H. Waite 
447 
The proposed " natural order " of the types is supported by the above Tables, 
only eight coeflScients out of the fifty-five not being in complete agreement. In 
four of these cases the difference is very small, most likely well within the probable 
errors, and they may therefore be regarded as insignificant. 
A similar arrangement of the correlation coefficients still further supports the 
proposed order, though not quite so conclusively, probably on account of spurious 
correlations. 
9. Association between the various Fingers. In this section I have calculated 
the contingency coefficients only, the classes being arranged in the order found in 
Section 8, p. 445. 
It would, of course, be possible to obtain Tables with much finer grouping 
either by further subdivision of the loops or by making use of the "secondary 
classification" described by Galton or Henry (see footnote, p. 421). All such finer 
grouping would raise the contingency ; the extra labour involved by the addition 
of some three or four rows and columns to each Table would, however, be so con- 
siderable that the question arises whether some allowance can be made for the 
coarser grouping employed. This can only be done if vpe may suppose a "natural 
order" of some kind with a frequency roughly approaching the normal. This 
gives a rough upper limit to the contingency and is the purport of the work in 
the earlier sections on " natural order " and corrections. 
As an example of the effect which finer grouping has on contingency I have 
found the contingency between the index fingers of the two hands by means of 
a " seven by seven " Table, the radial and ulnar loops being separated, and also by 
means of a "five by five" Table in which no distinction is drawn between the 
radial and ulnar loops. The results in this case, not corrected for grouping, are 
"653 and '626 ; when corrected for grouping these results become '704 and '698, 
respectively. They are so nearly identical as to suggest that no very material 
advantage would be gained by a further subdivision of classes. 
On the assumption that there is a certain degree of continuity in the distri- 
bution I have corrected all the results for grouping as well as for the number of 
cells. The method employed for the former correction is fully described by 
Professor Pearson in Biometrika*. 
The following Tables give the contingency coefficients for each finger with 
each other finger. The two sets of coefficients are included, viz. those which are 
not corrected for grouping, that is, which ai-e obtained without any assumption of 
a "natural order" and those which are so corrected, in order that the conclusions 
based on the latter may be compared with those based on the former. 
* "On the Measurement of the Influence of 'Broad Categories' on Correlation," by Karl Pearson, 
F.E.S., Biometrika, Vol. ix. pp. 116—139. 
