_Fraternal relationship._--In 105 fraternities the _observed_ figures were as in Table XXII.:--
TABLE XXII.
_Observed Fraternal Couplets._
+----------------------------------------------------+A children.Totals inB children.----------------------B children.Arches.Loops.Whorls.------------------------------------------------Arches5122_19_-------+------Loops44215_61_--------------------Whorls11410_25_---------------------+------+---------------------Totals in A }children }_10__68__27_105+----------------------------------------------------+
The squares that run diagonally from the top at the left, to the bottom at the right, contain the double events, and it is with these that we are now concerned. Are the entries in those squares larger or not than the randoms, calculated as above, viz. the values of 10 19, 68 61, 27 25, all divided by 105? The calculated Randoms are shown in the first line of Table XXIII., the third line gives the greatest feasible number of correspondences which would occur if the kinship were as close as possible, subject to the reservation explained in p. 127. As there shown, the _lower_ of the A and B values is taken in each case, for Arches, Loops, and Whorls respectively.
TABLE XXIII.
+----------------------------------------------+A and B both being----------------------------Arches.Loops.Whorls.-------------------------------------------Random1737662Observed50420100Utmost feasible100610250+----------------------------------------------+
In every instance, the Observed values are seen to exceed the Random.
Many other cases of this description were calculated, all yielding the same general result, but these results are not as satisfactory as can be wished, owing to their dilution by inappropriate cases, the A. L. W.
system being somewhat artificial.
[Ill.u.s.tration: PLATE 16.
FIG. 24. The "C" set of standard patterns, for prints of the Right Hand.]
With the view of obtaining a more satisfactory result the patterns were subdivided under fifty-three heads, and an experiment was made with the fore, middle, and ring-fingers of 150 fraternal couplets (300 individuals and 900 digits) by Mr. F. Howard Collins, who kindly undertook the considerable labour of indexing and tabulating them.
The provisional list of standard patterns published in the _Phil. Trans._ was not appropriate for this purpose. It related chiefly to thumbs, and consequently omitted the tented arch; it also referred to the left hand, but in the following tabulations the right hand has been used; and its numbering is rather inconvenient. The present set of fifty-three patterns has faults, and cannot be considered in any way as final, but it was suitable for our purposes and may be convenient to others; as Mr. Collins worked wholly by it, it may be distinguished as the "C. set." The banded patterns, 24-31, are very rarely found on the fingers, but being common on the thumb, were retained, on the chance of our requiring the introduction of thumb patterns into the tabulations. The numerals refer to the patterns as seen in impressions of the _right hand_ only. [They would be equally true for the patterns as seen on the _fingers themselves_ of the left hand.] For impressions of the left hand the numerals up to 7 inclusive would be the same, but those of all the rest would be changed. These are arranged in couplets, the one member of the couplet being a reversed picture of the other, those in each couplet being distinguished by severally bearing an odd and an even number. Therefore, in impressions of the left hand, 8 would have to be changed into 9, and 9 into 8; 10 into 11, and 11 into 10; and so on, up to the end, viz. 52 and 53. The numeral 54 was used to express nondescript patterns.
The finger prints had to be gone through repeatedly, some weeks elapsing between the inspections, and under conditions which excluded the possibility of unconscious bias; a subject of frequent communication between Mr. Collins and myself. Living at a distance apart, it was not easy at the time they were made, to bring our respective interpretations of transitional and of some of the other patterns, especially the invaded loops, into strict accordance, so I prefer to keep his work, in which I have perfect confidence, independent from my own. Whenever a fraternity consisted of more than two members, they were divided, according to a prearranged system, into as many couplets as there were individuals. Thus, while a fraternity of three individuals furnished all of its three possible varieties of couplets, (1, 2), (1, 3), (2, 3), one of four individuals was not allowed to furnish more than four of its possible couplets, the two italicised ones being omitted, (1, 2), (1, 3), (_1, 4_), (_2, 3_), (2, 4), (3, 4), and so on. Without this precaution, a single very large family might exercise a disproportionate and even overwhelming statistical influence.
It would be essential to exact working, that the mutual relations of the patterns should be taken into account; for example, suppose an arch to be found on the fore-finger of one brother and a nascent loop on that of the other; then, as these patterns are evidently related, their concurrence ought to be interpreted as showing some degree of resemblance. However, it was impossible to take cognizance of partial resemblances, the mutual relations of the patterns not having, as yet, been determined with adequate accuracy.
The completed tabulations occupied three large sheets, one for each of the fingers, ruled crossways into fifty-three vertical columns for the A brothers, and fifty-three horizontal rows for the B brothers. Thus, if the register number of the pattern of A was 10, and that of B was 42, then a mark would be put in the square limited by the ninth and tenth horizontal lines, and by the forty-first and forty-second vertical ones. The marks were scattered spa.r.s.ely over the sheet. Those in each square were then added up, and finally the numbers in each of the rows and in each of the columns were severally totalled.
If the number of couplets had been much greater than they are, a test of the accuracy with which their patterns had been cla.s.sed under the appropriate heads, would be found in the frequency with which the same patterns were registered in the corresponding finger of the A and B brothers. The A and B groups are strictly h.o.m.ogeneous, consequently the frequency of their patterns in corresponding fingers ought to be alike.
The success with which this test has been fulfilled in the present case, is pa.s.sably good, its exact degree being shown in the following paragraphs, where the numbers of entries under each head are arranged in as orderly a manner as the case admits, the smaller of the two numbers being the one that stands first, whether it was an A or a B. All instances in which there were at least five entries under either A or B, are included; the rest being disregarded. The result is as follows:--
I. Thirteen cases of more or less congruity between the number of A and B entries under the same head:--5-7; 5-7; 5-8; 6-8; 7-10; 8-9; 8-12; 9-12; 10-10; 11-13; 12-16; 14-18; 72-73. (This last refers to loops on the middle finger.)
II. Six cases of more or less incongruity:--1-7; 6-12; 14-20; 14-22; 22-35; 39-50.
The three Tables, XXIV., XXV., XXVI., contain the results of the tabulations and the deductions from them.
TABLE XXIV.
_Comparison of three Fingers of the Right Hand in 150 Fraternal Couplets._
+------------------------------------------------------------------------+Fore-fingers.Middle fingers.Ring-fingers.------------------------------------------------------------IndexDownAlongDoubleDownAlongDoubleDownAlongDoubleNo. ofcolumnslineseventscolumnslineseventscolumnslineseventsPattern------------------------------------------------------AAAABandABandABandBBB-------------------------------------------------------------115124852751232326221247221751819174117112121321144344120141151612342341623231072174331841181461933251201312112241812231162713211344333111331343241352359122382139431401311114226984112813142223557372353950164310103413442122451146861311473448612146234911521531+------------------------------------------------------------------------+
TABLE XXV.
_Comparison between Random and Observed Events._
+-------------------------------------------------------------+Fore.Middle.Ring.---------------------------------------------------------Random.Observed.Random.Observed.Random.Observed.------------------------------------------------------120402620231008...0111005...1283005...023...008...007...1871006...005...008...095120560462064...34083516865185016...011...0673006103210722008...048...0481130016--------Allothers.029202810121------------------------------------------------------113120371145190930+-------------------------------------------------------------+
TABLE XXVI.
_Centesimal Scale (to nearest whole numbers)._
+-----------------------------------------------------------------------+150 fraternalRandom.Observed.UtmostReducedReduced tocouplets.possibilities.to lowerupperlimit=0.limit=100.------------------------------------------------------------------Centesimalscale.--------------Fore-finger1131201150 9 1040 9 100Middle3711451170 10 800 10 100Ring1909311180 12 990 12 100-----------------------------------------------------------------------Mean0 10 100-----------------------------------------------------------------------50 additionalcouplets.-------------Middle fingeronly8211220 3 140 21 100------------------------------------------------------------------Loops only,and on middlefinger only.-------------150 couplets34035720 1 720 1-1/4 10050 couplets647140 06 80 8 100+-----------------------------------------------------------------------+
Table XXIV. contains all the Observed events, and is to be read thus, beginning at the first entry. Pattern No. 1 occurs on the right fore-finger fifteen times among the A brothers, and twelve times among the B brothers; while in four of these cases both brothers have that same pattern.
Table XXV. compares the Random events with the Observed ones. Every case in which the calculated expectation is equal to or exceeds 005, is inserted in detail; the remaining group of petty cases are summed together and their totals entered in the bottom line. For fear of misapprehension or forgetfulness, one other example of the way in which the Randoms are calculated will be given here, taking for the purpose the first entry in Table XXIV. Thus, the number of all the different combinations of the 150 A with the 150 B individuals in the 150 couplets, is 150 150. Out of these, the number of double events in which pattern No. 1 would appear in the same combination, is 15 12 = 180. Therefore in 150 trials, the double event of pattern No. 1 would appear upon the average, on 180 divided by 150, or on 120 occasions. As a matter of fact, it appeared four times. These figures will be found in the first line of Table XXV.; the rest of its contents have been calculated in the same way.
Leaving aside the Randoms that exceed 0 but are less than 1, there are nineteen cases in which the Random may be compared with the Observed values; in all but two of these the Observed are the highest, and in these two the Random exceed the Observed by only trifling amounts, namely, 518 Random against 500 Observed; 187 Random against 100 Observed. It is impossible, therefore, to doubt from the steady way in which the Observed values overtop the Randoms, that there is a greater average likeness in the finger marks of two brothers, than in those of two persons taken at hazard.
Table XXVI. gives the results of applying the centesimal scale to the measurement of the average closeness of fraternal resemblance, in respect to finger prints, according to the method and under the reservations already explained in page 125. The average value thus a.s.signed to it is a little more than 10. The values obtained from the three fingers severally, from which that average was derived, are 9, 10, and 12; they agree together better than might have been expected. The value obtained from a set of fifty additional couplets of the middle fingers only, of fraternals, is wider, being 21. Its inclusion with the rest raises the average of all to between 10 and 11.
In the pre-eminently frequent event of loops with an outward slope on the middle finger, it is remarkable that the Random cases are nearly equal to the Observed ones; they are 3408 to 3500. It was to obtain some a.s.surance that this equality was not due to statistical accident, that the additional set of fifty couplets were tabulated. They tell, however, the same tale, viz. 64 Randoms to 70 Observed. The loops on the fore-fingers confirm this, showing 518 Randoms to 500 Observed; those on the ring-finger have the same peculiarity, though in a slighter degree, 13 to 16: the average of other patterns shows a much greater difference than that. I am unable to account for this curious behaviour of the loops, which can hardly be due to statistical accident, in the face of so much concurrent evidence.
_Twins._--The signs of heredity between brothers and sisters ought to be especially apparent between twins of the same s.e.x, who are physiologically related in a peculiar degree and are sometimes extraordinarily alike. More rarely, they are remarkably dissimilar. The instances of only a moderate family resemblance between twins of the same s.e.x are much less frequent than between ordinary brothers and sisters, or between twins of opposite s.e.x. All this has been discussed in my _Human Faculty_. In order to test the truth of the expectation, I procured prints of the fore, middle, and ring-fingers of seventeen sets of twins, and compared them, with the results shown in Table XXVII.
TABLE XXVII.
17 SETS OF TWINS (A and B).
_Comparison between the patterns on the Fore, Middle, and Ring-fingers respectively of the Right hand._
Agreement (=), 19 cases; partial (), 13 cases; disagreement (), 19 cases.
+----------------------------------------------------------------+A BA BA BA BA B----------------------------------------------------------------Fore42 = 4221 = 2140 = 406 = 61 = 1Middle42 = 428 = 832 4215 3242 = 42Ring42 = 428 = 842 = 4233 = 3340 19Fore42 = 4243 151 = 115 342 42Middle42 = 4242 401 4042 = 4242 = 42Ring42 4635 = 3540 4214 3242 14Fore49 1415 4915 161 421 15Middle42 = 4223 1419 4242 4832 22Ring9 3214 166 1842 818 23Fore48 33(loop) 9Middle42 2248 22Ring14 69 35+----------------------------------------------------------------+
The result is that out of the seventeen sets (=51 couplets), two sets agree in all their three couplets of fingers; four sets agree in two; five sets agree in one of the couplets. There are instances of partial agreement in five others, and a disagreement throughout in only one of the seventeen sets. In another collection of seventeen sets, made to compare with this, six agreed in two of their three couplets, and five agreed in one of them. There cannot then be the slightest doubt as to the strong tendency to resemblance in the finger patterns in twins.
This remark must by no means be forced into the sense of meaning that the similarity is so great, that the finger print of one twin might occasionally be mistaken for that of the other. When patterns fall into the same cla.s.s, their general forms may be conspicuously different (see p.
74), while their smaller details, namely, the number of ridges and the minutiae, are practically independent of the pattern.
It may be mentioned that I have an inquiry in view, which has not yet been fairly begun, owing to the want of sufficient data, namely to determine the minutest biological unit that may be hereditarily transmissible. The minutiae in the finger prints of twins seem suitable objects for this purpose.
_Children of like-patterned Parents._--When two parents are alike, the average resemblance, in stature at all events, which their children bear to them, is as close as the fraternal resemblance between the children, and twice as close as that which the children bear to either parent separately, when the parents are unlike.
The fifty-eight parentages affording fifty couplets of the fore, middle, and ring-fingers respectively give 58 3 = 174 parental couplets in all; of these, 27 or 14 per cent are alike in their pattern, as shown by Table XXVIII. The total number of children to these twenty-seven pairs is 109, of which 59 (or 54 per cent) have the same pattern as their parents. This fact requires a.n.a.lysis, as on account of the great frequency of loops, and especially of the pattern No. 42 on the middle finger, a large number of the cases of similarity of pattern between child and parents would be mere random coincidences.
TABLE XXVIII.--_Children of like-patterned Parents._
+-------------------------------------------------------------------+The 27Patterns of-- F. M.--of Sons.Alike.Totalcases.sons.---------------------------------------------------------------1Fore 1 1111234 343411340 4041...1442 4248...15Middle 40 404011642 424211742 424211842 4242, 38, 42, 4234942 4242111042 4248, 48, 14141142 4242111242 4240...11342 421...11442 4242111542 4242, 46, 42231642 4234, 42121742 4242111842 42.........19Ring 14 1433, 42, 14132014 1442, 16...22114 146...12242 4240...12342 4242, 42, 42332442 42.........2542 4242, 42222642 4249, 14...22746 4648, 40, 16...4---------------2241+-------------------------------------------------------------------+