Ethel M. Elderton 
61 
they were made, to bring our respective interpretations of transitional and of 
some of the other invaded loops, into strict accordance, so I jjrefer to kee}) his 
vvoi'k, in which I have perfect confidence, independent from my own." 
On the basis of my own experience I should prefer to arrange finger-prints in 
five groups and in the following order, arch, plain loop, " not plain " loop, com- 
posite, whorl, and if I had to combine two of these groups I should put " not 
plain " loop with composite but I am not yet in a position to prove that this 
is the correct order and the difficulty of using such an order is that plain loops 
still remain too large a group and " not plain " loops and composites are both 
very small. I therefore decided to follow Dr Waite* and divide the loops in my 
table according to the number of ridges, i.e. into small and large loops. The 
method used for working out all the tables is mean square contingency, and in 
applying this method we must use the class index correction for grouping. This 
correction assumes that the categories under consideration are approximately 
normal and continuous and depends upon a knowledge of the " natural order." 
As I said before I have no doubt that the types of finger-print form a continuous 
variation, and that with a more extensive study of more ample data we should be 
able to determine this "natural order." I do not consider that we have yet found 
a wholly satisfiictory one, but as we shall see presently the corrective factor for 
grouping in this data seems to depend rather more on the number in each group 
than on the exact order of the grouping and that we can apply this factor without 
a knowledge of the absolutely correct "natural order." This question of a natural 
order of finger-print type attracted Francis Galton's attention and on p. 178 
of his Finger-Prints he writes : 
" It would be essential in exact working that the mutual relations of the 
patterns should be taken into account ; for example, suppose an arch to be found 
on the forefinger of one brother and a nascent loop on that of the other ; then, as 
these patterns are evidently related, their concurrence ought to be interpreted as 
showing some degree of resemblance." 
Thus the discovery of a " natural order " is not merely essential to the com- 
pleteness of mathematical reduction ; it arises at once when we begin to classify 
our characters from the standpoint of inheritance. 
(3) The provisional JSfataml Order of tlie present paper. 
We have next to investigate how far a natural order has been established if we 
divide loops into small and large loopsf and have as our other groups, arches, 
composites and whorls. Certain types of patterns are associated with small and 
large loops respectively. Thus small loops are more nearly associated with arches 
and large loops with whorls. "Not plain" loops occur much more frequently in 
* Biometrika , Vol. x. p. 419. 
t Dr Waite defines a small loop as one having twelve or fewer ridges, a large loop as one with more 
than twelve ridges. 
