114 
Proceedings of the Royal Society of Edinburgh. [Sess. 
It may be objected that Topinard’s average indices, while useful for the 
comparison of averages, are of little value as standards of comparison in 
individual cases. To obviate this objection a method of comparison has 
been devised. In this the length of the bone is first taken, and from it 
the minimum and maximum possible statures of a normally-proportioned 
individual possessing such a bone are calculated. The calculation is 
based upon the known range of variations in the proportions of individuals, 
and the factors employed are those given in Professor Cunningham’s 
Text-book of Anatomy, viz. humerus, 4‘93-5'25 ; ulna, G^G-G-GG ; radius, 
6*70-7*11, ■ — (17). 
Thereafter, utilising the same factors, the probable lengths of the 
different bones in an individual of stature 1732 mm. are calculated. The 
minimum and maximum percentage of excess in the length of the bones of 
A 9 are then readily obtainable. 
Table XX. 
Nanie of Bone. 
Length, 
mm. 
Corresponding 
Stature Range 
in normally 
proportioned 
Individuals. 
Normal Range 
of Bone Lengths 
in Individuals 
of Stature 1732. 
Minimum and Maxi- 
mum Percentages of 
Excess of Length 
in A 9. 
Humerus 
335 
1651 -5-1758-7 
359-5-329-9 
-7*3 . . +1-5 
Ulna . 
275 
1721-5-1831-5 
276-6-260 
- -5 . . +5-4 
Radius 
259 
1735-3-1841 -4 
258-5-243-5 
+ *6 . . +6 
. 
This table shows that the humerus was relatively the shortest bone of 
the trio, the radius relatively the longest. 
The minus signs do not necessarily mean that the humerus and ulna 
were absolutely short. The tibial and femoral lengths are included in 
stature, and the possibility is that it means that the humerus grew less 
than the tibia. It is shown later that this was the case. 
5. Hand . — The aggregate length of the bones of the middle column of 
the hand, viz. the semilunar, the os magnum, the middle metacarpal, and 
the phalanges of the middle digit, is 187 mm. This is only 10*8 per cent, 
of the total stature in place of the normal 11*7 per cent. This, however, 
does not necessarily mean that the hand is absolutely short, only that it 
is short relatively to a stature which includes variables of unknown values. 
The most reliable standard for comparison, because it contains fewest 
variables, is furnished by the basi-nasal length. Using this as the basis 
of comparison, the relative size of the hand is shown by the measurements 
in Table XXI. 
