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.
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 individualdepartures 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 inNatural Inheritance, and again in the Memoir on Finger Prints in thePhil. 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 toeach 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 theuppermost 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, asit 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 inPlate 4, Fig. 8; in some it may coincide with H. (SeePlate 6for 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 arecases 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 isnot“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.
Table XXXI.
Table XXXII.
Table XXXIII.
Table XXXII. is derived from Table XXXI. by a process described by myself in many publications, more especially inNatural Inheritance, and will now be assumed as understood. Each of the six pairs of columns contain, side by side, the Observed and Calculated values of one of the six series, the data on which the calculations were made being also entered at the top. The calculated figures agree with the observed ones very respectably throughout, as can be judged even by those who are ignorant of the principles of the method. Let us take the value that 10 per cent of each of the six series falls short of, and 90 per cent exceed; they are entered in the line opposite 10; we find for the six pairs successively,
The correspondence between the more mediocre cases is much closer than these, and very much closer than between the extreme cases given in the table, namely, the values that 5 per cent fall short of, and 95 exceed. These are of course less regular, the observed instances being very few; but even here the observations are found to agree respectably well with the proportions given by calculation, which is necessarily based upon the supposition of an infinite number of cases having been included in the series.
As the want of agreement between calculation and observation must be caused in part by thepaucity of observations, it is worth while to make a larger group, by throwing the six series together, as in Table XXXIII., making a grand total of 965 observations. Their value is not so great as if they were observations taken from that number of different persons, still they are equivalent to a large increase of those already discussed. The six series of observed values were made comparable on equal terms by first reducing them to a uniform PE and then by assigning to M, the point of departure, the value of 0. The results are given in the last column but one, where the orderly run of the observed data is much more conspicuous than it was before. Though there is an obvious want of exact symmetry in the observed values, their general accord with those of the calculated values is very fair. It is quite close enough to establish the general proposition, that we are justified in the conception of a typical form of loop, different for the two thumbs; the departure from the typical form being usually small, sometimes rather greater, and rarely greater still.
I do not see my way to discuss the variations of the arches, because they possess no distinct points of reference. But their general appearance does not give the impression of clustering around a typical centre. They suggest the idea of a fountain-head, whose stream begins to broaden out from the first.
As regards other patterns, I have made many measurements altogether, but the specimens of each sort were comparatively few, except in whorled patterns. In all cases where I was able to form awell-founded opinion, the existence of a typical centre was indicated.
It would be tedious to enumerate the many different trials made for my own satisfaction, to gain assurance that the variability of the several patterns is really of the quasi-normal kind just described. In the first trial I measured in various ways the dimensions of about 500 enlarged photographs of loops, and about as many of other patterns, and found that the measurements in each and every case formed a quasi-normal series. I do not care to submit these results, because they necessitate more explanation and analysis than the interest of the corrected results would perhaps justify, to eliminate from them the effect of variety of size of thumb, and some other uncertainties. Those measurements referred to some children, a few women, many youths, and a fair number of adults; and allowance has to be made for variability in stature in each of these classes.
The proportions of a typical loop on the thumb are easily ascertained if we may assume that the most frequent values of its variable elements, taken separately, are the same as those that enter into the most frequent combination of the elements taken collectively. This would necessarily be true if the variability of each element separately, and that of the sum of them in combination, were all strictly normal, but as they are only quasi-normal, the assumption must be tested. I have done so by making the comparisons (A) and (B) shown in Table XXXIV.,which come out correctly to within the first decimal place.
Table XXXIV.
It has been shown that the patterns are hereditary, and we have seen that they are uncorrelated with race or temperament or any other noticeable peculiarity, inasmuch as groups of very different classes are alike in their finger marks. They cannot exercise the slightest influence on marriage selection, the very existence both of the ridges and of the patterns having been almost overlooked; they are too small to attract attention, or to be thought worthy of notice. We therefore possess a perfect instance of promiscuity in marriage, or, as it is now called, panmixia, in respect to these patterns. We might consequently have expected them to be hybridised. But that is not the case; theyrefuse to blend. Their classes are as clearly separated as those ofany of the genera of plants and animals. They keep pure and distinct, as if they had severally descended from a thorough-bred ancestry, each in respect to its own peculiar character.
As regards other forms of natural selection, we know that races are kept pure by the much more frequent destruction of those individuals who depart the more widely from the typical centre. But natural selection was shown to be inoperative in respect to individual varieties of patterns, and unable to exercise the slightest check upon their vagaries. Yet, for all that, the loops and other classes of patterns are isolated from one another just as thoroughly and just in the same way as are the genera or species of plants and animals. There is no statistical difference between the form of the law of distribution of individual Loops about their respective typical centres, and that of the law by which, say, the Shrimps described in Mr. Weldon’s recent memoirs (Proc. Roy. Soc., 1891 and 1892) are distributed about theirs. In both cases the distribution is in quasi-accordance with the theoretical law of Frequency of Error, this form of distribution being entirely caused in the patterns, byinternalconditions, and in no way by natural selection in the ordinary sense of that term.
It is impossible not to recognise the fact so clearly illustrated by these patterns in the thumbs, that natural selection has no monopoly of influence in the construction of genera, but that it could be wholly dispensed with, the internal conditions acting by themselves being sufficient. When the internalconditions are in harmony with the external ones, as they appear to be in all long-established races, their joint effects will curb individual variability more tightly than either could do by itself. The normal character of the distribution about the typical centre will not be thereby interfered with. The probable divergence (= probable error) of an individual taken at random, will be lessened, and that is all.
Not only is it impossible to substantiate a claim for natural selection, that it is the sole agent in forming genera, but it seems, from the experience of artificial selection, that it is scarcely competent to do so by favouring merevarieties, in the sense in which I understand the term.
My contention is that it acts by favouring smallsports. Mere varieties from a common typical centre blend freely in the offspring, and the offspring of every race whosestatisticalcharacters are constant, necessarily tend, as I have often shown, to regress towards their common typical centre. Sports, on the other hand, do not blend freely; they are fresh typical centres or sub-species, which suddenly arise we do not yet know precisely through what uncommon concurrence of circumstance, and which observations show to be strongly transmissible by inheritance.
A mere variety can never establish a sticking-point in the forward course of evolution, but each new sport affords one. A substantial change of type is effected, as I conceive, by a succession of small changes of typical centre, each more or less stable,and each being in its turn favoured and established by natural selection, to the exclusion of its competitors. The distinction between a mere variety and a sport is real and fundamental. I argued this point inNatural Inheritance, but had then to draw my illustrations from non-physiological experiences, no appropriate physiological ones being then at hand: this want is now excellently supplied by observations of the patterns on the digits.