Finger Prints

by Francis Galton

Of course these conclusions must not be applied to the general shape of the hand, which as yet I have not studied, but which seems to offer a very interesting field for exact inquiry.

---

CHAPTER XIII

GENERA

The same familiar patterns recur in every large collection of finger prints, and the eye soon selects what appear to be typical forms; but are they truly “typical” or not? By a type I understand an ideal form around which the actual forms are grouped, very closely in its immediate neighbourhood, and becoming more rare with increasing rapidity at an increasing distance from it, just as is the case with shot marks to the right or left of a line drawn vertically through the bull’s eye of a target. The analogy is exact; in both cases there is a well-defined point of departure; in both cases the departure of individual instances from that point is due to a multitude of independently variable causes. In short, both are realisations of the now well-known theoretical law of Frequency of Error. The problem then is this:—take some one of the well-marked patterns, such as it appears on a particular digit,—say a loop on the right thumb; find the average number of ridges that cross a specified portion of it; then this average value will determine an ideal centre from which individual departures may be measured; next, tabulate the frequency of the departures that attain to each of many successive specified distances from that ideal centre; then see whether their diminishing frequency as the distances increase, is or is not in accordance with the law of frequency of error. If it is, then the central form has the attributes of a true type, and such will be shown to be the case with the loops of either thumb. I shall only give the data and the results, not the precise way in which they are worked out, because an account of the method employed in similar cases will be found in Natural Inheritance, and again in the Memoir on Finger Prints in the Phil. Trans.; it is too technical to be appropriate here, and would occupy too much space. The only point which need be briefly explained and of which non-mathematical readers might be ignorant, is how a single numerical table derived from abstract calculations can be made to apply to such minute objects as finger prints, as well as to the shot marks on a huge target; what is the common unit by which departures on such different scales are measured? The answer is that it is a self-contained unit appropriate to each series severally, and technically called the Probable Error, or more briefly, P.E., in the headings to the following tables. In order to determine it, the range of the central half of the series has to be measured, namely, of that part of the series which remains after its two extreme quarters have been cut off and removed. The series had no limitation before, its two ends tailing away indefinitely into nothingness, but, by the artifice of lopping off a definite fraction of the whole series from both ends of it, a sharply-defined length, call it PQ, is obtained. Such series as have usually to be dealt with are fairly symmetrical, so the position of the half-way point M, between P and Q, corresponds with rough accuracy to the average of the positions of all the members of the series, that is to the point whence departures have to be measured. MP, or MQ,—or still better, ½(MP + MQ) is the above-mentioned Probable Error. It is so called because the amount of Error, or Departure from M of any one observation, falls just as often within the distance PE as it falls without it. In the calculated tables of the Law of Frequency, PE (or a multiple of it) is taken as unity. In each observed series, the actual measures have to be converted into another scale, in which the PE of that series is taken as unity. Then observation and calculation may be compared on equal terms.

Observations were made on the loops of the right and left thumbs respectively. AHB is taken as the primary line of reference in the loop; it is the line that, coinciding with the axis of the uppermost portion, and that only, of the core, cuts the summit of the core at H, the upper outline at A, and the lower outline, if it cuts it at all, as it nearly always does, at B. K is the centre of the single triangular plot that appears in the loop, which may be either I or O. KNL is a perpendicular from K to the axis, cutting it at N, and the outline beyond at L. In some loops N will lie above H, as in [Plate 4], Fig. 8; in some it may coincide with H. (See [Plate 6] for numerous varieties of loop.) These points were pricked in each print with a fine needle; the print was then turned face downwards and careful measurements made between the prick holes at the back. Also the number of ridges in AH were counted, the ridge at A being reckoned as 0, the next ridge as 1, and so on up to H. Whenever the line AH passed across the neck of a bifurcation, there was necessarily a single ridge on one side of the point of intersection and two ridges on the other, so there would clearly be doubt whether to reckon the neck as one or as two ridges. A compromise was made by counting it as 1½. After the number of ridges in AH had been counted in each case, any residual fractions of ½ were alternately treated as 0 and as 1. Finally, six series were obtained; three for the right thumb, and three for the left. They referred respectively (1) to the Number of Ridges in AH; (2) to KL/NB; (3) to AN/AH, all the three being independent of stature. The number of measures in each of the six series varied from 140 to 176; they are reduced to percentages in Table XXXI.

We see at a glance that the different numbers of ridges in AH do not occur with equal frequency, that a single ridge in the thumb is a rarity, and so are cases above fifteen in number, but those of seven, eight, and nine are frequent. There is clearly a rude order in their distribution, the number of cases tailing away into nothingness, at the top and bottom of the column. A vast amount of statistical analogy assures us that the orderliness of the distribution would be increased if many more cases had been observed, and later on, this inference will be confirmed. There is a sharp inferior limit to the numbers of ridges, because they cannot be less than 0, but independently of this, we notice the infrequency of small numbers as well as of large ones. There is no strict limit to the latter, but the trend of the entries shows that forty, say, or more ridges in AH are practically impossible. Therefore, in no individual case can the number of ridges in AH depart very widely from seven, eight, or nine, though the range of possible departures is not sharply defined, except at the lower limit of 0. The range of variation is not “rounded off,” to use a common but very inaccurate expression often applied to the way in which genera are isolated. The range of possible departures is not defined by any rigid boundary, but the rarity of the stragglers rapidly increases with the distance at which they are found, until no more of them are met with.

The values of KL/NB and of AN/AH run in a less orderly sequence, but concur distinctly in telling a similar tale. Considering the paucity of the observations, there is nothing in these results to contradict the expectation of increased regularity, should a large addition be made to their number.