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, entitled _Commentatio 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 all subsequent 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 (see
Plate 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.
[Illustration: PLATE 12.
FIG. 19. THE STANDARD PATTERNS OF PURKENJE.]
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_, or _Elliptical Whorl_.--The semicircular space described
in 6 is here filled with concentric ellipses enclosing a short single
line in their middle.
8. _Circle_, or _Circular 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 transverse and 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.)
CHAPTER VI
PERSISTENCE
The evidence that the minutiae 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
prints of 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 in Plate 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 mentioned
pp. 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 be readjusted, 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 the _details_ of two minutiae 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. The _apparent_ origin is therefore of little
importance, the main fact to be attended to is that a new ridge comes into
existence at a particular point; _how_ it came into existence is a
secondary matter. Similarly, an apparently broken ridge may in reality be
due to an imperfectly printed enclosure; 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. In _a_ a 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 either _b_ or _c_, 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 in _d_ may give rise to the appearance of broken
continuity shown in _e_, and how a distinct island _f_ in 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 minutiae 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.
[Illustration: PLATE 13.
FIG. 20. V. H. H-D aet. 2-1/2 in 1877, and again as a boy in Nov. 1890.]
Plate 13 gives impressions taken from the fingers of a child of 2-1/2
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.
[Illustration: PLATE 14.
FIG. 21.]
Plate 14, Fig. 21 contains rather less than a quarter of each of eight
pairs that were published in the _Phil. 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 of ~1~ and ~2~
are 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 point ~4~
(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.
[Illustration: 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.
+-----------------------------------------------------------------------+
| | Age | | Age | Ages, 0--80 years. |
|Persons. | at |Interval| at | |
| |first| in |second| |
| |print| years |print | 10 20 30 40 50 60 70 |
|------------------------------------|----|----|----|----|----|----|----|
| H. H--d| 2 | 13 | 15 |----+-- | | | | | | |
| | | | | | | | | | | | |
| A. H--l| 4 | 12 | 16 | ---+--- | | | | | | |
| | | | | | | | | | | | |
| J. H--l| 8 | 13 | 21 | --+----+ | | | | | |
| | | | | | | | | | | | |
| E. H--l| 10 | 13 | 23 | |----+-- | | | | | |
| | | | | | | | | | | | |
|W.J. H--l| 26 | 30 | 56 | | | --+----+----+-- | | |
| | | | | | | | | | | | |
|R.F. H--n| 26 | 31 | 57 | | | --+----+----+--- | | |
| | | | | | | | | | | | |
|N.H. T--n| 27 | 28 | 55 | | | -+----+----+-- | | |
| | | | | | | | | | | | |
|F.H. H--t| 27 | 26 | 53 | | | -+----+----+- | | |
| | | | | | | | | | | | |
| W. G--e| 62 | 17 | 79 | | | | | | |----+----|
+-----------------------------------------------------------------------+
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 the _Nineteenth 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 the _Phil. 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:--
+-----------------------------------------------------------------------+
| Order | Initials. |Digit | Age |Dates of| Years | Total points |
| in | | of | at |the two |elapsed| of agreement in |
| the | |right | date |prints. |between|-------------------|
| Figs. | |hand. | of |--------|the two|Figs. 20|Figs. 20, |
| | | |first | |prints.|and 21. |22, and in|
| | | |print.|1st 2nd| | |Ph. Trans.|
|-------|------------|------|------|--------|-------|--------|----------|
|FIG. 20| | | | | | | |
| 1. |V. H. Hd. |Fore | 2-1/2| 1877-90| 13 | 26 | 26 |
| 2. |V. H. Hd. |Ring | 2-1/2| 1877-90| 13 | 42 | 42 |
| | | | | | | | |
|FIG. 21| | | | | | | |
| 1. |A. E. H. Hl.|Fore | 8 | 1881-90| 9 | 11 | 33 |
| 2. |A. E. H. Hl.|Ring | 8 | 1881-90| 9 | 5 | 36 |
| 3. |N. H. Tn. |Fore |28 | 1862-90| 28 | 6 | 27 |
| 4. |N. H. Tn. |Middle|28 | 1862-90| 28 | 10 | 36 |
| 5. |F. K. Ht. |Fore |28 | 1862-88| 26 | 12 | 55 |
| 6. |R. F. Hn. |Middle|31 | 1859-90| 31 | 6 | 27 |
| 7. |W. J. Hl. |Thumb |30 | 1860-90| 30 | 9 | 50 |
| 8. |W. J. Hl. |Ring |31 | 1859-90| 31 | 6 | 32 |
| | | | | | | | |
|FIG. 22| | | | | | | |
| 1. |W. J. Hl. |Fore |31 | 1859-90| 31 | 24 | 24 |
|---------------------------------------------------|--------|----------|
| Total points of agreement | 157 | 388 |
| Do. of disagreement | 1 | 1 |
+-----------------------------------------------------------------------+
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 minutiae 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 the ten
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 minutiae, and _not_ in 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
minutiae 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 every thread, 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
minutiae, 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.
CHAPTER VII
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 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 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 identity, 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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} x 2{4} x 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 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 minutiae 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 x 5{2} or 35 x 25 being much the same as 24 x 6{2}
or 24 x 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} x 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
x 46)/(1 x 2) in all but two; (47 x 46 x 45)/(1 x 2 x 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
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 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 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.
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 classes in the 5000 digits was
as follows:--
Arches 6.5 per cent.
Loops 67.5 "
Whorls 26.0 "
------
Total 100.0
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 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._
+-----------------------------------------------------------------+
| | 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 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.
+-----------------------------------------------------------------+
| | ARCHES. || LOOPS. || WHORLS. |
| Digit. |----------------||----------------||----------------|
| | Right. | Left. || Right. | Left. || Right. | Left. |
|------------|--------|-------||--------|-------||----------------|
| Fore-finger| 17 | 17 || 53 | 53 || 30 | 28 |
| Middle do. | 7 | 8 || 78 | 76 || 15 | 16 |
| Little do. | 1 | 2 || 86 | 90 || 13 | 8 |
| | | || | || | |
| Thumb | 3 | 5 || 53 | 65 || 44 | 30 |
| Ring do. | 2 | 3 || 53 | 66 || 45 | 31 |
|------------|--------|-------||--------|-------||----------------|
| Total 1000 | 30 | 35 || 323 | 350 || 147 | 113 |
+-----------------------------------------------------------------+
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 resemblance between 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.
+--------------------------------------------+
| _Percentage frequency of Arches._ |
|--------------------------------------------|
|Hand.|Thumb.| Fore- |Middle | Ring- |Little |
| | |finger.|finger.|finger.|finger.|
|-----|------|-------|-------|-------|-------|
|Right| 3 | 17 | 7 | 2 | 1 |
|Left | 5 | 17 | 8 | 3 | 4 |
|-----|------|-------|-------|-------|-------|
|Mean | 4 | 17 | 7.5 | 2.5 | 2.5 |
+--------------------------------------------+
The frequency of Loops (Table IV.) has two maxima; the principal one is on
the little finger, the secondary on the middle finger.
TABLE IV.
+--------------------------------------------+
| _Percentage frequency of Loops._ |
|--------------------------------------------|
|Hand.|Thumb.|Fore- |Middle |Ring- |Little |
| | |finger.|finger.|finger.|finger.|
|-----|------|-------|-------|-------|-------|
|Right| 53 | 53 | 78 | 66 | 86 |
|Left | 65 | 55 | 76 | 53 | 90 |
|-----|------|-------|-------|-------|-------|
|Mean | 59 | 54 | 77 | 59.5 | 88 |
+--------------------------------------------+
Whorls (Table V.) are most common on the thumb and the ring-finger, most
rare on the middle and little fingers.
TABLE V.
+--------------------------------------------+
| _Percentage frequency of Whorls._ |
|--------------------------------------------|
|Hand.|Thumb.|Fore- |Middle |Ring- |Little |
| | |finger.|finger.|finger.|finger.|
|-----|------|-------|-------|-------|-------|
|Right| 44 | 30 | 15 | 45 | 13 |
|Left | 30 | 28 | 16 | 31 | 8 |
|-----|------|-------|-------|-------|-------|
|Mean | 37 | 29 | 15.5 | 38 | 10.5 |
+--------------------------------------------+
The fore-finger is peculiar in the frequency with which the direction of
the slopes of its loops differs from that which is by far the most common
in all other digits. A loop _must_ have a slope, being caused by the
disposition of the ridges into the form of a pocket, opening downwards to
one or other side of the finger. If it opens towards the inner or thumb
side of the hand, it will be called an inner slope; if towards the outer
or little-finger side, it will be called an outer slope. In all digits,
except the fore-fingers, the inner slope is much the more rare of the two;
but in the fore-fingers the inner slope appears two-thirds as frequently
as the outer slope. Out of the percentage of 53 loops of the one or other
kind on the right fore-finger, 21 of them have an inner and 32 an outer
slope; out of the percentage of 55 loops on the left fore-finger, 21 have
inner and 34 have outer slopes. These subdivisions 21-21 and 32-34
corroborate the strong statistical similarity that was observed to exist
between the frequency of the several patterns on the right and left
fore-fingers; a condition which was also found to characterise the middle
and little fingers.
It is strange that Purkenje considers the "inner" slope on the fore-finger
to be more frequent than the "outer" (p. 86, ~4~). My nomenclature differs
from his, but there is no doubt as to the disagreement in meaning. The
facts to be adduced hereafter make it most improbable that the persons
observed were racially unlike in this particular.
The tendencies of digits to resemble one another will now be considered in
their various combinations. They will be taken two at a time, in order to
learn the frequency with which both members of the various couplets are
affected by the same A. L. W. class of pattern. Every combination will be
discussed, except those into which the little finger enters. These are
omitted, because the overwhelming frequency of loops in the little fingers
would make the results of comparatively little interest, while their
insertion would greatly increase the size of the table.
TABLE VI_a_.
_Percentage of cases in which the same class of pattern occurs in the_
same digits _of the two hands_.
(From observation of 5000 digits of 500 persons.)
+----------------------------------------------------+
| Couplets of Digits. |Arches.|Loops.|Whorls.|Total.|
|----------------------|-------|------|-------|------|
|The two thumbs | 2 | 48 | 24 | 74 |
| " fore-fingers | 9 | 38 | 20 | 67 |
| " middle fingers| 3 | 65 | 9 | 77 |
| " ring-fingers | 2 | 46 | 26 | 74 |
|----------------------------------------------------|
| Mean of the Totals 72 |
+----------------------------------------------------+
TABLE VI_b_.
_Percentage of cases in which the same class of pattern occurs in various
couplets of_ different digits.
(From 500 persons as above.)
+-----------------------------------------------------------------------+
| Couplets of | OF SAME HANDS. || OF OPPOSITE HANDS. |
| Digits. |---------------------------||---------------------------|
| |Arch.|Loops.|Whorls.|Total.||Arch.|Loops.|Whorls.|Total.|
|--------------|-----|------|-------|------||-----|------|-------|------|
|Thumb and | | | | || | | | |
| fore-finger | 2 | 35 | 16 | 53 || 2 | 33 | 15 | 50 |
|Thumb and | | | | || | | | |
| middle finger| 1 | 48 | 9 | 58 || 1 | 47 | 8 | 56 |
|Thumb and | | | | || | | | |
| ring-finger | 1 | 40 | 20 | 61 || 1 | 38 | 18 | 57 |
|Fore and | | | | || | | | |
| middle finger| 5 | 48 | 12 | 65 || 5 | 46 | 11 | 62 |
|Fore and | | | | || | | | |
| ring-finger | 2 | 35 | 17 | 54 || 2 | 35 | 17 | 54 |
|Middle and | | | | || | | | |
| ring-finger | 2 | 50 | 13 | 65 || 2 | 50 | 12 | 64 |
|-----------------------------------------------------------------------|
| Means of the Totals 59 || 57 |
+-----------------------------------------------------------------------+
A striking feature in this last table is the close similarity between
corresponding entries relating to the same and to the opposite hands.
There are eighteen sets to be compared; namely, six couplets of different
names, in each of which the frequency of three different classes of
patterns is discussed. The eighteen pairs of corresponding couplets are
closely alike in every instance. It is worth while to rearrange the
figures as below, for the greater convenience of observing their
resemblances.
TABLE VII.
+---------------------------------------------------------------+
| | Arches in || Loops in || Whorls in |
| |--------------||--------------||--------------|
| Couplet. |Same |Opposite||Same |Opposite||Same |Opposite|
| |hand.| hand. ||hand.| hand. ||hand.| hand. |
|----------------|-----|--------||-----|--------||-----|--------|
|Thumb and | | || | || | |
| fore-finger | 2 | 2 || 35 | 33 || 16 | 15 |
|Thumb and | | || | || | |
| middle finger | 1 | 1 || 48 | 47 || 9 | 8 |
|Thumb and ring- | | || | || | |
| finger | 1 | 1 || 40 | 38 || 20 | 18 |
|Fore and middle | | || | || | |
| finger | 5 | 5 || 48 | 46 || 12 | 11 |
|Fore and ring- | | || | || | |
| finger | 2 | 2 || 35 | 35 || 17 | 17 |
|Middle and ring-| | || | || | |
| finger | 2 | 2 || 50 | 50 || 13 | 12 |
+---------------------------------------------------------------+
The agreement in the above entries is so curiously close as to have
excited grave suspicion that it was due to some absurd blunder, by which
the same figures were made inadvertently to do duty twice over, but
subsequent checking disclosed no error. Though the unanimity of the
results is wonderful, they are fairly arrived at, and leave no doubt that
the relationship of any one particular digit, whether thumb, fore, middle,
ring or little finger, to any other particular digit, is the same, whether
the two digits are on the same or on opposite hands. It would be a most
interesting subject of statistical inquiry to ascertain whether the
distribution of malformations, or of the various forms of skin disease
among the digits, corroborates this unexpected and remarkable result. I am
sorry to have no means of undertaking it, being assured on good authority
that no adequate collection of the necessary data has yet been published.
It might be hastily inferred from the statistical identity of the
connection between, say, the right thumb and each of the two fore-fingers,
that the patterns on the two fore-fingers ought always to be alike,
whether arch, loop, or whorl. If X, it may be said, is identical both with
Y and with Z, then Y and Z must be identical with one another. But the
statement of the problem is wrong; X is not identical with Y and Z, but
only bears an identical amount of statistical resemblance to each of them;
so this reasoning is inadmissible. The character of the pattern on any
digit is determined by causes of whose precise nature we are ignorant; but
we may rest assured that they are numerous and variable, and that their
variations are in large part independent of one another. We can in
imagination divide them into groups, calling those that are common to the
thumb and the fore-finger of either hand, and to those couplets
exclusively, the A causes; those that are common to the two thumbs and to
these exclusively, the B causes; and similarly those common to the two
fore-fingers exclusively, the C causes.
Then the sum of the variable causes determining the class of pattern in
the four several digits now in question are these:--
Right thumb A + B + an unclassed residue called X(=1=)
Left thumb A + B + " " " X(=2=)
Right fore-finger A + C + " " " Z(=1=)
Left fore-finger A + C + " " " Z(=2=)
The nearness of relationship between the two thumbs is sufficiently
indicated by a fraction that expresses the proportion between all the
causes common to the two thumbs exclusively, and the totality of the
causes by which the A. L. W. class of the patterns of the thumbs is
determined, that is to say, by
A + B
----------------------- (1).
A + B + X(=1=) + X(=2=)
Similarly, the nearness of the relationship between the two fore-fingers
by
A + C
----------------------- (2).
A + C + Z(=1=) + Z(=2=)
And that between a thumb and a fore-finger by
A
--------------------------------------------------- (3).
A + B + C + X(=1=) (or X(=2=)) + Z(=1=) (or Z(=2=))
The fractions (1) and (2) being both greater than (3), it follows that the
relationships between the two thumbs, or between the two fore-fingers, are
closer than that between the thumb and either fore-finger; at the same
time it is clear that neither of the two former relationships is so close
as to reach identity. Similarly as regards the other couplets of digits.
The tabular entries fully confirm this deduction, for, without going now
into further details, it will be seen from the "Mean of the Totals" at the
bottom line of Table VI_b_ that the average percentage of cases in which
two different digits have the same class of patterns, whether they be on
the same or on opposite hands, is 59 or 57 (say 58), while the average
percentage of cases in which right and left digits bearing the same name
have the same class of pattern (Table VI_a_) is 72. This is barely
two-thirds of the 100 which would imply identity. At the same time, the 72
considerably exceeds the 58.
Let us now endeavour to measure the relationships between the various
couplets of digits on a well-defined centesimal scale, first recalling the
fundamental principles of the connection that subsists between
relationships of all kinds, whether between digits, or between kinsmen, or
between any of those numerous varieties of related events with which
statisticians deal.
Relationships are all due to the joint action of two groups of variable
causes, the one common to both of the related objects, the other special
to each, as in the case just discussed. Using an analogous nomenclature to
that already employed, the peculiarity of one of the two objects is due to
an aggregate of variable causes that we may call C+X, and that of the
other to C+Z, in which C are the causes common to both, and X and Z the
special ones. In exact proportion as X and Z diminish, and C becomes of
overpowering effect, so does the closeness of the relationship increase.
When X and Z both disappear, the result is identity of character. On the
other hand, when C disappears, all relationship ceases, and the variations
of the two objects are strictly independent. The simplest case is that in
which X and Z are equal, and _in this_, it becomes easy to devise a scale
in which 0 deg. shall stand for no relationship, and 100 deg. for identity, and
upon which the intermediate degrees of relationship may be marked at their
proper value. Upon this assumption, but with some misgiving, I will
attempt to subject the digits to this form of measurement. It will save
time first to work out an example, and then, after gaining in that way, a
clearer understanding of what the process is, to discuss its defects. Let
us select for our example the case that brings out these defects in the
most conspicuous manner, as follows:--
Table V. tells us that the percentage of whorls in the right ring-finger
is 45, and in the left ring-finger 31. Table VI_a_ tells us that the
percentage of the double event of a whorl occurring on both the
ring-fingers of the same person is 26. It is required to express the
relationship between the right and left ring-fingers on a centesimal
scale, in which 0 deg. shall stand for no relationship at all, and 100 deg. for
the closest possible relationship.
If no relationship should exist, there would nevertheless be a certain
percentage of instances, due to pure chance, of the double event of whorls
occurring in both ring-fingers, and it is easy to calculate their
frequency from the above data. The number of possible combinations of 100
right ring-fingers with 100 left ones is 100 x 100, and of these 45 x 31
would be double events as above (call these for brevity "double whorls").
Consequently the chance of a double whorl in any single couplet is
(45x31)/(100x100), and their average frequency in 100 couplets,--in other
words, their average percentage is (45x31)/100 = 13.95, say 14. If, then,
the observed percentage of double whorls should be only 14, it would be a
proof that the A. L. W. classes of patterns on the right and left
ring-fingers were quite independent; so their relationship, as expressed
on the centesimal scale, would be 0 deg. There could never be less than 14
double whorls under the given conditions, except through some statistical
irregularity.
Now consider the opposite extreme of the closest possible relationship,
subject however, and this is the weak point, to the paramount condition
that the average frequencies of the A. L. W. classes may be taken as
_pre-established_. As there are 45 per cent of whorls on the right
ring-finger, and only 31 on the left, the tendency to form double whorls,
however stringent it may be, can only be satisfied in 31 cases. There
remains a superfluity of 14 per cent cases in the right ring-finger which
perforce must have for their partners either arches or loops. Hence the
percentage of frequency that indicates the closest feasible relationship
under the pre-established conditions, would be 31.
The range of all possible relationships in respect to whorls, would
consequently lie between a percentage frequency of the minimum 14 and the
maximum 31, while the observed frequency is of the intermediate value of
26. Subtracting the 14 from these three values, we have the series of 0,
12, 17. These terms can be converted into their equivalents in a
centesimal scale that reaches from 0 deg. to 100 deg. instead of from 0 deg. to 17 deg.,
by the ordinary rule of three, 12:_x_::17:100; _x_=70 or 71, whence the
value _x_ of the observed relationship on the centesimal scale would be
70 deg. or 71 deg., neglecting decimals.
This method of obtaining the value of 100 deg. is open to grave objection in
the present example. We have no right to consider that the 45 per cent of
whorls on the right ring-finger, and the 31 on the left, can be due to
pre-established conditions, which would exercise a paramount effect even
though the whorls were due entirely to causes common to both fingers.
There is some self-contradiction in such a supposition. Neither are we at
liberty to assume that the respective effects of the special causes X and
Z are equal in average amount; if they were, the percentage of whorls on
the right and on the left finger would invariably be equal.
In this particular example the difficulty of determining correctly the
scale value of 100 deg. is exceptionally great; elsewhere, the percentages of
frequency in the two members of each couplet are more alike. In the two
fore-fingers, and again in the two middle fingers, they are closely alike.
Therefore, in these latter cases, it is not unreasonable to pass over the
objection that X and Z have not been proved to be equal, but we must
accept the results in all other cases with great caution.
When the digits are of different names,--as the thumb and the
fore-finger,--whether the digits be on the same or on opposite hands,
there are two cases to be worked out; namely, such as (1) right thumb and
left fore-finger, and (2) left thumb and right fore-finger. Each accounts
for 50 per cent of the observed cases; therefore the mean of the two
percentages is the correct percentage. The relationships calculated in the
following table do not include arches, except in two instances mentioned
in a subsequent paragraph, as the arches are elsewhere too rare to furnish
useful results.
It did not seem necessary to repeat the calculation for couplets of digits
of different names, situated on opposite hands, as those that were
calculated on closely the same data for similar couplets situated on the
same hands, suffice for both. It is evident from the irregularity in the
run of the figures that the units in the several entries cannot be more
than vaguely approximate. They have, however, been retained, as being
possibly better than nothing at all.
TABLE VIII.
_Approximate Measures of Relationship between the various Digits, on a
Centesimal Scale._
(0 deg. = no relationship; 100 deg. = the utmost feasible likeness.)
+------------------------------------------------------------+
| Couplets. | Loops. | Whorls.| Means. |
|---------------------------------|--------|--------|--------|
| _Digits of the same name._ | | | |
| | | | |
| Right and left thumbs | 57 | 64 | 61 |
| " " fore-fingers | 37 | 59 | 48 |
| " " middle fingers | 34 | 52 | 43 |
| " " ring fingers | 61 | 70 | 65 |
|---------------------------------|--------|--------|--------|
| Means | 47 deg. | 61 deg. | 54 deg. |
|---------------------------------|--------|--------|--------|
| _Digits of different names on | | | |
| the same or on opposite hands._ | | | |
| | | | |
| Thumb and fore-finger | 19 | 29 | 24 |
| " middle finger | 19 | 34 | 27 |
| " ring-finger | 33 | 44 | 39 |
| Fore and middle finger | 52 | 68 | 60 |
| " ring finger | 13 | 34 | 23 |
| Middle and ring finger | 31 | 74 | 52 |
|---------------------------------|--------|--------|--------|
| Means | 28 deg. | 47 deg. | 37 deg. |
+------------------------------------------------------------+
The arches were sufficiently numerous in the fore-fingers (17 per cent) to
fully justify the application of this method of calculation. The result
was 43 deg., which agrees fairly with 48 deg., the mean of the loops and the
whorls. In the middle finger the frequency of the arches was only half the
above amount and barely suffices for calculation. It gave the result of
38 deg., which also agrees fairly with 43 deg., the mean of the loops and the
whorls for that finger.
Some definite results may be gathered from this table notwithstanding the
irregularity with which the figures run. Its upper and lower halves
clearly belong to different statistical groups, the entries in the former
being almost uniformly larger than those in the latter, in the proportion
of 54 deg. to 37 deg., say 3 to 2, which roughly represents in numerical terms the
nearer relationship between digits of the same name, as compared to that
between digits of different names. It seems also that of the 6 couplets of
digits bearing different names, the relationship is closest between the
middle finger and the two adjacent ones (60 deg. and 52 deg., as against 24 deg., 27 deg.,
39 deg. and 23 deg.). It is further seen in every pair of entries that whorls are
related together more closely than loops. I note this, but cannot explain
it. So far as my statistical inquiries into heredity have hitherto gone,
all peculiarities were found to follow the same law of transmission, none
being more surely inherited than others. If there were a tendency in any
one out of many alternative characters to be more heritable than the rest,
that character would become universally prevalent, in the absence of
restraining influences. But it does not follow that there are no peculiar
restraining influences here, nor that what is true for heredity, should be
true, in all its details, as regards the relationships between the
different digits.
CHAPTER IX
METHODS OF INDEXING
In this chapter the system of classification by Arches, Loops, and Whorls
described in Chapter V. will be used for indexing two, three, six or ten
digits, as the case may be.
An index to each set of finger marks made by the same person, is needful
in almost every kind of inquiry, whether it be for descriptive purposes,
for investigations into race and heredity, or into questions of symmetry
and correlation. It is essential to possess an index to the finger marks
of known criminals before the method of finger prints can be utilised as
an organised means of detection.
The ideal index might be conceived to consist of a considerable number of
compartments, or their equivalents, each bearing a different
index-heading, into which the sets of finger prints of different persons
may be severally sorted, so that all similar sets shall lie in the same
compartment.
The principle of the proposed method of index-headings is, that they
should depend upon a few conspicuous differences of pattern in many
fingers, and not upon many minute differences in a few fingers. It is
carried into effect by distinguishing the A. L. W. class of pattern on
each digit in succession, by a letter,--_a_ for Arch, _l_ for Loop, _w_
for Whorl; or else, as an alternative method, to subdivide _l_ by using
_i_ for a loop with an Inner slope, and _o_ for one with an Outer slope,
as the case may be. In this way, the class of pattern in each set of ten
digits is described by a sequence of ten letters, the various combinations
of which are alphabetically arranged and form the different
index-headings. Let us now discuss the best method of carrying out this
principle, by collating the results of alternative methods of applying it.
We have to consider the utility of the _i_ and _o_ as compared to the
simple _l_, and the gain through taking all ten digits into account,
instead of only some of them.
It will be instructive to print here an actual index to the finger prints
of 100 different persons, who were not in any way selected, but taken as
they came, and to use it as the basis of a considerable portion of the
following remarks, to be checked where necessary, by results derived from
an index to 500 cases, in which these hundred are included.
This index is compiled on the principle shortly to be explained, entitled
the "_i_ and _o_ fore-finger" method.
TABLE IX.--INDEX TO 100 SETS OF FINGER PRINTS.
+------------------------------------+
| | A B C D |
|Order | Right. Left. Rt. Lt. |
| of |-----------------------------|
|Entry.| F.M.R. F.M.R. T.L. T.L. |
|------|-----------------------------|
| 1 | _a a a a a a a a l a_ |
| 2 | _ " " a l a l_ |
| 3 | _ " " " " _ |
| 4 | _ " " w l l l_ |
| 5 | _a a l a a l a l a l_ |
| 6 | _ " " l l l l_ |
| 7 | _ " " " " _ |
| 8 | _ " a a w l l l l_ |
| 9 | _ " a l l l l l l_ |
| 10 | _ " " l w w l_ |
| 11 | _ " o l l l l l l_ |
| 12 | _a a w a a l l l l l_ |
| 13 | _ " a l l l l l l_ |
| 14 | _a l a a a a l a l a_ |
| 15 | _ " " l a l w_ |
| 16 | _ " o l l w l l l_ |
| 17 | _a l l a a l l l a l_ |
| 18 | _ " " l l l l_ |
| 19 | _ " " " " _ |
| 20 | _ " " " " _ |
| 21 | _ " " " " _ |
| 22 | _ " " " " _ |
| 23 | _ " a l w l l l l_ |
| 24 | _ " i l l l l l l_ |
| 25 | _ " " " " _ |
| 26 | _a l l i l l w l l l_ |
| 27 | _ " o a l w l l l_ |
| 28 | _ " o l l w l l l_ |
| 29 | _ " w w w w l l l_ |
| 30 | _a l w i l w l l l l_ |
| 31 | _ " o a l l l l l_ |
| 32 | _ " o l l l w l l_ |
| 33 | _ " " w l w l_ |
| 34 | _ " o l w a l a l_ |
| 35 | _i l l a l l w l l l_ |
| 36 | _ " " w l w l_ |
| 37 | _ " i l l l l l l_ |
| 38 | _ " " " " _ |
| 39 | _ " " " " _ |
| 40 | _ " " " " _ |
| 41 | _i l l i l l w l l l_ |
| 42 | _ " i w w w l w l_ |
| 43 | _i l w i l l l l w l_ |
| 44 | _ " " w w w l_ |
| 45 | _ " i l w w w w l_ |
| 46 | _ " i w l l l l l_ |
| 47 | _ " w l w w l w l_ |
| 48 | _ " w w l l l l l_ |
| 49 | _i w w a l l w l w l_ |
| 50 | _ " w w w w l w l_ |
| 51 | _ " " " " _ |
| 52 | _o a w o l l l l l l_ |
| 53 | _o l l o l l l l l l_ |
| 54 | _ " " " " _ |
| 55 | _ " " " " _ |
| 56 | _ " " w l w l_ |
| 57 | _ " i l l l l l l_ |
| 58 | _ " " " " _ |
| 59 | _ " " " " _ |
| 60 | _ " o l l l l l l_ |
| 61 | _ " " " " _ |
| 62 | _ " " " " _ |
| 63 | _ " " " " _ |
| 64 | _ " " " " _ |
| 65 | _ " " " " _ |
| 66 | _ " w a l l l w l_ |
| 67 | _ " w w w l l w l_ |
| 68 | _o l w a l l l l l l_ |
| 69 | _ " " w l w l_ |
| 70 | _ " i l l w l w l_ |
| 71 | _ " o l l l l l l_ |
| 72 | _ " " " " _ |
| 73 | _ " o l w l l l l_ |
| 74 | _ " " " " _ |
| 75 | _w l l i l l l l w l_ |
| 76 | _ " " " " _ |
| 77 | _w l l w l l l l l l_ |
| 78 | _ " " " " _ |
| 79 | _ " " w l w l_ |
| 80 | _ " w l w l l l l_ |
| 81 | _w l w o l w l l l l_ |
| 82 | _ " " l l a l_ |
| 83 | _ " " w l l l_ |
| 84 | _ " w w w w l w l_ |
| 85 | _ " " w w l l_ |
| 86 | _ " " w w l w_ |
| 87 | _ " " w w w w_ |
| 88 | _ " " " " _ |
| 89 | _w w l i l l l l l l_ |
| 90 | _ " w l l w l l l_ |
| 91 | _w w w o l w w l l l_ |
| 92 | _ " w l w w l w l_ |
| 93 | _ " " " " _ |
| 94 | _ " w w l l l l w_ |
| 95 | _ " w w w i l l l_ |
| 96 | _ " " w l l l_ |
| 97 | _ " " w l w l_ |
| 98 | _ " " w w w l_ |
| 99 | _ " " " " _ |
| 100 | _ " " w w w w_ |
+------------------------------------+
The sequence in which the digits have been registered is not from the
thumb outwards to the little finger, but, on account of various good
reasons that will be appreciated as we proceed, in the following order.
The ten digits are registered in four groups, which are distinguished in
the Index by the letters A, B, C, D:--
A. _First._ The fore, middle, and ring-fingers of the _right_ hand
taken in that order.
B. _Second._ The fore, middle, and ring-fingers of the _left_ hand
taken in that order.
C. _Third._ The thumb and little finger of the _right_ hand.
D. _Fourth._ The thumb and little finger of the _left_ hand.
Consequently an index-heading will be of the form--
First Second Third Fourth
group. group. group. group.
_a a l_ _a a w_ _l l_ _l l_
These index-headings are catalogued in alphabetical order. The method used
in the Index is that which takes note of no slopes, except those of loops
in the fore-finger of either hand. Consequently the index-heading for my
own digits, printed on the title-page, is _wlw oll wl wl_. Those of the
eight sets in Plate VI. are as follows:--
_i l w i l l w w w l_
_o l w o l w w l l l_
_o l w o l w w l l l_
_o l w o l l l l l l_
_i l w i l w w l w l_
_i l w i w l l l l l_
_i l l w w l l l l l_
_o l l a a l l l a l_
_o a a a a a l a l a_
For convenience of description and reference, the successive entries in
the specimen index have been numbered from 1 to 100, but that is no part
of the system: those figures would be replaced in a real index by names
and addresses.
A preliminary way of obtaining an idea of the differentiating power of an
index is to count the number of the different headings that are required
to classify a specified number of cases. A table is appended which shows
the numbers of the headings in the three alternative methods (1) of noting
slopes of all kinds in all digits, (2) of noting slopes of Loops only and
in the fore-fingers only, and (3) of disregarding the slopes altogether.
Also in each of these three cases taking account of--
(_a_) All the ten digits;
(_b_) the fore, middle, and ring-fingers of both hands;
(_c_) those same three fingers, but of the right hand only;
(_d_) the fore and middle fingers of the right hand.
TABLE X.
_No. of different index-heads in 100 sets of Finger Prints._
+---------------------------------------------------------------+
| | | Account taken of |
| No. of | |------------------------------|
| digits | Digits noted. | All |_i_ and _o_| No |
| regarded. | | slopes. | in fore- | slope. |
| | | | fingers. | |
|-----------|--------------------|---------|-----------|--------|
| 10 | All the 10 digits | 82 | 76 | 71 |
| | | | | |
| | Fore, middle, | | | |
| 6 | and ring-fingers | 65 | 50 | 43 |
| | of both hands | | | |
| | | | | |
| 3 | Of right hand only | 25 | 16 | 14 |
| | | | | |
| 2 | Fore and middle of | 12 | 8 | 7 |
| | right hand only | | | |
+---------------------------------------------------------------+
The column headed "all slopes" refers to the method first used with
success, and described in my Memoir, already alluded to (_Proc. Roy.
Soc._, 1891), accompanied by a specimen index, from which the present one
was derived. There the direction of the slope of every pattern that has
one, is taken into account, and in order to give as much scope as
possible to the method, the term Arch (I then called it a Primary) was
construed somewhat over-liberally (see p. 114). It was made to include the
forked-arch Fig. 12 (~2~), and even the nascent-loop (~9~), so long as not
more than a single recurved ridge lay within the outline of the pattern;
therefore many of the so-called arches had slopes. It is not necessary to
trouble the reader with the numerical nomenclature that was then used, the
method itself being now obsolete. Full particulars of it are, however,
given in the Memoir.
A somewhat large experience in sorting finger prints in various ways and
repeatedly, made it only too evident that the mental strain and risk of
error caused by taking all slopes into account was considerable. The
judgment became fatigued and the eye puzzled by having to assign opposite
meanings to the same actual direction of a slope in the right and left
hands respectively. There was also a frequent doubt as to the existence of
a slope in large whorls of the spiral- and circlet-in-loop patterns (Fig.
13, ~21~, ~22~) when the impressions had not been rolled. A third
objection is the rarity of the inner slopes in any other digit than the
fore-finger. It acted like a soporific to the judgment not only of myself
but of others, so that when an inner slope did occur it was apt to be
overlooked. The first idea was to discard slopes altogether,
notwithstanding the accompanying loss of index power, but this would be an
unnecessarily trenchant measure. The slope of a loop, though it be on the
fore-finger alone, decidedly merits recognition, for it differentiates
such loops into two not very unequal classes. Again, there is little
chance of mistake in noting it, the impression of the thumb on the one
side and those of the remaining fingers on the other, affording easy
guidance to the eye and judgment. These considerations determined the
method I now use exclusively, by which Table IX. was compiled, and to
which the second column of Table X., headed "_i_ and _o_ in fore-fingers,"
refers.
The heading of the third column, "no slope," explains itself, no account
having been there taken of any slopes whatever, so _i_ and _o_ disappear,
having become merged under _l_.
The table gives a very favourable impression of the differentiating power
of all these methods of indexing. By the "_i_ and _o_ fore-finger" method,
it requires as many as 76 different index-headings to include the finger
prints of 100 different persons, 195 of 300 persons, and 285 of 500.
The number of entries under each index-heading varies greatly; reference
to the index of 100 sets showing no less than six entries (Nos. 60-65)
under one of them, and four entries (Nos. 18-21 and 37-40) under each of
two others. Thus, although a large portion of the 100 sets are solitary
entries under their several headings, and can be found by a single
reference, the remainder are grouped together like the commoner surnames
in a directory. They are troublesome to distinguish, and cannot be
subdivided at all except by supplementary characteristics, such as the
number of ridges in some specified part of the pattern, or the character
of the cores.
In other respects the difference of merit between the three methods is
somewhat greater, as is succinctly indicated by the next table.
TABLE XI.--_In 100 Sets._
+-----------------------------------------------------+
| |No. of different index-headings.|
| Number of Entries |--------------------------------|
|under the same head.| All | _i_ and _o_ | No |
| | slopes. | fore-fingers | slope.|
| | | only. | |
|--------------------|---------|--------------|-------|
| 1 | 71 | 63 | 58 |
| 2 | 10 | 8 | 9 |
| 3 | 1 | 3 | 1 |
| 4 | ... | 2 | 2 |
| 5 | ... | ... | ... |
| 6 | 1 | ... | ... |
| 13 | ... | ... | 1 |
|--------------------|---------|--------------|-------|
| Total | 83 | 76 | 71 |
+-----------------------------------------------------+
Hence it is evident that the second method of "_i-o_ fore-finger" is
capable of dealing rapidly with 100 cases, but that the method of "no
slope" will give trouble in twelve out of the hundred cases.
TABLE XII.
_Index-headings under which more than 1 per cent of the sets of Finger
Prints were registered._
(500 sets observed.)
+----------------------------------------------------
| _i_ and _o_ in fore-fingers. ||
|----------------------------------------------------
| No. | |Frequency||
| for | Index-heading. | per ||
|Reference.| | cent. ||
|----------|-----------------------------|---------||
| 1 | _a l l a l l l l l l_ | 1.2 ||
| 2 | _a l l i l l " " _ | 1.6 ||
|----------|-----------------------------|---------||
| 3 | _i l l i l l " " _ | 2.8 ||
| 4 | _o l l i l l " " _ | 1.4 ||
| 5 | _o l l o l l " " _ | 4.0 ||
|----------|-----------------------------|---------||
| 6 | _i l l o l l w l l l_ | 1.2 ||
| 7 | _o l l o l l " " _ | 1.4 ||
|----------|-----------------------------|---------||
| 8 | _o l l a l l l l l l_ | 2.2 ||
| 9 | _o l w u l l " " _ | 2.0 ||
| 10 | _w l l w l l " " _ | 1.2 ||
| 11 | _w w w w w w w w w w_ | 1.4 ||
+----------------------------------------------------
--------------------------------------------------+
No slope. |
--------------------------------------------------|
No. | |Frequency|
for | Index-heading. | per |
Reference.| | cent. |
----------|-----------------------------|---------|
I. | _a l l a l l l l l l_ | 1.2 |
II. | _a l l l l l " " _ | 2.2 |
----------|-----------------------------|---------|
| | |
III. | _l l l l l l " " _ | 9.2 |
| | |
----------|-----------------------------|---------|
IV. | _l l l l l l w l l l_ | 3.2 |
| | |
----------|-----------------------------|---------|
V. | _l l l a l l l l l l_ | 3.0 |
VI. | _l l w l l l " " _ | 3.0 |
VII. | _w l l w l l " " _ | 1.2 |
VIII. | _w w w w w w w w w w_ | 1.4 |
--------------------------------------------------+
The headings in the right half of the table include more cases than
the left half, because a combination of two or more cases that
severally contain less than 1 per cent of the finger prints, and are
therefore ignored in the first half of the table, may exceed 1 per
cent and find a place in the second half.
The entries in Table XII. are derived from a catalogue of 500 sets, and
include all entries that appeared more than five times; in other words,
whose frequency exceeded 1 per cent. These are the index-headings that
give enough trouble to deserve notice in catalogues of, say, from 500 to
1000 sets.
In the left half of Table XII. all the index-headings are given, under
each of which more than 1 per cent of the sets fell, when the method of
"_i_ and _o_ in fore-fingers" was adopted; also the respective percentage
of the cases that fell under them. In the right half of the table are the
corresponding index-headings, together with the percentages of frequency,
when the "no slope" method is employed. These are distinguished by Roman
numerals. The great advantage of the "_i_ and _o_ fore-finger" method lies
in its power of breaking up certain large groups which are very
troublesome to deal with by the "no slope" method. According to the latter
as many as 9.2 per cent of all the entries fall under the index-heading
marked III., but according to the "_i-o_ fore-finger" method these are
distributed among the headings 3, 4, and 5. The "all slopes" method has
the peculiar merit of breaking up the large group Nos. 11 and VIII. of
"all whorls," but its importance is not great on that account, as whorls
are distinguishable by their cores, which are less troublesome to observe
than their slopes.
The percentage of all the entries that fall under a single index-heading,
according to the "_i-o_ fore-finger" method, diminishes with the number of
entries at the following rate:--
TABLE XIII.
+----------------------------------------------------------+
| | Total number of entries. |
| |--------------------------|
| | 100 | 300 | 500 |
|-------------------------------|--------|--------|--------|
| Percentage of entries falling | | | |
| under a single head | 63 | 49.0 | 39.8 |
+----------------------------------------------------------+
It may be that every one of the 4{2} x 3{8}, or one hundred and five
thousand possible varieties of index-headings, according to the "_i-o_
fore-finger" method, may occur in Nature, but there is much probability
that some of them may be so rare that instances of no entry under certain
heads would appear in the register, even of an enormous number of persons.
* * * * *
Hitherto we have supposed that prints of the ten fingers have in each case
been indexed. The question now to be considered is the gain through
dealing in each case with all ten digits, instead of following the easier
practice of regarding only a few of them. The following table, drawn up
from the hundred cases by the "all slopes" method, will show its amount.
TABLE XIV.--_From 100 Sets._
+----------------------------------------------------------------------+
| | | No. of different index-headings. |
| Digits. | No. of |------------------------------------|
| | digits. | All | _i_ and _o_ | No slope. |
| | | slopes. | fore-finger. | |
|-----------------------|---------|---------|--------------|-----------|
| Fore and middle of | | | | |
| right hand | 2 | 11 | 8 | 7 |
| | | | | |
| Fore, middle and ring | | | | |
| of right hand | 3 | 23 | 16 | 14 |
| | | | | |
| Fore, middle and ring | | | | |
| of both hands | 6 | 65 | 50 | 45 |
| | | | | |
| All ten digits | 10 | 83 | 76 | 73 |
+----------------------------------------------------------------------+
The trouble of printing, reading off, and indexing the ten digits, is
practically twice that of dealing with the six fingers; namely, three on
each of the hands; the thumb being inconvenient to print from, and having
to be printed separately, even for a dabbed impression, while the fingers
of either hand can be dabbed down simultaneously.
For a large collection the ten digit method is certainly the best, as it
breaks up the big battalions; also in case of one or more fingers having
been injured, it gives reserve material to work upon.
* * * * *
We now come to the great difficulty in all classifications; that of
transitional cases. What is to be done with those prints which cannot be
certainly classed as Arches, Loops, or Whorls, but which lie between some
two of them? These occur about once in every forty digits, or once in
every four pairs of hands. The roughest way is to put a mark by the side
of the entry to indicate doubt, a better one is to make a mark that shall
express the nature of the peculiarity; thus a particular eyed pattern
(Plate 10, Fig. 16, _n_) may be transitional between a loop and a whorl;
under whichever of the two it is entered, the mark might be an _e_ to show
that anyhow it is an eye. Then, when it is required to discover whether an
index contains a duplicate of a given specimen in which a transitional
pattern occurs, the two headings between which the doubt lies have to be
searched, and the marked entries will limit the search. Many alternative
ways of marking may be successfully used, but I am not yet prepared to
propose one as being distinctly the best. When there are two of these
marks in the same set, it seldom happens that more than two references
have to be made, as it is usual for the ambiguity to be of the same kind
in both of the doubtful fingers. If the ambiguities were quite
independent, then two marks would require four references, and three marks
would require nine. There are a few nondescript prints that would fall
under a separate heading, such as Z. Similarly, as regards lost or injured
fingers.
I have tried various methods of sub-classification, and find no difficulty
in any of them, but general rules seem inadvisable; it being best to treat
each large group on its own merits.
One method that I have adopted and described in the _Proc. Royal Soc._, is
to sketch in a cursive and symbolic form the patterns of the several
fingers in the order in which they appear in the print, confining myself
to a limited number of symbols, such as might be used for printer's types.
They sufficed fairly for some thousands of the finger marks upon which
they were tried, but doubtless they could be improved. A little violence
has of course to be used now and then, in fitting some unusual patterns to
some one or other of these few symbols. But we are familiar with such
processes in ordinary spelling, making the same letter do duty for
different sounds, as _a_ in the words _as_, _ale_, _ask_, and _all_. The
plan of using symbols has many secondary merits. It facilitates a
leisurely revision of first determinations, it affords a pictorial record
of the final judgment that is directly comparable with the print itself,
and it almost wholly checks blunders between inner and outer slopes. A
beginner in finger reading will educate his judgment by habitually using
them at first.
[Illustration: PLATE 2.
FIG. 3. Form of card used for impressions of the ten digits. 11-1/2 x 5
inches.
FIG. 4. Roller and its bearings, of a pocket printing apparatus.]
The cores give great assistance in breaking up the very large groups of
all-loops (see Table XII., Nos. 11 and VIII.); so does an entry of the
approximate number of ridges in some selected fingers, that lie between
the core and the upper outline of the loop.
* * * * *
The plan I am now using for keeping finger prints in regular order, is
this:--In the principal collection, the prints of each person's ten digits
are taken on the same large card; the four fingers of either hand being
_dabbed_ down simultaneously above, and all the ten digits _rolled_
separately below. (Plate 2, Fig. 3.) Each card has a hole three-eighths of
an inch in diameter, punched in the middle near to the bottom edge, and
the cards are kept in trays, which they loosely fit, like the card
catalogues used in many libraries. Each tray holds easily 500 cards, which
are secured by a long stout wire passing like a skewer through the ends of
the box and the holes in the cards. The hinder end of the box is sloped,
so the cards can be tilted back and easily examined; they can be inserted
or removed after withdrawing the wire.
It will be recollected that the leading and therefore the most conspicuous
headings in the index refer to the fore, middle, and ring-fingers of the
right hand, as entered in column A of the Specimen Register (Table IX.)
The variety of these in the "_i_ and _o_ fore-finger" method, of which we
are now speaking, cannot exceed thirty-six, there being only four
varieties (_a_, _i_, _o_, _w_) in the fore-finger, and three varieties
(_a_, _l_, _w_) in each of the other two; so their maximum number is 4 x 3
x 3 = 36. The actual number of such index-headings in 500 cases, and the
number of entries that fell under each, was found to be as follows:--
TABLE XV.
_No. of entries in 500 cases, under each of the thirty-six possible
index-letters for the fore, middle, and ring-fingers of the right hand by
the "i-o fore-finger" method._
+--------------------------------------------------------------+
| _a a a_ | 4 || _i a a_ | 1 || _o a a_ | 1 || _w a a_ | -- |
| _l_ | 17 || _l_ | 3 || _l_ | 2 || _l_ | -- |
| _w_ | 5 || _w_ | -- || _w_ | 1 || _w_ | 1 |
| | || | || | || | |
| _a l a_ | 3 || _i l a_ | -- || _o l a_ | 2 || _w l a_ | 1 |
| _l_ | 45 || _l_ | 54 || _l_ | 88 || _l_ | 40 |
| _w_ | 11 || _w_ | 33 || _w_ | 59 || _w_ | 52 |
| | || | || | || | |
| _a w a_ | -- || _i w a_ | -- || _o w a_ | -- || _w w a_ | -- |
| _l_ | -- || _l_ | 3 || _l_ | -- || _l_ | 10 |
| _w_ | -- || _w_ | 11 || _w_ | 6 || _w_ | 47 |
+--------------------------------------------------------------+
_a_ = Arch.
_i_ = Inward-sloped Loop on the fore-finger.
_o_ = Outward-sloped Loop on the fore-finger.
_l_ = Loop of either kind on the middle or ring finger.
_w_ = Whorl.
These 500 cases supply no entries at all to eleven of the thirty-six
index-headings, less than five entries (or under 1 per cent) to ten
others, and the supply is distributed very unevenly among the remaining
fifteen. This table makes it easy to calculate beforehand the spaces
required for an index of any specified number of prints, whether they be
on the pages of a Register, or in compartments, or in drawers of movable
cards.
CHAPTER X
PERSONAL IDENTIFICATION
We shall speak in this chapter of the aid that finger prints can give to
personal identification, supposing throughout that facilities exist for
taking them well and cheaply, and that more or less practice in reading
them has been acquired by many persons. A few introductory words will show
this supposition to be reasonable. At the present moment any printer, and
there are many printers in every town, would, at a small charge, blacken a
slab and take the prints effectively, after being warned to use very
little ink, as described in Chapter III. The occupation of finger printing
would, however, fall more naturally into the hands of photographers, who,
in addition to being found everywhere, are peculiarly well suited to it,
for, taken as a class, they are naturally gifted with manual dexterity and
mechanical ingenuity. Having secured good impressions, they could multiply
them when necessary, and enlarge when desired, while the ticketing and
preservation of the negatives would fall into their usual business
routine. As they already occupy themselves with one means of
identification, a second means of obtaining the same result is allied to
their present work.
Were it the custom for persons about to travel to ask for prints of their
fingers when they were photographed, a familiarity with the peculiarities
of finger prints, and the methods of describing and classifying them,
would become common. Wherever finger prints may be wanted for purposes of
attestation and the like, the fact mentioned by Sir W. Herschel (p. 45) as
to the readiness with which his native orderlies learnt to take them with
the ink of his office stamp, must not be forgotten.
The remarks about to be made refer to identification generally, and are
not affected by the fact that the complete process may or may not include
the preliminary search of a catalogue; the two stages of search and of
comparison will be treated separately towards the close of the chapter.
In civilised lands, honest citizens rarely need additional means of
identification to their signatures, their photographs, and to personal
introductions. The cases in which other evidence is wanted are chiefly
connected with violent death through accident, murder, or suicide, which
yield the constant and gruesome supply to the Morgue of Paris, and to
corresponding institutions in other large towns, where the bodies of
unknown persons are exposed for identification, often in vain. But when
honest persons travel to distant countries where they have few or no
friends, the need for a means of recognition is more frequently felt. The
risk of death through accident or crime is increased, and the probability
of subsequent identification diminished. There is a possibility not too
remote to be disregarded, especially in times of war, of a harmless person
being arrested by mistake for another man, and being in sore straits to
give satisfactory proof of the error. A signature may be distrusted as a
forgery. There is also some small chance, when he returns to his own
country after a long absence, of finding difficulty in proving who he is.
But in civilised lands and in peaceable times, the chief use of a sure
means of identification is to benefit society by detecting rogues, rather
than to establish the identity of men who are honest. Is this criminal an
old offender? Is this new recruit a deserter? Is this professed pensioner
personating a man who is dead? Is this upstart claimant to property the
true heir, who was believed to have died in foreign lands?
In India and in many of our Colonies the absence of satisfactory means for
identifying persons of other races is seriously felt. The natives are
mostly unable to sign; their features are not readily distinguished by
Europeans; and in too many cases they are characterised by a strange
amount of litigiousness, wiliness, and unveracity. The experience of Sir
W. Herschel, and the way in which he met these unfavourable conditions by
the method of finger prints, has been briefly described in p. 27. Lately
Major Ferris, of the Indian Staff Corps, happening to visit my laboratory
during my absence, and knowing but little of what Sir W. Herschel had
done, was greatly impressed by the possibilities of finger prints. After
acquainting himself with the process, we discussed the subject together,
and he very kindly gave me his views for insertion here. They are as
follow, with a few trifling changes of words:--
"During a period of twenty-three years, eighteen of which have been
passed in the Political Department of the Bombay Government, the great
need of an official system of identification has been constantly
forced on my mind.
"The uniformity in the colour of hair, eyes, and complexion of the
Indian races renders identification far from easy, and the difficulty
of recording the description of an individual, so that he may be
afterwards recognised, is very great. Again, their hand-writing,
whether it be in Persian or Devanagri letters, is devoid of character
and gives but little help towards identification.
"The tenacity with which a native of India cleaves to his ancestral
land, his innate desire to acquire more and more, and the obligation
that accrues to him at birth of safeguarding that which has already
been acquired, amounts to a religion, and passes the comprehension of
the ordinary Western mind. This passion, or religion, coupled with a
natural taste for litigation, brings annually into the Civil Courts an
enormous number of suits affecting land. In a native State at one time
under my political charge, the percentage of suits for the possession
of land in which the title was disputed amounted to no less than 92,
while in 83 per cent of these the writing by which the transfer of
title purported to have been made, was repudiated by the former
title-holder as fraudulent and not executed by him. When it is
remembered that an enormous majority of the landholders whose titles
come into court are absolutely illiterate, and that their execution of
the documents is attested by a mark made by a third party, frequently,
though not always apparently, interested in the transfer, it will be
seen that there is a wide door open to fraud, whether by false
repudiation or by criminal attempt at dispossession.
"It has frequently happened in my experience that a transfer of title
or possession was repudiated; the person purporting to have executed
the transfer asserting that he had no knowledge of it, and never
authorised any one to write, sign, or present it for registration.
This was met by a categorical statement on the part of the beneficiary
and of the attesting witnesses, concerning the time, date, and
circumstances of the execution and registration, that demolished the
simple denial of the man whom it was sought to dispossess. Without
going into the ethics of falsehood among Western and Eastern peoples,
it would be impossible to explain how what is repugnant to the one as
downright lying, is very frequently considered as no more than venial
prevarication by the other. This, however, is too large a subject for
present purposes, but the fact remains that perjury is perpetrated in
Indian Courts to an extent unknown in the United Kingdom.
"The interests of landholders are partially safeguarded by the Act
that requires all documents effecting the transfer of immovable
property to be registered, but it could be explained, though not in
the short space of this letter, how the provisions of the Act can be,
and frequently are, fulfilled in the absence of the principal person,
the executor.
"Enough has been said to show that if some simple but efficient means
could be contrived to identify the person who has executed a bond,
cases of fraud such as these would practically disappear from the
judicial registers. Were the legislature to amend the Registration Act
and require that the original document as well as the copy in the
Registration Book should bear the imprint of one or more fingers of
the parties to the deed, I have little hesitation in saying that not
only would fraud be detected, but that in a short time the facility of
that detection would act as a deterrent for the future. [This was
precisely the experience of Sir W. Herschel.--F.G.] In the majority of
cases, the mere question would be, Is the man A the same person as B,
or is he not? and of that question the finger marks would give
unerring proof. For example, to take the simplest case, A is sued for
possession of some land, the title of which he is stated to have
parted with to another for a consideration. The document and the
Registration Book both bear the imprint of the index finger of the
right hand of A. A repudiates, and a comparison shows that whereas
the finger pattern of A is a whorl, the imprint on the document is a
loop; consequently A did not execute it.
"In the identification of Government pensioners the finger print
method would be very valuable. At one period, I had the payment of
many hundreds of military pensioners. Personation was most difficult
to detect in persons coming from a distance, who had no local
acquaintances, and more especially where the claimants were women. The
marks of identification noted in the pension roll were usually
variations of:--"Hair black--Eyes brown--Complexion wheat
colour--Marks of tattooing on fore-arm"--terms which are equally
appropriate to a large number of the pensioners. The description was
supplemented in some instances, where the pensioner had some
distinguishing mark or scar, but such cases are considerably rarer
than might be supposed, and in women the marks are not infrequently in
such a position as to practically preclude comparison. Here also the
imprint of one or more finger prints on the pension certificate, would
be sufficient to settle any doubt as to identity.
"As a large number of persons pass through the Indian gaols not only
while undergoing terms of imprisonment, but in default of payment of a
fine, it could not but prove of value were the finger prints of one
and all secured. They might assist in identifying persons who have
formerly been convicted, of whom the local police have no knowledge,
and who bear a name that may be the common property of half a hundred
in any small town."
Whatever difficulty may be felt in the identification of Hindoos, is
experienced in at least an equal degree in that of the Chinese residents
in our Colonies and Settlements, who to European eyes are still more alike
than the Hindoos, and in whose names there is still less variety. I have
already referred (p. 26) to Mr. Tabor, of San Francisco, and his proposal
in respect to the registration of the Chinese. Remarks showing the need
of some satisfactory method of identifying them, have reached me from
various sources. The _British North Borneo Herald_, August 1, 1888, that
lies before me as I write, alludes to the difficulty of identifying
coolies, either by photographs or measurements, as likely to become
important in the early future of that country.
For purposes of registration, the method of printing to be employed, must
be one that gives little trouble on the one hand, and yields the maximum
of efficiency for that amount of trouble on the other. Sir W. Herschel
impressed simultaneously the fore and middle fingers of the right hand. To
impress simultaneously the fore, middle, and ring-fingers of the right
hand ought, however, to be better, the trouble being no greater, while
three prints are obviously more effective than two, especially for an
off-hand comparison. Moreover, the patterns on the ring-finger are much
more variable than those on the middle finger. Much as rolled impressions
are to be preferred for minute and exhaustive comparisons, they would
probably be inconvenient for purposes of registration or attestation. Each
finger has to be rolled separately, and each separate rolling takes more
time than a dab of all the fingers of one hand simultaneously. Now a
dabbed impression of even two fingers is more useful for registration
purposes than the rolled impression of one; much more is a dabbed
impression of three, especially when the third is the variable
ring-finger. Again, in a simultaneous impression, there is no doubt as to
the sequence of the finger prints being correct, but there may be some
occasional bungling when the fingers are printed separately.
* * * * *
For most criminal investigations, and for some other purposes also, the
question is not the simple one just considered, namely, "Is A the same
person, or a different person from B?" but the much more difficult problem
of "Who is this unknown person X? Is his name contained in such and such a
register?" We will now consider how this question may be answered.
Registers of criminals are kept in all civilised countries, but in France
they are indexed according to the method of M. Alphonse Bertillon, which
admits of an effective search being made through a large collection. We
shall see how much the differentiating power of the French or of any other
system of indexing might be increased by including finger prints in the
register.
M. Bertillon has described his system in three pamphlets:--
(1) _Une application pratique de l'anthropometrie_, Extrait des
Annales de Demographie Interne. Paris 1881. (2) _Les signalements
anthropometriques_, Conference faite au Congres Penitentiare
International de Rome, Nov. 22, 1885. (3) _Sur le fonctionnement du
service des signalements_. All the above are published by Masson, 120
Boulevard St. Germain, Paris. To these must be added a very
interesting but anonymous pamphlet, based on official documents, and
which I have reason to know is authorised by M. Bertillon, namely, (4)
_L'anthropometrie Judiciare en Paris, en 1889_: G. Stenheil, 2 Rue
Casimir-Delavigne, Paris.
Besides these a substantial volume is forthcoming, which may give a
satisfactory solution to some present uncertainties.
The scale on which the service is carried on, is very large. It was begun
in 1883, and by the end of 1887 no less than 60,000 sets of measures were
in hand, but thus far only about one half of the persons arrested in Paris
were measured, owing to the insufficiency of the staff. Arrangements were
then made for its further extension. There are from 100 to 150 prisoners
sentenced each day by the Courts of Law in Paris to more than a few days'
imprisonment, and every one of these is sent to the Depot for twenty-four
hours. While there, they are now submitted to _Bertillonage_, a newly
coined word that has already come into use. This is done in the forenoon,
by three operators and three clerks; six officials in all. About half of
the prisoners are old offenders, of whom a considerable proportion give
their names correctly, as is rapidly verified by an alphabetically
arranged catalogue of cards, each of which contains front and profile
photographs, and measurements. The remainder are examined strictly; their
bodily marks are recorded according to a terse system of a few letters,
and they are variously measured. Each person occupies seven or eight
minutes. They are then photographed. From sixty to seventy-five prisoners
go through this complete process every forenoon. In the afternoon the
officials are engaged in making numerous copies of each set of records,
one of which is sent to Lyon, and another to Marseille, where there are
similar establishments. They also classify the copies of records that are
received from those towns and elsewhere in France, of which from seventy
to one hundred arrive daily. Lastly, they search the Registers for
duplicate sets of measures of those, whether in Paris or in the provinces,
who were suspected of having given false names. The entire staff consists
of ten persons. It is difficult to rightly interpret the figures given in
the pamphlet (4) at pp. 22-24, as they appear to disagree, but as I
understand them, 562 prisoners who gave false names in the year 1890 were
recognised by _Bertillonage_, and only four other persons were otherwise
discovered to have been convicted previously, who had escaped recognition
by its means.
I had the pleasure of seeing the system in operation in Paris a few years
ago, and was greatly impressed by the deftness of the measuring, and with
the swiftness and success with which the assistants searched for the cards
containing entries similar to the measures of the prisoner then under
examination.
It is stated in the _Signalements_ (p. 12) that the basis of the
classification are the four measurements (1) Head-length, (2)
Head-breadth, (3) Middle-finger-length, (4) Foot-length, their constancy
during adult life nearly always [as stated] holding good. Each of these
four elements severally is considered as belonging to one or other of
three equally numerous classes--small, medium, and large; consequently
there are 3{4} or 81 principal headings, under some one of which the card
of each prisoner is in the first instance sorted. Each of these primary
headings is successively subdivided, on the same general principle of a
three-fold classification, according to other measures that are more or
less subject to uncertainties, namely, the height, the span, the cubit,
the length and breadth of the ear, and the height of the bust. The
eye-colour alone is subjected to seven divisions. The general result is
(pp. 19, 22) that a total of twelve measures are employed, of which eleven
are classed on the three-fold principle, and one on the seven-fold, giving
a final result of 3{11} x 7, or more than a million possible combinations.
M. Bertillon considers it by no means necessary to stop here, but in his
chapter (p. 22) on the "Infinite Extension of the Classification," claims
that the method may be indefinitely extended.
The success of the system is considered by many experts to be fully
proved, notwithstanding many apparent objections, one of which is the
difficulty due to transitional cases: a belief in its success has
certainly obtained a firm hold upon the popular imagination in France. Its
general acceptance elsewhere seems to have been delayed in part by a
theoretical error in the published calculations of its efficiency: the
measures of the limbs which are undoubtedly correlated being treated as
independent, and in part by the absence of a sufficiently detailed account
of the practical difficulties experienced in its employment. Thus in the
_Application pratique_, p. 9: "We are embarrassed what to choose, the
number of human measures which vary independently of each other being
considerable." In the _Signalements_, p. 19: "It has been shown" (by
assuming this independent variability) "that by seven measurements, 60,000
photographs can be separated into batches of less than ten in each." (By
the way, even on that assumption, the result is somewhat exaggerated, the
figures having been arrived at by successively taking the higher of the
two nearest round values.) In short, the general tone of these two memoirs
is one of enthusiastic belief in the method, based almost wholly, so far
as is there shown, on questionable _theoretic_ grounds of efficiency.
To learn how far correlation interferes with the regularity of
distribution, causing more entries to be made under some index-heads than
others, as was the case with finger prints, I have classified on the
Bertillon system, 500 sets of measures taken at my laboratory. It was not
practicable to take more than three of the four primary measures, namely,
the head-length, its breadth, and the middle-finger-length. The other
measure, that of foot-length, is not made at my laboratory, as it would
require the shoes to be taken off, which is inconvenient since persons of
all ranks and both sexes are measured there; but this matters little for
the purpose immediately in view. It should, however, be noted that the
head-length and head-breadth have especial importance, being only slightly
correlated, either together or with any other dimension of the body. Many
a small man has a head that is large in one or both directions, while a
small man rarely has a large foot, finger, or cubit, and conversely with
respect to large men.
The following set of five measures of each of the 500 persons were then
tabulated: (1) head-length; (2) head-breadth; (3) span; (4) body-height,
that is the height of the top of the head from the seat on which the
person sits; (5) middle-finger-length. The measurements were to the
nearest tenth of an inch, but in cases of doubt, half-tenths were recorded
in (1), (2), and (5). With this moderate minuteness of measurement, it was
impossible so to divide the measures as to give better results than the
following, which show that the numbers in the three classes are not as
equal as desirable. But they nevertheless enable us to arrive at an
approximate idea of the irregular character of the distribution.
TABLE XVI.
+-----------------------------------------------------------------------+
| | Medium |Nos. in the three classes respectively.|
| Dimensions | measures in |---------------------------------------|
| measured. | inches and | - | 0 | + | Total. |
| | tenths. | below. | medium. | above. | |
|----------------|--------------|--------|---------|---------|----------|
|1. Head-length | 7.5 to 7.7 | 101 | 191 | 208 | 500 |
|2. Head-breadth | 6.0 " 6.1 | 173 | 201 | 126 | 500 |
|3. Span | 68.0 " 70.5 | 137 | 165 | 198 | 500 |
|4. Body-height | 35.0 " 36.0 | 139 | 168 | 193 | 500 |
|5. Middle-finger| 4.5 " 4.6 | 180 | 176 | 144 | 500 |
+-----------------------------------------------------------------------+
The distribution of the measures is shown in Table XVII.
TABLE XVII.
_Distribution of 500 sets of measures into classes. Each set consists of
five elements; each element is classed as + or above medium class; M, or
mediocre; -, or below medium class._
(Total number of classes is 3{5} = 243.)
+----------------------------------------------------------------+
| +---- 3 Span. | |
| | | |
| | +--4 Body- | 1 Head-length, 2 Head-breadth. |
| | | height.| |
| | | | |
| | | 5 Middle-|-----------------------------------------------|
| | | | finger.| 1 2 1 2 1 2 | 1 2 1 2 1 2 | 1 2 1 2 1 2 |
| | | | |---------------|---------------|---------------|
| | | | | - - - M - + | M - M M M + | + - + M + + |
|----------------|---------------|---------------|---------------|
| - - - | 14 7 4 | 14 11 5 | 3 3 2 |
| M | - 2 - | 2 4 1 | - 2 4 |
| + | - - - | 1 - - | - - - |
| | | | |
| - M - | 5 2 2 | 7 4 2 | 1 4 3 |
| M | - 2 - | 3 1 3 | 2 3 - |
| + | - - - | - - - | - - 2 |
| | | | |
| - + - | 2 - - | 1 1 1 | - - 1 |
| M | - 2 - | - - - | - 1 1 |
| + | - - - | 1 - - | - 1 - |
|----------------|---------------|---------------|---------------|
| M - - | 4 - 1 | 3 4 3 | 1 2 2 |
| M | 3 2 - | 3 2 3 | 2 4 - |
| + | - - - | - 1 2 | - 1 - |
| | | | |
| M M - | 1 3 1 | 4 3 2 | 4 4 3 |
| M | 5 3 - | 7 5 2 | 2 6 5 |
| + | 2 1 1 | 1 1 - | 1 4 2 |
| | | | |
| M + - | 2 1 1 | 5 2 - | - 2 2 |
| M | 2 2 - | 3 3 1 | 1 6 7 |
| + | - - 1 | 2 - - | 3 2 2 |
|----------------|---------------|---------------|---------------|
| + - - | - - 1 | - 1 - | - - - |
| M | 1 - - | 1 2 - | 1 3 - |
| + | 1 2 - | 1 1 - | - - 2 |
| | | | |
| + M - | 1 - 1 | 3 2 - | - - 2 |
| M | 2 - 1 | 1 4 - | 3 2 4 |
| + | 2 1 - | 2 4 1 | 4 6 3 |
| | | | |
| + + - | 1 2 - | 1 - 1 | 1 2 2 |
| M | - 1 - | 5 10 3 | 3 8 9 |
| + | 2 2 2 | 11 10 3 | 9 24 19 |
+----------------------------------------------------------------+
The frequency with which 1, 2, 3, 4, etc., sets were found to fall under
the same index-heading, is shown in Table XVIII.
TABLE XVIII.