Finger Prints Part 6

EVIDENTIAL VALUE

The object of this chapter is to give an approximate numerical idea of the value of finger prints as a means of Personal Identification. Though the estimates that will be made are professedly and obviously far below the truth, they are amply sufficient to prove that the evidence afforded by finger prints may be trusted in a most remarkable degree.

Our problem is this: given two finger prints, which are alike in their minutiae, what is the chance that they were made by different persons?

The first attempt at comparing two finger prints would be directed to a rough general examination of their respective patterns. If they do not agree in being arches, loops, or whorls, there can be no doubt that the prints are those of different fingers, neither can there be doubt when they are distinct forms of the same general cla.s.s. But to agree thus far goes only a short way towards establishing ident.i.ty, for the number of patterns that are promptly distinguishable from one another is not large.

My earlier inquiries showed this, when endeavouring to sort the prints of 1000 thumbs into groups that differed each from the rest by an "equally discernible" interval. While the attempt, as already mentioned, was not successful in its main object, it showed that nearly all the collection could be sorted into 100 groups, in each of which the prints had a fairly near resemblance. Moreover, twelve or fifteen of the groups referred to different varieties of the loop; and as two-thirds of all the prints are loops, two-thirds of the 1000 specimens fell into twelve or fifteen groups. The chance that an unseen pattern is some particular variety of loop, is therefore compounded of 2 to 3 against its being a loop at all, and of 1 to 12 or 15, as the case may be, against its being the specified kind of loop. This makes an adverse chance of only 2 to 36, or to 45, say as 2 to 40, or as 1 to 20. This very rude calculation suffices to show that on the average, no great reliance can be placed on a general resemblance in the appearance of two finger prints, as a proof that they were made by the same finger, though the obvious disagreement of two prints is conclusive evidence that they were made by different fingers.

When we proceed to a much more careful comparison, and collate successively the numerous minutiae, their coincidence throughout would be an evidence of ident.i.ty, whose value we will now try to appraise.

Let us first consider the question, how far may the minutiae, or groups of them, be treated as _independent_ variables?

Suppose that a tiny square of paper of only one average ridge-interval in the side, be cut out and dropped at random on a finger print; it will mask from view a minute portion of one, or possibly of two ridges. There can be little doubt that what was hidden could be correctly interpolated by simply joining the ends of the ridge or ridges that were interrupted.

It is true, the paper might possibly have fallen exactly upon, and hidden, a minute island or enclosure, and that our reconstruction would have failed in consequence, but such an accident is improbable in a high degree, and may be almost ignored.

Repeating the process with a much larger square of paper, say of twelve ridge-intervals in the side, the improbability of correctly reconstructing the masked portion will have immensely increased. The number of ridges that enter the square on any one side will perhaps, as often as not, differ from the number which emerge from the opposite side; and when they are the same, it does not at all follow that they would be continuous each to each, for in so large a s.p.a.ce forks and junctions are sure to occur between some, and it is impossible to know which, of the ridges.

Consequently, there must exist a certain size of square with more than one and less than twelve ridge-intervals in the side, which will mask so much of the print, that it will be an even chance whether the hidden portion can, on the average, be rightly reconstructed or not. The size of that square must now be considered.

If the reader will refer to Plate 14, in which there are eight much enlarged photographs of portions of different finger prints, he will observe that the length of each of the portions exceeds the breadth in the proportion of 3 to 2. Consequently, by drawing one line down the middle and two lines across, each portion may be divided into six squares.

Moreover, it will be noticed that the side of each of these squares has a length of about six ridge-intervals. I cut out squares of paper of this size, and throwing one of them at random on any one of the eight portions, succeeded almost as frequently as not in drawing lines on its back which comparison afterwards showed to have followed the true course of the ridges. The provisional estimate that a length of six ridge-intervals approximated to but exceeded that of the side of the desired square, proved to be correct by the following more exact observations, and by three different methods.

I. The first set of tests to verify this estimate were made upon photographic enlargements of various thumb prints, to double their natural size. A six-ridge-interval square of paper was damped and laid at random on the print, the core of the pattern, which was too complex in many cases to serve as an average test, being alone avoided. The prints being on ordinary alb.u.minised paper, which is slightly adherent when moistened, the patch stuck temporarily wherever it was placed and pressed down. Next, a sheet of tracing-paper, which we will call No. 1, was laid over all, and the margin of the square patch was traced upon it, together with the course of the surrounding ridges up to that margin. Then I interpolated on the tracing-paper what seemed to be the most likely course of those ridges which were hidden by the square. No. 1 was then removed, and a second sheet, No. 2, was laid on, and the margin of the patch was outlined on it as before, together with the ridges leading up to it. Next, a corner only of No. 2 was raised, the square patch was whisked away from underneath, the corner was replaced, the sheet was flattened down, and the actual courses of the ridges within the already marked outline were traced in.

Thus there were two tracings of the margin of the square, of which No. 1 contained the ridges as I had interpolated them, No. 2 as they really were, and it was easy to compare the two. The results are given in the first column of the following table:--

INTERPOLATION OF RIDGES IN A SIX-RIDGE-INTERVAL SQUARE.

+---------------------------------------------------------+ Result. Double Six-fold scale Twenty-fold Total. Enlargements. with prism. scale with chequer-work. ------- ------------- -------------- ------------- ------ Right 12 8 7 27 Wrong 20 12 16 48 ------- ------------- -------------- ------------- ------ Total 32 20 23 75 +---------------------------------------------------------+

II. In the second method the tracing-papers were discarded, and the prism of a camera lucida used. It threw an image three times the size of the photo-enlargement, upon a card, and there it was traced. The same general principle was adopted as in the first method, but the results being on a larger scale, and drawn on stout paper, were more satisfactory and convenient. They are given in the second column of the table. In this and the foregoing methods two different portions of the same print were sometimes dealt with, for it was a little more convenient and seemed as good a way of obtaining average results as that of always using portions of different finger prints. The total number of fifty-two trials, by one or other of the two methods, were made from about forty different prints.

(I am not sure of the exact number.)

The results in each of the two methods were sometimes quite right, sometimes quite wrong, sometimes neither one nor the other. The latter depended on the individual judgment as to which cla.s.s it belonged, and might be battled over with more or less show of reason by advocates on opposite sides. Equally dividing these intermediate cases between "right"

and "wrong," the results were obtained as shown. In one, and only one, of the cases, the most reasonable interpretation had not been given, and the result had been wrong when it ought to have been right. The purely personal error was therefore disregarded, and the result entered as "right."

III. A third attempt was made by a different method, upon the lineations of a finger print drawn on about a twenty-fold scale. It had first been enlarged four times by photography, and from this enlargement the axes of the ridges had been drawn with a five-fold enlarging pantagraph. The aim now was to reconstruct the entire finger print by two successive and independent acts of interpolation. A sheet of transparent tracing-paper was ruled into six-ridge-interval squares, and every one of its alternate squares was rendered opaque by pasting white paper upon it, giving it the appearance of a chess-board. When this chequer-work was laid on the print, exactly one half of the six-ridge squares were masked by the opaque squares, while the ridges running up to them could be seen. They were not quite so visible as if each opaque square had been wholly detached from its neighbours, instead of touching them at the extreme corners, still the loss of information thereby occasioned was small, and not worth laying stress upon. It is easily understood that when the chequer-work was moved parallel to itself, through the s.p.a.ce of one square, whether upwards or downwards, or to the right or left, the parts that were previously masked became visible, and those that were visible became masked. The object was to interpolate the ridges in every opaque square under one of these conditions, then to do the same for the remaining squares under the other condition, and finally, by combining the results, to obtain a complete scheme of the ridges wholly by interpolation. This was easily done by using two sheets of tracing-paper, laid in succession over the chequer-work, whose position on the print had been changed meanwhile, and afterwards tracing the lineations that were drawn on one of the two sheets upon the vacant squares of the other. The results are given in the third column of the table.

The three methods give roughly similar results, and we may therefore accept the ratios of their totals, which is 27 to 75, or say 1 to 3, as representing the chance that the reconstruction of any six-ridge-interval square would be correct under the given conditions. On reckoning the chance as 1 to 2, which will be done at first, it is obvious that the error, whatever it may be, is on the safe side. A closer equality in the chance that the ridges in a square might run in the observed way or in some other way, would result from taking a square of five ridge-intervals in the side. I believe this to be very closely the right size. A four-ridge-interval square is certainly too small.

When the reconstructed squares were wrong, they had none the less a natural appearance. This was especially seen, and on a large scale, in the result of the method by chequer-work, in which the lineations of an entire print were constructed by guess. Being so familiar with the run of these ridges in finger prints, I can speak with confidence on this. My a.s.sumption is, that any one of these reconstructions represents lineations that might have occurred in Nature, in a.s.sociation with the conditions outside the square, just as well as the lineations of the actual finger print. The courses of the ridges in each square are subject to uncertainties, due to petty _local_ incidents, to which the conditions outside the square give no sure indication. They appear to be in great part determined by the particular disposition of each one or more of the half hundred or so sweat-glands which the square contains. The ridges rarely run in evenly flowing lines, but may be compared to footways across a broken country, which, while they follow a general direction, are continually deflected by such trifles as a tuft of gra.s.s, a stone, or a puddle. Even if the number of ridges emerging from a six-ridge-interval square equals the number of those which enter, it does not follow that they run across in parallel lines, for there is plenty of room for any one of the ridges to end, and another to bifurcate. It is impossible, therefore, to know beforehand in which, if in any of the ridges, these peculiarities will be found. When the number of entering and issuing ridges is unequal, the difficulty is increased. There may, moreover, be islands or enclosures in any particular part of the square. It therefore seems right to look upon the squares as independent variables, in the sense that when the surrounding conditions are alone taken into account, the ridges within their limits may either run in the observed way or in a different way, the chance of these two contrasted events being taken (for safety's sake) as approximately equal.

In comparing finger prints which are alike in their general pattern, it may well happen that the proportions of the patterns differ; one may be that of a slender boy, the other that of a man whose fingers have been broadened or deformed by ill-usage. It is therefore requisite to imagine that only one of the prints is divided into exact squares, and to suppose that a reticulation has been drawn over the other, in which each mesh included the corresponding parts of the former print. Frequent trials have shown that there is no practical difficulty in actually doing this, and it is the only way of making a fair comparison between the two.

These six-ridge-interval squares may thus be regarded as independent units, each of which is equally liable to fall into one or other of two alternative cla.s.ses, when the surrounding conditions are alone known. The inevitable consequence from this datum is that the chance of an exact correspondence between two different finger prints, in each of the six-ridge-interval squares into which they may be divided, and which are about 24 in number, is at least as 1 to 2 multiplied into itself 24 times (usually written 2{24}), that is as 1 to about ten thousand millions. But we must not forget that the six-ridge square was taken in order to ensure under-estimation, a five-ridge square would have been preferable, so the adverse chances would in reality be enormously greater still.

It is hateful to blunder in calculations of adverse chances, by overlooking correlations between variables, and to falsely a.s.sume them independent, with the result that inflated estimates are made which require to be proportionately reduced. Here, however, there seems to be little room for such an error.

We must next combine the above enormously unfavourable chance, which we will call _a_, with the other chances of not guessing correctly beforehand the surrounding conditions under which _a_ was calculated. These latter are divisible into _b_ and _c_; the chance _b_ is that of not guessing correctly the general course of the ridges adjacent to each square, and _c_ that of not guessing rightly the number of ridges that enter and issue from the square. The chance _b_ has already been discussed, with the result that it might be taken as 1 to 20 for two-thirds of all the patterns. It would be higher for the remainder, and very high indeed for some few of them, but as it is advisable always to underestimate, it may be taken as 1 to 20; or, to obtain the convenience of dealing only with values of 2 multiplied into itself, the still lower ratio of 1 to 2{4}, that is as 1 to 16. As to the remaining chance _c_ with which _a_ and _b_ have to be compounded, namely, that of guessing aright the number of ridges that enter and leave each side of a particular square, I can offer no careful observations. The number of the ridges would for the most part vary between five and seven, and those in the different squares are certainly not quite independent of one another. We have already arrived at such large figures that it is surplusage to heap up more of them, therefore, let us say, as a mere nominal sum much below the real figure, that the chance against guessing each and every one of these data correctly is as 1 to 250, or say 1 to 2{8} (= 256).

The result is, that the chance of lineations, constructed by the imagination according to strictly natural forms, which shall be found to resemble those of a single finger print in all their minutiae, is less than 1 to 2{24} 2{4} 2{8}, or 1 to 2{36}, or 1 to about sixty-four thousand millions. The inference is, that as the number of the human race is reckoned at about sixteen thousand millions, it is a smaller chance than 1 to 4 that the print of a _single_ finger of any given person would be exactly like that of the same finger of any other member of the human race.

When two fingers of each of the two persons are compared, and found to have the same minutiae, the improbability of 1 to 2{36} becomes squared, and reaches a figure altogether beyond the range of the imagination; when three fingers, it is cubed, and so on.

A single instance has shown that the minutiae are _not_ invariably permanent throughout life, but that one or more of them may possibly change. They may also be destroyed by wounds, and more or less disintegrated by hard work, disease, or age. Ambiguities will thus arise in their interpretation, one person a.s.serting a resemblance in respect to a particular feature, while another a.s.serts dissimilarity. It is therefore of interest to know how far a conceded resemblance in the great majority of the minutiae combined with some doubt as to the remainder, will tell in favour of ident.i.ty. It will now be convenient to change our datum from a six-ridge to a five-ridge square of which about thirty-five are contained in a single print, 35 5{2} or 35 25 being much the same as 24 6{2} or 24 36. The reason for the change is that this number of thirty-five happens to be the same as that of the minutiae. We shall therefore not be acting unfairly if, with reservation, and for the sake of obtaining some result, however rough, we consider the thirty-five minutiae themselves as so many independent variables, and accept the chance now as 1 to 2{35}.

This has to be multiplied, as before, into the factor of 2{4} 2{8} (which may still be considered appropriate, though it is too small), making the total of adverse chances 1 to 2{47}. Upon such a basis, the calculation is simple. There would on the average be 47 instances, out of the total 2{47} combinations, of similarity in all but one particular; (47 46)/(1 2) in all but two; (47 46 45)/(1 2 3) in all but three, and so on according to the well-known binomial expansion. Taking for convenience the powers of 2 to which these values approximate, or rather with the view of not overestimating, let us take the power of 2 that falls short of each of them; these may be reckoned as respectively equal to 2{6}, 2{10}, 2{14}, 2{18}, etc. Hence the roughly approximate chances of resemblance in all particulars are as 2{47} to 1; in all particulars but one, as 2{47-6}, or 2{41} to 1; in all but two, as 2{37} to 1; in all but three, as 2{33} to 1; in all but four, as 2{29} to 1. Even 2{29} is so large as to require a row of nine figures to express it. Hence a few instances of dissimilarity in the two prints of a single finger, still leave untouched an enormously large residue of evidence in favour of ident.i.ty, and when two, three, or more fingers in the two persons agree to that extent, the strength of the evidence rises by squares, cubes, etc., far above the level of that amount of probability which begins to rank as certainty.

Whatever reductions a legitimate criticism may make in the numerical results arrived at in this chapter, bearing in mind the occasional ambiguities pictured in Fig. 18, the broad fact remains, that a complete or nearly complete accordance between two prints of a single finger, and vastly more so between the prints of two or more fingers, affords evidence requiring no corroboration, that the persons from whom they were made are the same. Let it also be remembered, that this evidence is applicable not only to adults, but can establish the ident.i.ty of the same person at any stage of his life between babyhood and old age, and for some time after his death.

We read of the dead body of Jezebel being devoured by the dogs of Jezreel, so that no man might say, "This is Jezebel," and that the dogs left only her skull, the palms of her hands, and the soles of her feet; but the palms of the hands and the soles of the feet are the very remains by which a corpse might be most surely identified, if impressions of them, made during life, were available.

CHAPTER VIII

PECULIARITIES OF THE DIGITS

The data used in this chapter are the prints of 5000 different digits, namely, the ten digits of 500 different persons; each digit can thus be treated, both separately and in combination, in 500 cases. Five hundred cannot be called a large number, but it suffices for approximate results; the percentages that it yields may, for instance, be expected to be trustworthy, more often than not, within two units.

When preparing the tables for this chapter, I gave a more liberal interpretation to the word "Arch" than subsequently. At first, every pattern between a Forked-Arch and a Nascent-Loop (Plate 7) was rated as an Arch; afterwards they were rated as Loops.

The relative frequency of the three several cla.s.ses in the 5000 digits was as follows:--

Arches 65 per cent.

Loops 675 "

Whorls 260 "

------ Total 1000

From this it appears, that on the average out of every 15 or 16 digits, one has an arch; out of every 3 digits, two have loops; out of every 4 digits, one has a whorl.

This coa.r.s.e statistical treatment leaves an inadequate impression, each digit and each hand having its own peculiarity, as we shall see in the following table:--

TABLE I.

_Percentage frequency of Arches, Loops, and Whorls on the different digits, from observations of the 5000 digits of 500 persons._

+-----------------------------------------------------------------+ RIGHT HAND. LEFT HAND. Digit. ----------------------------------------------------- Arch. Loop. Whorl. Total. Arch. Loop. Whorl. Total. -----------+----------------------------------------------------- Thumb 3 53 44 100 5 65 30 100 Fore-finger 17 53 30 100 17 55 28 100 Middle do. 7 78 15 100 8 76 16 100 Ring do. 2 53 45 100 3 66 31 100 Little do. 1 86 13 100 2 90 8 100 -----------+-----+-----+------+------ -----+-----+-------+------ Total 30 323 147 500 35 352 113 500 +-----------------------------------------------------------------+

The percentage of arches on the various digits varies from 1 to 17; of loops, from 53 to 90; of whorls, from 13 to 45, consequently the statistics of the digits must be separated, and not ma.s.sed indiscriminately.

Are the A. L. W. patterns distributed in the same way upon the corresponding digits of the two hands? The answer from the last table is distinct and curious, and will be best appreciated on rearranging the entries as follows:--

TABLE II.