The column headed "all slopes" refers to the method first used with success, and described in my Memoir, already alluded to (_Proc. Roy. Soc._, 1891), accompanied by a specimen index, from which the present one was derived. There the direction of the slope of every pattern that has one, is taken into account, and in order to give as much scope as possible to the method, the term Arch (I then called it a Primary) was construed somewhat over-liberally (see p. 114). It was made to include the forked-arch Fig. 12 (~2~), and even the nascent-loop (~9~), so long as not more than a single recurved ridge lay within the outline of the pattern; therefore many of the so-called arches had slopes. It is not necessary to trouble the reader with the numerical nomenclature that was then used, the method itself being now obsolete. Full particulars of it are, however, given in the Memoir. A somewhat large experience in sorting finger prints in various ways and repeatedly, made it only too evident that the mental strain and risk of error caused by taking all slopes into account was considerable. The judgment became fatigued and the eye puzzled by having to assign opposite meanings to the same actual direction of a slope in the right and left hands respectively. There was also a frequent doubt as to the existence of a slope in large whorls of the spiral- and circlet-in-loop patterns (Fig. 13, ~21~, ~22~) when the impressions had not been rolled. A third objection is the rarity of the inner slopes in any other digit than the fore-finger. It acted like a soporific to the judgment not only of myself but of others, so that when an inner slope did occur it was apt to be overlooked. The first idea was to discard slopes altogether, notwithstanding the accompanying loss of index power, but this would be an unnecessarily trenchant measure. The slope of a loop, though it be on the fore-finger alone, decidedly merits recognition, for it differentiates such loops into two not very unequal classes. Again, there is little chance of mistake in noting it, the impression of the thumb on the one side and those of the remaining fingers on the other, affording easy guidance to the eye and judgment. These considerations determined the method I now use exclusively, by which Table IX. was compiled, and to which the second column of Table X., headed "_i_ and _o_ in fore-fingers," refers. The heading of the third column, "no slope," explains itself, no account having been there taken of any slopes whatever, so _i_ and _o_ disappear, having become merged under _l_. The table gives a very favourable impression of the differentiating power of all these methods of indexing. By the "_i_ and _o_ fore-finger" method, it requires as many as 76 different index-headings to include the finger prints of 100 different persons, 195 of 300 persons, and 285 of 500.