+-----------------------------------------------------------------+ARCHES.LOOPS.WHORLS.Digit.------------------------------------------------Right.Left.Right.Left.Right.Left.----------------------------------------------------------Fore-finger171753533028Middle do.7878761516Little do.128690138Thumb3553654430Ring do.2353664531----------------------------------------------------------Total 10003035323350147113+-----------------------------------------------------------------+
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 circ.u.mstanced 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-MiddleRing-Littlefinger.finger.finger.finger.---------------------------------------Right317721Left517834---------------------------------------Mean417752525+--------------------------------------------+
The frequency of Loops (Table IV.) has two maxima; the princ.i.p.al one is on the little finger, the secondary on the middle finger.
TABLE IV.
+--------------------------------------------+_Percentage frequency of Loops._--------------------------------------------Hand.Thumb.Fore-MiddleRing-Littlefinger.finger.finger.finger.---------------------------------------Right5353786686Left6555765390---------------------------------------Mean59547759588+--------------------------------------------+
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-MiddleRing-Littlefinger.finger.finger.finger.---------------------------------------Right4430154513Left302816318---------------------------------------Mean372915538105+--------------------------------------------+
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. cla.s.s 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 cla.s.s 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 thumbs2482474" fore-fingers9382067" middle fingers365977" ring-fingers2462674----------------------------------------------------Mean of the Totals 72+----------------------------------------------------+
TABLE VI_b_.
_Percentage of cases in which the same cla.s.s of pattern occurs in various couplets of_ different digits.
(From 500 persons as above.)
+-----------------------------------------------------------------------+Couplets ofOF SAME HANDS.OF OPPOSITE HANDS.Digits.------------------------------------------------------Arch.Loops.Whorls.Total.Arch.Loops.Whorls.Total.--------------------------------------------------------------Thumb andfore-finger23516532331550Thumb andmiddle finger148958147856Thumb andring-finger14020611381857Fore andmiddle finger54812655461162Fore andring-finger23517542351754Middle andring-finger25013652501264-----------------------------------------------------------------------Means of the Totals 5957+-----------------------------------------------------------------------+
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 cla.s.ses 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 inLoops inWhorls in------------------------------------------Couplet.SameOppositeSameOppositeSameOppositehand.hand.hand.hand.hand.hand.-------------------------------------------------------Thumb andfore-finger2235331615Thumb andmiddle finger11484798Thumb and ring-finger1140382018Fore and middlefinger5548461211Fore and ring-finger2235351717Middle and ring-finger2250501312+---------------------------------------------------------------+
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 a.s.sured on good authority that no adequate collection of the necessary data has yet been published.
It might be hastily inferred from the statistical ident.i.ty 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 a.s.sured 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 cla.s.s of pattern in the four several digits now in question are these:--
Right thumb A + B + an uncla.s.sed 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. cla.s.s 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 ident.i.ty. 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 cla.s.s 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 cla.s.s of pattern (Table VI_a_) is 72. This is barely two-thirds of the 100 which would imply ident.i.ty. 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 a.n.a.logous 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 ident.i.ty 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 shall stand for no relationship, and 100 for ident.i.ty, and upon which the intermediate degrees of relationship may be marked at their proper value. Upon this a.s.sumption, 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 shall stand for no relationship at all, and 100 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 100 100, and of these 45 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 (4531)/(100100), and their average frequency in 100 couplets,--in other words, their average percentage is (4531)/100 = 1395, say 14. If, then, the observed percentage of double whorls should be only 14, it would be a proof that the A. L. W. cla.s.ses of patterns on the right and left ring-fingers were quite independent; so their relationship, as expressed on the centesimal scale, would be 0. 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. cla.s.ses 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 to 100 instead of from 0 to 17, 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 or 71, neglecting decimals.
This method of obtaining the value of 100 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 a.s.sume 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 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 pa.s.s 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.