 per cent) of the remainder 

 still overlap. Moreover, the overlapping includes three millimeters, 

 namely, 46, 47 and 48 mm., instead of only two, as in both diameters 

 of the humerus. 



^ That part of the curves represented by a continuous line shows them as 

 they would be after this elimination. 



