In prints of adults, measurements may be made in absolute units of length, as in fractions of an inch, or else in millimetres. An average ridge-interval makes, however, a better unit, being independent of growth; it is strictly necessary to adopt it in prints made by children, if present measurements are hereafter to be compared with future ones. The simplest plan of determining and employing this unit is to count the number of ridges to the nearest half-ridge, within the space of one-tenth of an inch, measured along the axis of the finger at and about the point where it cuts thesummitof the outline; then, having already prepared scales suitable for the various likely numbers, to make the measurements with the appropriate scale. Thus, if five ridges were crossed by the axis at that part, in the space of one-tenth of an inch, each unit of the scale to be used would be one-fiftieth of an inch; if there were four ridges, eachunit of the scale would be one-fortieth of an inch; if six ridges one-sixtieth, and so forth. There is no theoretical or practical difficulty, only rough indications being required.
It is unnecessary to describe in detail how the bearings of any point may be expressed after the fashion of compass bearings, the direction I-O taking the place of East-West, the uppermost direction that of North, and the lowermost of South. Little more is practically wanted than to be able to describe roughly the position of some remarkable feature in the print, as of an island or an enclosure. A ridge that is characterised by these or any other marked peculiarity is easily identified by the above means, and it thereupon serves as an exact basis for the description of other features.
Purkenje’s “Commentatio.”
Reference has already been made to Purkenje, who has the honour of being the person who first described the inner scrolls (as distinguished from the outlines of the patterns) formed by the ridges. He did so in a University Thesis delivered at Breslau in 1823, entitledCommentatio de examine physiologico organi visus et systematis cutanei(a physiological examination of the visual organ and of the cutaneous system). The thesis is an ill-printed small 8vo pamphlet of fifty-eight pages, written in a form of Latin that is difficult to translate accurately into free English. It is, however, of great historical interest and reputation, having been referred to by nearly allsubsequent writers, some of whom there is reason to suspect never saw it, but contented themselves with quoting a very small portion at second-hand. No copy of the pamphlet existed in any public medical library in England, nor in any private one so far as I could learn; neither could I get a sight of it at some important continental libraries. One copy was known of it in America. The very zealous Librarian of the Royal College of Surgeons was so good as to take much pains at my instance, to procure one: his zeal was happily and unexpectedly rewarded by success, and the copy is now securely lodged in the library of the College.
The Title
Commentatio de Examine physiologico organi visus et systematis cutanei quam pro loco in gratioso medicorum ordine rite obtinendo die Dec. 22, 1823. H.X.L.C. publice defendit Johannes Evangelista Purkenje, Med. doctor, Phys. et Path. Professor publicus ordinarius des. Assumto socio Guilielmo Kraus Medicinae studioso.
Translation, p. 42.
“Our attention is next engaged by the wonderful arrangement and curving of the minute furrows connected with the organ of touch[4]on the inner surfaces of the hand and foot,especially on the last phalanx of each finger. Some general account of them is always to be found in every manual of physiology and anatomy, but in an organ of such importance as the human hand, used as it is for very varied movements, and especially serviceable to the sense of touch, no research, however minute, can fail in yielding some gratifying addition to our knowledge of that organ. After numberless observations, I have thus far met with nine principal varieties of curvature according to which the tactile furrows are disposed upon the inner surface of the last phalanx of the fingers. I will describe them concisely, and refer to the diagrams for further explanation (seePlate 12, Fig. 19).1.Transverse flexures.—The minute furrows starting from the bend of the joint, run from one side of the phalanx to the other; at first transversely in nearly straight lines, then by degrees they become more and more curved towards the middle, until at last they are bent into arches that are almost concentric with the circumference of the finger.2.Central Longitudinal Stria.—This configuration is nearly the same as in 1, the only difference being that a perpendicular stria is enclosed within the transverse furrows, as if it were a nucleus.3.Oblique Stria.—A solitary line runs from one or other of the two sides of the finger, passing obliquely between the transverse curves in 1, and ending near the middle.4.Oblique Sinus.—If this oblique line recurves towards the side from which it started, and is accompanied by several others, all recurved in the same way, the result is an oblique sinus, more or less upright, or horizontal, as the case may be. A junction at its base, of minute lines proceeding from either of its sides, forms a triangle. This distribution of the furrows, in which an oblique sinus is found, is by far the most common, and it may be considered as a special characteristic of man; the furrows that are packed in longitudinal rows are, on the other hand, peculiar to monkeys. The vertex of the oblique sinus is generally inclined towards the radial side of the hand, but it must be observed that the contrary is more frequently the case in the fore-finger, the vertex there tending towards the ulnar side. Scarcely any other configuration is to be found on the toes. The ring finger, too, is often marked with one of the more intricate kinds of pattern, while the remaining fingers have either the oblique sinus or one of the other simpler forms.
“Our attention is next engaged by the wonderful arrangement and curving of the minute furrows connected with the organ of touch[4]on the inner surfaces of the hand and foot,especially on the last phalanx of each finger. Some general account of them is always to be found in every manual of physiology and anatomy, but in an organ of such importance as the human hand, used as it is for very varied movements, and especially serviceable to the sense of touch, no research, however minute, can fail in yielding some gratifying addition to our knowledge of that organ. After numberless observations, I have thus far met with nine principal varieties of curvature according to which the tactile furrows are disposed upon the inner surface of the last phalanx of the fingers. I will describe them concisely, and refer to the diagrams for further explanation (seePlate 12, Fig. 19).
1.Transverse flexures.—The minute furrows starting from the bend of the joint, run from one side of the phalanx to the other; at first transversely in nearly straight lines, then by degrees they become more and more curved towards the middle, until at last they are bent into arches that are almost concentric with the circumference of the finger.
2.Central Longitudinal Stria.—This configuration is nearly the same as in 1, the only difference being that a perpendicular stria is enclosed within the transverse furrows, as if it were a nucleus.
3.Oblique Stria.—A solitary line runs from one or other of the two sides of the finger, passing obliquely between the transverse curves in 1, and ending near the middle.
4.Oblique Sinus.—If this oblique line recurves towards the side from which it started, and is accompanied by several others, all recurved in the same way, the result is an oblique sinus, more or less upright, or horizontal, as the case may be. A junction at its base, of minute lines proceeding from either of its sides, forms a triangle. This distribution of the furrows, in which an oblique sinus is found, is by far the most common, and it may be considered as a special characteristic of man; the furrows that are packed in longitudinal rows are, on the other hand, peculiar to monkeys. The vertex of the oblique sinus is generally inclined towards the radial side of the hand, but it must be observed that the contrary is more frequently the case in the fore-finger, the vertex there tending towards the ulnar side. Scarcely any other configuration is to be found on the toes. The ring finger, too, is often marked with one of the more intricate kinds of pattern, while the remaining fingers have either the oblique sinus or one of the other simpler forms.
PLATE 12.
Fig. 19.
THE STANDARD PATTERNS OF PURKENJE.
The Cores of the above Patterns.
5.Almond.—Here the oblique sinus, as already described, encloses an almond-shaped figure, blunt above, pointed below, and formed of concentric furrows.6.Spiral.—When the transverse flexures described in 1 do not pass gradually from straight lines into curves, but assume that form suddenly with a more rapid divergence, a semicircular space is necessarily created, which stands upon the straight and horizontal lines below, as it were upon a base. This space is filled by a spiral either of a simple or composite form. The term ‘simple’ spiral is to be understood in the usual geometric sense. I call the spiral ‘composite’ when it is made up of several lines proceeding from the same centre, or of lines branching at intervals and twisted upon themselves. At either side, where the spiral is contiguous to the place at which the straight and curved lines begin to diverge, in order to enclose it, two triangles are formed, just like the single one that is formed at the side of the oblique sinus.7.Ellipse, orElliptical Whorl.—The semicircular space described in 6 is here filled with concentric ellipses enclosing a short single line in their middle.8.Circle, orCircular Whorl.—Here a single point takes the place of the short line mentioned in 7. It is surrounded by a number of concentric circles reaching to the ridges that bound the semicircular space.9.Double Whorl.—One portion of the transverse lines runs forward with a bend and recurves upon itself with a half turn, and is embraced by another portion which proceeds from the other side in the same way. This produces a doubly twisted figure which is rarely met with except on the thumb, fore, and ring fingers. The ends of the curved portions may be variously inclined; they may be nearly perpendicular, of various degrees of obliquity, or nearly horizontal.In all of the forms 6, 7, 8, and 9, triangles may be seen at the points where the divergence begins between the transverseand the arched lines, and at both sides. On the remaining phalanges, the transverse lines proceed diagonally, and are straight or only slightly curved.”
5.Almond.—Here the oblique sinus, as already described, encloses an almond-shaped figure, blunt above, pointed below, and formed of concentric furrows.
6.Spiral.—When the transverse flexures described in 1 do not pass gradually from straight lines into curves, but assume that form suddenly with a more rapid divergence, a semicircular space is necessarily created, which stands upon the straight and horizontal lines below, as it were upon a base. This space is filled by a spiral either of a simple or composite form. The term ‘simple’ spiral is to be understood in the usual geometric sense. I call the spiral ‘composite’ when it is made up of several lines proceeding from the same centre, or of lines branching at intervals and twisted upon themselves. At either side, where the spiral is contiguous to the place at which the straight and curved lines begin to diverge, in order to enclose it, two triangles are formed, just like the single one that is formed at the side of the oblique sinus.
7.Ellipse, orElliptical Whorl.—The semicircular space described in 6 is here filled with concentric ellipses enclosing a short single line in their middle.
8.Circle, orCircular Whorl.—Here a single point takes the place of the short line mentioned in 7. It is surrounded by a number of concentric circles reaching to the ridges that bound the semicircular space.
9.Double Whorl.—One portion of the transverse lines runs forward with a bend and recurves upon itself with a half turn, and is embraced by another portion which proceeds from the other side in the same way. This produces a doubly twisted figure which is rarely met with except on the thumb, fore, and ring fingers. The ends of the curved portions may be variously inclined; they may be nearly perpendicular, of various degrees of obliquity, or nearly horizontal.
In all of the forms 6, 7, 8, and 9, triangles may be seen at the points where the divergence begins between the transverseand the arched lines, and at both sides. On the remaining phalanges, the transverse lines proceed diagonally, and are straight or only slightly curved.”
(He then proceeds to speak of the palm of the hand in men and in monkeys.)
PERSISTENCE
The evidence that the minutiæ persist throughout life is derived from the scrutiny and comparison of various duplicate impressions, one of each pair having been made many years ago, the other recently. Those which I have studied more or less exhaustively are derived from the digits of fifteen different persons. In some cases repeated impressions of one finger only were available; in most cases of two fingers; in some of an entire hand. Altogether the whole or part of repeated impressions of between twenty and thirty different digits have been studied. I am indebted to Sir W. J. Herschel for almost all these valuable data, without which it would have been impossible to carry on the inquiry. The only other prints are those of Sir W. G——, who, from curiosity, took impressions of his own fingers in sealing-wax in 1874, and fortunately happened to preserve them. He was good enough to make others for me last year, from which photographic prints were made. The following table gives an analysis of the above data. It would be well worth while to hunt up and take the present finger printsof such of the Hindoos as may now be alive, whose impressions were taken in India by Sir W. J. Herschel, and are still preserved. Many years must elapse before my own large collection of finger prints will be available for the purpose of testing persistence during long periods.
The pattern in every distinct finger print, even though it be only a dabbed impression, contains on a rough average thirty-five different points of reference, in addition to its general peculiarities of outline and core. They consist of forkings, beginnings or ends of ridges, islands, and enclosures. These minute details are by no means peculiar to the pattern itself, but are distributed with almost equal abundance throughout the whole palmar surface. In order to make an exhaustive comparison of two impressions they ought to be photographically enlarged to a size not smaller than those shown inPlate 15. Two negatives of impressions can thus be taken side by side on an ordinary quarter-plate, and any number of photographic prints made from them; but, for still more comfortable working, a further enlargement is desirable, say by the prism,p. 52. Some of the prints may be made on ferro-prussiate paper, as already mentionedpp. 51,53; they are more convenient by far than prints made by the silver or by the platinum process.
Having placed the enlarged prints side by side, two or three conspicuous and convenient points of reference, whether islands, enclosures, or particularly distinct bifurcations, should be identified and marked. By their help, the position of the prints should bereadjusted, so that they shall be oriented exactly alike. From each point of reference, in succession, the spines of the ridges are then to be followed with a fine pencil, in the two prints alternately, neatly marking each new point of comparison with a numeral in coloured ink (Plate 13). When both of the prints are good and clear, this is rapidly done; wherever the impressions are faulty, there may be many ambiguities requiring patience to unravel. At first I was timid, and proceeded too hesitatingly when one of the impressions was indistinct, making short alternate traces. Afterwards on gaining confidence, I traced boldly, starting from any well-defined point of reference and not stopping until there were reasonable grounds for hesitation, and found it easy in this way to trace the unions between opposite and incompletely printed ends of ridges, and to disentangle many bad impressions.
An exact correspondence between thedetailsof two minutiæ is of secondary importance. Thus, the commonest point of reference is a bifurcation; now the neck or point of divergence of a new ridge is apt to be a little low, and sometimes fails to take the ink; hence a new ridge may appear in one of the prints to have an independent origin, and in the other to be a branch. Theapparentorigin is therefore of little importance, the main fact to be attended to is that a new ridge comes into existence at a particular point;howit came into existence is a secondary matter. Similarly, an apparently broken ridge may in reality be due to an imperfectly printedenclosure; and an island in one print may appear as part of an enclosure in the other. Moreover, this variation in details may be the effect not only of imperfect inking or printing, but of disintegration due to old age, which renders the impressions of the ridges ragged and broken, as in my own finger prints on the title-page.
Plate 11, Fig. 18 explains the nature of the apparent discrepancies better than a verbal description. Inaa new ridge appears to be suddenly intruded between two adjacent ones, which have separated to make room for it; but a second print, taken from the same finger, may have the appearance of eitherborc, showing that the new ridge is in reality a fork of one or other of them, the low connecting neck having failed to leave an impression. The second line of examples shows how an enclosure which is clearly defined indmay give rise to the appearance of broken continuity shown ine, and how a distinct islandfin one of the prints may be the remnant of an enclosure which is shown in the other. These remarks are offered as a caution against attaching undue importance to disaccord in the details of the minutiæ that are found in the same place in different prints. Usually, however, the distinction between a fork and the beginning of a new ridge is clear enough; the islands and enclosures are also mostly well marked.
PLATE 13.
Fig. 20.
V. H. H-D æt. 2½ in 1877, and again as a boy in Nov. 1890.
Plate 13gives impressions taken from the fingers of a child of 2½ years in 1877, and again in 1890, when a boy of 15. They are enlarged photographically to the same size, and are therefore on different scales. The impressions from the baby-hand are not sharp, but sufficiently distinct for comparison. Every bifurcation, and beginning or ending of a ridge, common to the two impressions, is marked with a numeral in blue ink. There is only one island in the present instance, and that is in the upper pair of prints; it is clearly seen in the right hand print, lying to the left of the inscribed number 13, but the badness of the left hand print makes it hardly decipherable, so it is not numbered. There are a total of twenty-six good points of comparison common to the upper pair of prints; there are forty-three points in the lower pair, forty-two of which appear in both, leaving a single point of disagreement; it is marked A on the fifth ridge counting from the top. Here a bifurcated ridge in the baby is filled up in the boy. This one exception, small though it be, is in my experience unique. The total result of the two pairs of prints is to afford sixty-eight successes and one failure. The student will find it well worth his while to study these and the following prints step by step, to satisfy himself of the extraordinarily exact coincidences between the two members of either of the pairs. Of course the patterns generally must be the same, if the ridges composing them are exactly alike, and the most cursory glance shows them to be so.
PLATE 14.
Fig. 21.
Plate 14, Fig. 21 contains rather less than a quarter of each of eight pairs that were published inthePhil. Trans.memoir above alluded to. They were there enlarged photographically to twice their natural size, which was hardly enough, as it did not allow sufficient space for inserting the necessary reference numbers. Consequently they have been again considerably enlarged, so much so that it is impossible to put more than a portion of each on the page. However, what is given suffices. The omitted portions may be studied in the memoir. The cases of1and2are prints of different fingers of the same individual, first as a child 8 years old, and then as a boy of 17. They have been enlarged on the same scale but not to the same size; so the print of the child includes a larger proportion of the original impression than that of the boy. It is therefore only a part of the child’s print which is comparable with that of the boy. The remaining six cases refer to four different men, belonging to three quite different families, although their surnames happen to have the same initial, H. They were adults when the first print was made, and from 26 to 31 years older on the second occasion. There is an exact agreement throughout between the two members of each of the eight several couplets.
In the pair 2. A. E. H. Hl., there is an interesting dot at the point4(being an island it deserved to have had two numbers, one for the beginning and one for the end). Small as it is, it persists; its growth in size corresponding to the growth of the child in stature.
PLATE 15.
Fig. 22.
RIGHT FOREFINGER of Sir W. J. H.in 1860 and in 1888.
Fig. 23.
DISTRIBUTION of the PERIODS of LIFE,to which the evidence of persistency refers.
For the sake of those who are deficient in the colour sense and therefore hardly able, if at all, to distinguish even the blue numerals in Figs. 20, 21, I give an eleventh example,Plate 15, Fig. 22, printed all in black. The numerals are here very legible, but space for their insertion had to be obtained by sacrificing some of the lineations. It is the right fore-finger of Sir W. Herschel and has been already published twice; first in the account of my lecture at the Royal Institution, and secondly, in its present conspicuous form, in my paper in theNineteenth Century. The number of years that elapsed between the two impressions is thirty-one, and the prints contain twenty-four points of comparison, all of which will be seen to agree. I also possess a later print than this, taken in 1890 from the same finger, which tells the same tale.
The final result of the prints in these pages is that they give photographic enlargements of the whole or portions of eleven couplets belonging to six different persons, who are members of five unrelated families, and which contain between them 158 points of comparison, of which only one failed. Adding the portions of the prints that are omitted here, but which will be found in thePhil. Trans., the material that I have thus far published contains 389 points of comparison, of which one failed. The details are given in the annexed table:—
It is difficult to give a just estimate of the number of points of comparison that I have studied in other couplets of prints, because they were not examined as exhaustively as in these. There were no less than one hundred and eleven of them in the ball of the thumb of the child V. H. Hd., besides twenty-five in the imperfect prints of his middle and little fingers; these alone raise the total of 389 to 525. I must on the whole have looked for more than 700 points of comparison, and have found agreement in every single case that was examined, except the one already mentioned in Fig. 20, of a ridge that was split in the child, but had closed up some few years later.
The prints in the two plates cover the intervals from childhood to boyhood, from boyhood to early manhood, from manhood to about the age of 60, and another set—that of Sir W. G.—covers the interval from 67 to 80. This is clearly expressed by the diagram (Plate 15, Fig. 23). As there is no sign, except in one case, of change during any one of these four intervals, which together almost wholly cover the ordinary life of man, we are justified in inferring that between birth and death there is absolutely no change in, say, 699 out of 700 of the numerous characteristics in the markings of the fingers of the same person, such as can be impressed by them whenever it is desirable to do so. Neither can there be any change after death, up to the time when the skin perishes through decomposition; for example, the marks on the fingers of many Egyptian mummies, and on the paws of stuffed monkeys, still remain legible. Very good evidence and careful inquiry is thus seen to justify the popular idea of the persistence of finger markings, that has hitherto been too rashly jumped at, and which wrongly ascribed the persistence to the general appearance of the pattern, rather than to the minutiæ it contains. There appear to be no external bodily characteristics, other than deep scars and tattoo marks, comparable in their persistence to these markings, whether they be on the finger, on other parts of the palmar surface of the hand, or on the sole of the foot. At the same time they are out of all proportion more numerous than any other measurable features; about thirty-five of them are situated on the bulb of each of theten digits, in addition to more than 100 on the ball of the thumb, which has not one-fifth of the superficies of the rest of the palmar surface. The total number of points suitable for comparison on the two hands must therefore be not less than one thousand and nearer to two; an estimate which I verified by a rough count on my own hand; similarly in respect to the feet. The dimensions of the limbs and body alter in the course of growth and decay; the colour, quantity, and quality of the hair, the tint and quality of the skin, the number and set of the teeth, the expression of the features, the gestures, the handwriting, even the eye-colour, change after many years. There seems no persistence in the visible parts of the body, except in these minute and hitherto too much disregarded ridges.
It must be emphasised that it is in the minutiæ, andnotin the measured dimensions of any portion of the pattern, that this remarkable persistence is observed, not even if the measurements be made in units of a ridge-interval. The pattern grows simultaneously with the finger, and its proportions vary with its fatness, leanness, usage, gouty deformation, or age. But, though the pattern as a whole may become considerably altered in length or breadth, the number of ridges, their embranchments, and other minutiæ remain unchanged. So it is with the pattern on a piece of lace. The piece as a whole may be stretched in this way, or shrunk in that, and its outline altogether altered; nevertheless every one of the component threads, and every knot in everythread, can easily be traced and identified in both. Therefore, in speaking of the persistence of the marks on the finger, the phrase must be taken to apply principally to the minutiæ, and to the general character of the pattern; not to the measure of its length, breadth, or other diameter; these being no more constant than the stature, or any other of the ordinary anthropometric data.
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 minutiæ, 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 class. But to agree thus far goes only a short way towards establishing identity, 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 printsof 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 minutiæ, their coincidence throughout would be an evidence of identity, whose value we will now try to appraise.
Let us first consider the question, how far may the minutiæ, or groups of them, be treated asindependentvariables?
Suppose that a tiny square of paper of only one average ridge-interval in the side, be cut out anddropped 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 space 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 toPlate 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 theproportion 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 albuminised 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 hiddenby 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.
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 ofthe 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 class 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 ruledinto 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 space 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 assumption is, that any one of these reconstructions represents lineations that might have occurred in Nature, in association 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 pettylocalincidents, 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 theyfollow a general direction, are continually deflected by such trifles as a tuft of grass, 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 doingthis, 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 classes, 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 224), 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 assume 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 calla, with the other chances of not guessing correctly beforehand the surrounding conditions under whichawas calculated. These latter are divisible intobandc; the chancebis that of not guessing correctly the general course of the ridges adjacent to each square, andcthat of not guessing rightly the number ofridges that enter and issue from the square. The chancebhas 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 24, that is as 1 to 16. As to the remaining chancecwith whichaandbhave 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 28(= 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 minutiæ, is less than 1 to 224× 24× 28, or 1 to 236, 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 asinglefinger of any givenperson 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 minutiæ, the improbability of 1 to 236becomes 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 minutiæ arenotinvariably 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 asserting a resemblance in respect to a particular feature, while another asserts dissimilarity. It is therefore of interest to know how far a conceded resemblance in the great majority of the minutiæ combined with some doubt as to the remainder, will tell in favour of identity. 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 × 52or 35 × 25 being much the same as 24 × 62or 24 × 36. The reason for the change is that this number of thirty-five happens to be the same as that of the minutiæ. 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 minutiæ themselves as so many independent variables, and accept the chance now as 1 to 235.
This has to be multiplied, as before, into the factor of 24× 28(which may still be consideredappropriate, though it is too small), making the total of adverse chances 1 to 247. Upon such a basis, the calculation is simple. There would on the average be 47 instances, out of the total 247combinations, of similarity in all but one particular;47 × 46⁄1 × 2in all but two;47 × 46 × 45⁄1 × 2 × 3in 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 26, 210, 214, 218, etc. Hence the roughly approximate chances of resemblance in all particulars are as 247to 1; in all particulars but one, as 247-6, or 241to 1; in all but two, as 237to 1; in all but three, as 233to 1; in all but four, as 229to 1. Even 229is 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 identity, 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 betweenthe 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 identity 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.
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 classes in the 5000 digits was as follows:—
From this it appears, that on the average out of every15 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 coarse 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.
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 massed 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.
The digits are seen to fall into two well-marked groups; the one including the fore, middle, and little fingers, the other including the thumb and ring-finger. As regards the first group, the frequency with which any pattern occurs in any named digit is statistically the same, whether that digit be on the right or on the left hand; as regards the second group, the frequency differs greatly in the two hands. But though in the first group the two fore-fingers, the two middle, and the two little fingers of the right hand are severally circumstanced alike in the frequency with which their various patterns occur, the difference between the frequency of the patterns on a fore, a middle, and a little finger, respectively, is very great.
In the second group, though the thumbs on opposite hands do not resemble each other in the statistical frequency of the A. L. W. patterns, nor do the ring-fingers, there is a great resemblancebetween the respective frequencies in the thumbs and ring-fingers; for instance, the Whorls on either of these fingers on the left hand are only two-thirds as common as those on the right. The figures in each line and in each column are consistent throughout in expressing these curious differences, which must therefore be accepted as facts, and not as statistical accidents, whatever may be their explanation.
One of the most noticeable peculiarities in Table I. is the much greater frequency of Arches on the fore-fingers than on any other of the four digits. It amounts to 17 per cent on the fore-fingers, while on the thumbs and on the remaining fingers the frequency diminishes (Table III.) in a ratio that roughly accords with the distance of each digit from the fore-finger.
Table III.
The frequency of Loops (Table IV.) has two maxima; the principal one is on the little finger, the secondary on the middle finger.