Finger Prints

Chapter XIII. the question is discussed and answered affirmatively, of the right of the nine fundamentally differing patterns to be considered as different genera; also of their more characteristic varieties to rank as different genera, or species, as the case may be. The chief test applied, respected the frequency with which the various Loops that occurred on the thumbs, were found to differ, in successive degrees of difference, from the central form of all of them; it was found to accord with the requirements of the well-known law of Frequency of Error, proving the existence of a central type, from which the departures were, in common phraseology, accidental. Now all the evidence in the last chapter concurs in showing that no sensible amount of correlation exists between any of the patterns on the one hand, and any of the bodily faculties or characteristics on the other. It would be absurd therefore to a.s.sert that in the struggle for existence, a person with, say, a loop on his right middle finger has a better chance of survival, or a better chance of early marriage, than one with an arch. Consequently genera and species are here seen to be formed without the slightest aid from either Natural or s.e.xual Selection, and these finger patterns are apparently the only peculiarity in which Panmixia, or the effect of promiscuous marriages, admits of being studied on a large scale. The result of Panmixia in finger markings, corroborates the arguments I have used in _Natural Inheritance_ and elsewhere, to show that "organic stability" is the primary factor by which the distinctions between genera are maintained; consequently, the progress of evolution is not a smooth and uniform progression, but one that proceeds by jerks, through successive "sports" (as they are called), some of them implying considerable organic changes, and each in its turn being favoured by Natural Selection.

Finger Prints.

by Francis Galton.

CHAPTER I

INTRODUCTION

The palms of the hands and the soles of the feet are covered with two totally distinct cla.s.ses of marks. The most conspicuous are the creases or folds of the skin which interest the followers of palmistry, but which are no more significant to others than the creases in old clothes; they show the lines of most frequent flexure, and nothing more. The least conspicuous marks, but the most numerous by far, are the so-called papillary ridges; they form the subject of the present book. If they had been only twice as large as they are, they would have attracted general attention and been commented on from the earliest times. Had Dean Swift known and thought of them, when writing about the Brobdingnags, whom he constructs on a scale twelve times as great as our own, he would certainly have made Gulliver express horror at the ribbed fingers of the giants who handled him. The ridges on their palms would have been as broad as the thongs of our coach-whips.

Let no one despise the ridges on account of their smallness, for they are in some respects the most important of all anthropological data. We shall see that they form patterns, considerable in size and of a curious variety of shape, whose boundaries can be firmly outlined, and which are little worlds in themselves. They have the unique merit of retaining all their peculiarities unchanged throughout life, and afford in consequence an incomparably surer criterion of ident.i.ty than any other bodily feature.

They may be made to throw welcome light on some of the most interesting biological questions of the day, such as heredity, symmetry, correlation, and the nature of genera and species. A representation of their lineations is easily secured in a self-recorded form, by inking the fingers in the way that will be explained, and pressing them on paper. There is no prejudice to be overcome in procuring these most trustworthy sign-manuals, no vanity to be pacified, no untruths to be guarded against.

My attention was first drawn to the ridges in 1888 when preparing a lecture on Personal Identification for the Royal Inst.i.tution, which had for its princ.i.p.al object an account of the anthropometric method of Bertillon, then newly introduced into the prison administration of France.

Wishing to treat the subject generally, and having a vague knowledge of the value sometimes a.s.signed to finger marks, I made inquiries, and was surprised to find, both how much had been done, and how much there remained to do, before establishing their theoretical value and practical utility.

Enough was then seen to show that the subject was of real importance, and I resolved to investigate it; all the more so, as the modern processes of photographic printing would enable the evidence of such results as might be arrived at, to be presented to the reader on an enlarged and easily legible form, and in a trustworthy shape. Those that are put forward in the following pages, admit of considerable extension and improvement, and it is only the fact that an account of them seems useful, which causes me to delay no further before submitting what has thus far been attained, to the criticism of others.

I have already published the following memoirs upon this subject:

1. "Personal Identification." _Journal Royal Inst._ 25th May 1888, and _Nature_, 28th June 1888.

2. "Patterns in Thumb and Finger Marks." _Phil. Trans. Royal Society_, vol. clx.x.xii. (1891) b. pp. 1-23. [This almost wholly referred to thumb marks.]

3. "Method of Indexing Finger Marks." _Proc. Royal Society_, vol.

xlix. (1891).

4. "Identification by Finger Tips." _Nineteenth Century_, August 1891.

This first and introductory chapter contains a brief and orderly summary of the contents of those that follow.

The second chapter treats of the previous employment of finger prints among various nations, which has been almost wholly confined to making daubs, without paying any regard to the delicate lineations with which this book is alone concerned. Their object was partly superst.i.tious and partly ceremonial; superst.i.tious, so far as a personal contact between the finger and the doc.u.ment was supposed to be of mysterious efficacy: ceremonial, as a formal act whose due performance in the presence of others could be attested. A few scattered instances are mentioned of persons who had made finger prints with enough care to show their lineations, and who had studied them; some few of these had used them as signatures. Attention is especially drawn to Sir William Herschel, who brought the method of finger prints into regular official employment when he was "Collector" or chief administrator of the Hooghly district in Bengal, and my large indebtedness to him is expressed in this chapter and in other places.

In the third chapter various methods of making good prints from the fingers are described at length, and more especially that which I have now adopted on a somewhat large scale, at my anthropometric laboratory, which, through the kindness of the authorities of South Kensington, is at present lodged in the galleries of their Science Collections. There, the ten digits of both hands of all the persons who come to be measured, are impressed with clearness and rapidity, and a very large collection of prints is steadily acc.u.mulating, each set being, as we shall see, a sign-manual that differentiates the person who made it, throughout the whole of his life, from all the rest of mankind.

Descriptions are also given of various methods of enlarging a finger print to a convenient size, when it is desired to examine it closely.

Photography is the readiest of all; on the other hand the prism (as in a camera lucida) has merits of its own, and so has an enlarging pantagraph, when it is furnished with a small microscope and cross wires to serve as a pointer.

In the fourth chapter the character and purpose of the ridges, whose lineations appear in the finger print, are discussed. They have been the topic of a considerable amount of careful physiological study in late years, by writers who have investigated their development in early periods of unborn life, as well as their evolutionary history. They are perfectly defined in the monkeys, but appear in a much less advanced stage in other mammalia. Their courses run somewhat independently of the lines of flexure. They are studded with pores, which are the open mouths of ducts proceeding from the somewhat deeply-seated glands which secrete perspiration, so one of their functions is to facilitate the riddance of that excretion. The ridges increase in height as the skin is thickened by hard usage, until callosities begin to be formed, which may altogether hide them. But the way in which they a.s.sist the touch and may tend to neutralise the dulling effect of a thick protective skin, is still somewhat obscure. They certainly seem to help in the discrimination of the character of surfaces that are variously rubbed between the fingers.

These preliminary topics having been disposed of, we are free in the fifth chapter to enter upon the direct course of our inquiry, beginning with a discussion of the various patterns formed by the lineations. It will be shown how systems of parallel ridges sweep in bold curves across the palmar surface of the hand, and how, whenever the boundaries of two systems diverge, the inters.p.a.ce is filled up by a compact little system of its own, variously curved or whorled, having a fict.i.tious resemblance to an eddy between two currents. An inters.p.a.ce of this kind is found in the bulb of each finger. The ridges run in parallel lines across the finger, up to its last joint, beyond which the insertion of the finger-nail causes a compression of the ridges on either side; their intermediate courses are in consequence so much broadened out that they commonly separate, and form two systems with an inters.p.a.ce between them. The independent patterns that appear in this inters.p.a.ce upon the bulbs of the fingers, are those with which this book is chiefly concerned.

At first sight, the maze formed by the minute lineations is bewildering, but it is shown that every inters.p.a.ce can be surely outlined, and when this is done, the character of the pattern it encloses, starts conspicuously into view. Examples are given to show how the outlining is performed, and others in which the outlines alone are taken into consideration. The cores of the patterns are also characteristic, and are described separately. It is they alone that have attracted the notice of previous inquirers. The outlines fall for the most part into nine distinct genera, defined by the relative directions of the divergent ridges that enclose them. The upper pair (those that run towards the finger-tip) may unite, or one or other of them may surmount the other, thus making three possibilities. There are three similar possibilities in respect to the lower pair; so, as any one of the first group may be combined with any one of the second, there are 3 3, or nine possibilities in all. The practice of somewhat rolling the finger when printing from it, is necessary in order to impress enough of its surface to ensure that the points at which the boundaries of the pattern begin to diverge, shall be always included.

Plates are given of the princ.i.p.al varieties of patterns, having regard only to their more fundamental differences, and names are attached for the convenience of description; specimens are also given of the outlines of the patterns in all the ten digits of eight different persons, taken at hazard, to afford a first idea of the character of the material to be dealt with. Another and less minute system of cla.s.sification under three heads is then described, which is very useful for rough preliminary purposes, and of which frequent use is made further on. It is into Arches, Loops, and Whorls. In the Arches, there is no pattern strictly speaking, for there is no inters.p.a.ce; the need for it being avoided by a successive and regular broadening out of the ridges as they cross the bulb of the finger. In Loops, the inters.p.a.ce is filled with a system of ridges that bends back upon itself, and in which no one ridge turns through a complete circle. Whorls contain all cases in which at least one ridge turns through a complete circle, and they include certain double patterns which have a whorled appearance. The transitional cases are few; they are fully described, pictured, and cla.s.sified. One great advantage of the rude A.

L. W. system is that it can be applied, with little risk of error, to impressions that are smudged or imperfect; it is therefore very useful so far as it goes. Thus it can be easily applied to my own finger prints on the t.i.tle-page, made as they are from digits that are creased and roughened by seventy years of life, and whose impressions have been closely clipped in order to fit them into a limited s.p.a.ce.

A third method of cla.s.sification is determined by the origin of the ridges which supply the inters.p.a.ce, whether it be from the thumb side or the little-finger side; in other words, from the Inner or the Outer side.

Lastly, a translation from the Latin is given of the famous Thesis or _Commentatio_ of Purkenje, delivered at the University of Breslau in 1823, together with his ill.u.s.trations. It is a very rare pamphlet, and has the great merit of having first drawn attention to the patterns and attempted to cla.s.sify them.

In the sixth chapter we reach the question of Persistence: whether or no the patterns are so durable as to afford a sure basis for identification.

The answer was different from what had been expected. So far as the proportions of the patterns go, they are _not_ absolutely fixed, even in the adult, inasmuch as they change with the shape of the finger. If the finger is plumped out or emaciated, or variously deformed by usage, gout, or age, the proportions of the pattern will vary also. Two prints of the same finger, one taken before and the other after an interval of many years, cannot be expected to be as closely alike as two prints similarly made from the same woodcut. They are far from satisfying the shrewd test of the stereoscope, which shows if there has been an alteration even of a letter in two otherwise duplicate pages of print. The measurements vary at different periods, even in the adult, just as much if not more than his height, span, and the lengths of his several limbs. On the other hand, the numerous bifurcations, origins, islands, and enclosures in the ridges that compose the pattern, are proved to be _almost beyond change_. A comparison is made between the pattern on a finger, and one on a piece of lace; the latter may be stretched or shrunk as a whole, but the threads of which it is made retain their respective peculiarities. The evidence on which these conclusions are founded is considerable, and almost wholly derived from the collections made by Sir W. Herschel, who most kindly placed them at my disposal. They refer to one or more fingers, and in a few instances to the whole hand, of fifteen different persons. The intervals before and after which the prints were taken, amount in some cases to thirty years. Some of them reach from babyhood to boyhood, some from childhood to youth, some from youth to advanced middle age, one from middle life to incipient old age. These four stages nearly include the whole of the ordinary life of man. I have compared altogether some 700 points of reference in these couplets of impressions, and only found a single instance of discordance, in which a ridge that was cleft in a child became united in later years.

Photographic enlargements are given in ill.u.s.tration, which include between them a total of 157 pairs of points of reference, all bearing distinctive numerals to facilitate comparison and to prove their unchangeableness.

Reference is made to another ill.u.s.trated publication of mine, which raises the total number of points compared to 389, all of which were successful, with the single exception above mentioned. The fact of an almost complete persistence in the peculiarities of the ridges from birth to death, may now be considered as determined. They existed before birth, and they persist after death, until effaced by decomposition.

In the seventh chapter an attempt is made to appraise the evidential value of finger prints by the common laws of Probability, paying great heed not to treat variations that are really correlated, as if they were independent. An artifice is used by which the number of portions is determined, into which a print may be divided, in each of which the purely local conditions introduce so much uncertainty, that a guess derived from a knowledge of the outside conditions is as likely as not to be wrong. A square of six ridge-intervals in the side was shown by three different sets of experiments to be larger than required; one of four ridge-intervals in the side was too small, but one of five ridge-intervals appeared to be closely correct. A six-ridge interval square was, however, at first adopted, in order to gain a.s.surance that the error should be on the safe side. As an ordinary finger print contains about twenty-four of these squares, the uncertainty in respect to the entire contents of the pattern _due to this cause alone_, is expressed by a fraction of which the numerator is 1, and the denominator is 2 multiplied into itself twenty-four times, which amounts to a number so large that it requires eight figures to express it.

A further attempt was made to roughly appraise the neglected uncertainties relating to the outside conditions, but large as they are, they seem much inferior in their joint effect to the magnitude of that just discussed.

Next it was found possible, by the use of another artifice, to obtain some idea of the evidential value of ident.i.ty when two prints agree in all but one, two, three, or any other number of particulars. This was done by using the five ridge-interval squares, of which thirty-five may be considered to go into a single finger print, being about the same as the number of the bifurcations, origins, and other points of comparison. The accidental similarity in their numbers enables us to treat them roughly as equivalent. On this basis the well-known method of binomial calculation is easily applied, with the general result that, notwithstanding a failure of evidence in a few points, as to the ident.i.ty of two sets of prints, each, say, of three fingers, amply enough evidence would be supplied by the remainder to prevent any doubt that the two sets of prints were made by the same person. When a close correspondence exists in respect to all the ten digits, the thoroughness of the differentiation of each man from all the rest of the human species is multiplied to an extent far beyond the capacity of human imagination. There can be no doubt that the evidential value of ident.i.ty afforded by prints of two or three of the fingers, is so great as to render it superfluous to seek confirmation from other sources.

The eighth chapter deals with the frequency with which the several kinds of patterns appear on the different digits of the same person, severally and in connection. The subject is a curious one, and the inquiry establishes unexpected relationships and distinctions between different fingers and between the two hands, to whose origin there is at present no clue. The relationships are themselves connected in the following way;--calling any two digits on one of the hands by the letters A and B respectively, and the digit on the other hand, that corresponds to B, by the symbol B1, then the kinship between A and B1 is identical, in a statistical sense, with the kinship between A and B.

The chief novelty in this chapter is an attempt to cla.s.sify nearness of relationship upon a centesimal scale, in which the number of correspondences due to mere chance counts as 0, and complete ident.i.ty as 100. It seems reasonable to adopt the scale with only slight reservation, when the average numbers of the Arches, Loops, and Whorls are respectively the same in the two kinds of digit which are compared together; but when they differ greatly, there are no means free from objection, of determining the 100 division of the scale; so the results, if noted at all, are subject to grave doubt.

Applying this scale, it appears that digits on opposite hands, which bear the same name, are more nearly related together than digits bearing different names, in about the proportion of three to two. It seems also, that of all the digits, none are so nearly related as the middle finger to the two adjacent ones.

In the ninth chapter, various methods of indexing are discussed and proposed, by which a set of finger prints may be so described by a few letters, that it can be easily searched for and found in any large collection, just as the name of a person is found in a directory. The procedure adopted, is to apply the Arch-Loop-Whorl cla.s.sification to all ten digits, describing each digit in the order in which it is taken, by the letter _a_, _l_, or _w_, as the case may be, and arranging the results in alphabetical sequence. The downward direction of the slopes of loops on the fore-fingers is also taken into account, whether it be towards the Inner or the Outer side, thus replacing L on the fore-finger by either _i_ or _o_.

Many alternative methods are examined, including both the recognition and the non-recognition of all sloped patterns. Also the gain in differentiation, when all the ten digits are catalogued, instead of only a few of them. There is so much correlation between the different fingers, and so much peculiarity in each, that theoretical notions of the value of different methods of cla.s.sification are of little worth; it is only by actual trial that the best can be determined. Whatever plan of index be adopted, many patterns must fall under some few headings and few or no patterns under others, the former cla.s.s resembling in that respect the Smiths, Browns, and other common names that occur in directories. The general value of the index much depends on the facility with which these frequent forms can be broken up by sub-cla.s.sification, the rarer forms being easily dealt with. This branch of the subject has, however, been but lightly touched, under the belief that experience with larger collections than my own, was necessary before it could be treated thoroughly; means are, however, indicated for breaking up the large battalions, which have answered well thus far, and seem to admit of considerable extension. Thus, the number of ridges in a loop (which is by far the commonest pattern) on any particular finger, at the part of the impression where the ridges are cut by the axis of the loop, is a fairly definite and effective datum as well as a simple one; so also is the character of its inmost lineation, or core.

In the tenth chapter we come to a practical result of the inquiry, namely, its possible use as a means of differentiating a man from his fellows. In civil as well as in criminal cases, the need of some such system is shown to be greatly felt in many of our dependencies; where the features of natives are distinguished with difficulty; where there is but little variety of surnames; where there are strong motives for prevarication, especially connected with land-tenure and pensions, and a proverbial prevalence of unveracity.

It is also shown that the value to honest men of sure means of identifying themselves is not so small among civilised nations even in peace time, as to be disregarded, certainly not in times of war and of strict pa.s.sports. But the value to honest men is always great of being able to identify offenders, whether they be merely deserters or formerly convicted criminals, and the method of finger prints is shown to be applicable to that purpose. For aid in searching the registers of a criminal intelligence bureau, its proper rank is probably a secondary one; the primary being some form of the already established Bertillon anthropometric method. Whatever power the latter gives of successfully searching registers, that power would be multiplied many hundredfold by the inclusion of finger prints, because their peculiarities are entirely unconnected with other personal characteristics, as we shall see further on. A brief account is given in this chapter of the Bertillon system, and an attempt is made on a small scale to verify its performance, by a.n.a.lysing five hundred sets of measures made at my own laboratory. These, combined with the quoted experiences in attempting to identify deserters in the United States, allow a high value to this method, though not so high as has been claimed for it, and show the importance of supplementary means. But whenever two suspected duplicates of measurements, bodily marks, photographs and finger prints have to be compared, the lineations of the finger prints would give an incomparably more trustworthy answer to the question, whether or no the suspicion of their referring to the same person was justified, than all the rest put together. Besides this, while measurements and photographs are serviceable only for adults, and even then under restrictions, the finger prints are available throughout life.

It seems difficult to believe, now that their variety and persistence have been proved, the means of cla.s.sifying them worked out, and the method of rapidly obtaining clear finger prints largely practised at my laboratory and elsewhere, that our criminal administration can long neglect the use of such a powerful auxiliary. It requires no higher skill and judgment to make, register, and hunt out finger prints, than is to be found in abundance among ordinary clerks. Of course some practice is required before facility can be gained in reading and recognising them, but not a few persons of whom I have knowledge, have interested themselves in doing so, and found no difficulty.

The eleventh chapter treats of Heredity, and affirmatively answers the question whether patterns are transmissible by descent. The inquiry proved more troublesome than was expected, on account of the great variety in patterns and the consequent rarity with which the same pattern, other than the common Loop, can be expected to appear in relatives. The available data having been attacked both by the Arch-Loop-Whorl method, and by a much more elaborate system of cla.s.sification--described and figured as the C system, the resemblances between children of either s.e.x, of the same parents (or more briefly "fraternal" resemblances, as they are here called, for want of a better term), have been tabulated and discussed. A batch of twins have also been a.n.a.lysed. Then cases have been treated in which both parents had the same pattern on corresponding fingers; this pattern was compared with the pattern on the corresponding finger of the child. In these and other ways, results were obtained, all testifying to the conspicuous effect of heredity, and giving results that can be measured on the centesimal scale already described. But though the qualitative results are clear, the quant.i.tative are as yet not well defined, and that part of the inquiry must lie over until a future time, when I shall have more data and when certain foreseen improvements in the method of work may perhaps be carried out. There is a decided appearance, first observed by Mr. F. Howard Collins, of whom I shall again have to speak, of the influence of the mother being stronger than that of the father, in transmitting these patterns.

In the twelfth chapter we come to a branch of the subject of which I had great expectations, that have been falsified, namely, their use in indicating Race and Temperament. I thought that any hereditary peculiarities would almost of necessity vary in different races, and that so fundamental and enduring a feature as the finger markings must in some way be correlated with temperament.

The races I have chiefly examined are English, most of whom were of the upper and middle cla.s.ses; the others chiefly from London board schools; Welsh, from the purest Welsh-speaking districts of South Wales; Jews from the large London schools, and Negroes from the territories of the Royal Niger Company. I have also a collection of Basque prints taken at Cambo, some twenty miles inland from Biarritz, which, although small, is large enough to warrant a provisional conclusion. As a first and only an approximately correct description, the English, Welsh, Jews, Negroes, and Basques, may all be spoken of as identical in the character of their finger prints; the same familiar patterns appearing in all of them with much the same degrees of frequency, the differences between groups of different races being not larger than those that occasionally occur between groups of the same race. The Jews have, however, a decidedly larger proportion of Whorled patterns than other races, and I should have been tempted to make an a.s.sertion about a peculiarity in the Negroes, had not one of their groups differed greatly from the rest. The task of examination has been laborious thus far, but it would be much more so to arrive with correctness at a second and closer approximation to the truth.

It is doubtful at present whether it is worth while to pursue the subject, except in the case of the Hill tribes of India and a few other peculiarly diverse races, for the chance of discovering some characteristic and perhaps a more monkey-like pattern.

Considerable collections of prints of persons belonging to different cla.s.ses have been a.n.a.lysed, such as students in science, and students in arts; farm labourers; men of much culture; and the lowest idiots in the London district (who are all sent to Darenth Asylum), but I do not, still as a first approximation, find any decided difference between their finger prints. The ridges of artists are certainly not more delicate and close than those of men of quite another stamp.

In Chapter XIII. the question is discussed and answered affirmatively, of the right of the nine fundamentally differing patterns to be considered as different genera; also of their more characteristic varieties to rank as different genera, or species, as the case may be. The chief test applied, respected the frequency with which the various Loops that occurred on the thumbs, were found to differ, in successive degrees of difference, from the central form of all of them; it was found to accord with the requirements of the well-known law of Frequency of Error, proving the existence of a central type, from which the departures were, in common phraseology, accidental. Now all the evidence in the last chapter concurs in showing that no sensible amount of correlation exists between any of the patterns on the one hand, and any of the bodily faculties or characteristics on the other. It would be absurd therefore to a.s.sert that in the struggle for existence, a person with, say, a loop on his right middle finger has a better chance of survival, or a better chance of early marriage, than one with an arch. Consequently genera and species are here seen to be formed without the slightest aid from either Natural or s.e.xual Selection, and these finger patterns are apparently the only peculiarity in which Panmixia, or the effect of promiscuous marriages, admits of being studied on a large scale. The result of Panmixia in finger markings, corroborates the arguments I have used in _Natural Inheritance_ and elsewhere, to show that "organic stability" is the primary factor by which the distinctions between genera are maintained; consequently, the progress of evolution is not a smooth and uniform progression, but one that proceeds by jerks, through successive "sports" (as they are called), some of them implying considerable organic changes, and each in its turn being favoured by Natural Selection.

The same word "variation" has been indiscriminately applied to two very different conceptions, which ought to be clearly distinguished; the one is that of the "sports" just alluded to, which are changes in the position of organic stability, and may, through the aid of Natural Selection, become fresh steps in the onward course of evolution; the other is that of the Variations proper, which are merely strained conditions of a stable form of organisation, and not in any way an overthrow of them. Sports do not blend freely together; variations proper do so. Natural Selection acts upon variations proper, just as it does upon sports, by preserving the best to become parents, and eliminating the worst, but its action upon mere variations can, as I conceive, be of no permanent value to evolution, because there is a constant tendency in the offspring to "regress" towards the parental type. The amount and results of this tendency have been fully established in _Natural Inheritance_. It is there shown, that after a certain departure from the central typical form has been reached in any race, a further departure becomes impossible without the aid of these sports. In the successive generations of such a population, the average tendency of filial regression towards the racial centre must at length counterbalance the effects of filial dispersion; consequently the best of the produce cannot advance beyond the level already attained by the parents, the rest falling short of it in various degrees.

In concluding these introductory remarks, I have to perform the grateful duty of acknowledging my indebtedness to Mr. F. Howard Collins, who materially helped me during the past year. He undertook the numerous and tedious tabulations upon which the chapters on Heredity, and on Races and Cla.s.ses, are founded, and he thoroughly revised nearly the whole of my MS., to the great advantage of the reader of this book.

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