Francis Galton’s Natural Inheritance is a work of Victorian statistical science, published by Macmillan and assembled from the author’s technical memoirs alongside a large body of new material. Its subject is the inheritance of ordinary, moderately exceptional qualities across whole brotherhoods and populations rather than in single individuals, and its method is numerical throughout. Galton writes as a naturalist and measurer: he gathers family records, weighs sweet-pea seeds, breeds moths, and tabulates the statures of parents and children, all in pursuit of laws that govern how one generation descends from the last.
The book’s governing premise is that heredity can be treated statistically, and that the apparent chaos of individual variation conceals a regularity as dependable as any in physics. Galton argues that a child receives less than half its heritage from each parent, that the unknown kinsman of any known man is on average more mediocre than he is, and that the same law of regression governs stature, eye-colour, artistic faculty, and even a susceptibility to consumption. Around this claim the twelve chapters build their evidence, from the particulate nature of inheritance through the tabulation of data to the final summary.
From Particles to Populations: How the Argument Builds
The Book’s Plan and the Three Problems of Heredity
The volume opens with a contents list that maps twelve chapters, from the introductory matter through the processes of heredity, organic stability, schemes of distribution and frequency, normal variability, and the data themselves, to discussions of stature, eye colour, the artistic faculty, disease, latent elements, and a closing summary. Twenty-two tables and seven appendices accompany the text, among them memoirs on heredity, problems worked by J. D. Hamilton Dickson, sweet-pea experiments on regression, temper in English families, the geometric mean, the probable extinction of families as discussed by the Rev. H. W. Watson, and the orderly arrangement of hereditary data.
Galton explains in his opening chapter that the book gathers results from technical memoirs published over many years, now set out in order with much new material. His subject is not the inheritance of exceptional qualities in single individuals but in brotherhoods and multitudes, and the methods are correspondingly refined. Three problems frame the inquiry. The first is the strange regularity of great populations: the large do not always beget the large, nor the small the small, yet the proportions of a nation hardly shift across generations. The second concerns the average share each ancestor contributes. A child may be said to derive half its heritage from either parent, but it can receive something from a distant progenitor that neither parent personally possessed, so the true share from each parent must be less than half—how much less? The third asks for the numerical nearness of kinship: a brother is nearer than a nephew, a nephew nearer than a cousin, but by how much? Answers, he warns, demand novel ideas and cannot be crammed into an introduction.
Natural and Acquired Peculiarities
The second chapter sorts the material of inheritance. Natural peculiarities are distinguished from acquired ones, with dissimilar twins offered as evidence that nature can diverge within a single family. Female measures are transmuted into male ones by multiplying stature by 1.08—one inch added per foot—so that the two sexes may be compared on one scale. Inheritance itself is particulate, illustrated by Italian buildings raised from pillaged stones, and by second-hand materials from a dealer’s yard that carry their old traits into a new structure. Family likeness and individual variation are compared to the vegetation of an island and of seedless islets; latent characteristics to buried seeds and to diseases that skip generations, though Galton thinks such skipping less usual than popular belief supposes. Some heritages blend, as skin colour does; others are mutually exclusive, as eye colour is, and exclusive heritages help incipient races keep their distinctness. On the inheritance of acquired faculties he is largely sceptical, criticising the drunkard-mother example and noting, after William O. Priestley’s lectures, that no nerve or blood connects mother and unborn child. Petty influences multiply until individual prediction becomes impossible, yet average results remain certain.
Fraternities, Stable Forms, and Types
Heredity, he argues, must be studied through fraternities rather than individuals, since brothers share similar total heritages yet differ personally; large fraternities serve better than small, and the group of parents, uncles, and aunts should be set against the group of children. Watching newly fertilised ova, he supposes segregations and aggregations, repulsions working with affinities, particles settling from unsteady equilibrium into close packing, a sphere touching twelve neighbours. Chance itself produces stable results: tangled strings knot, rubbish arches across a pipe and chokes it, and stones falling from the ruinous walls of Kenilworth Castle bridged an old window’s jambs and held firm for years until a storm shook them down. Such recurrent groupings are temporarily stable forms, fewer than all possible combinations. Governments show the same economy—autocracies, constitutional monarchies, oligarchies, and republics as primary forms, with numberless secondary ones; scientific societies everywhere settle into president, vice-presidents, council, honorary and paid secretaries, trustees, and treasurer, some adding an ornamental patron. Pageants, evening parties, race-courses, marriages, and funerals recur habitually; landscapes repeat their solutions, as when the Nile expedition was planned from Red River experience with Canadian voyageurs, and Swiss guides were employed in the Himalayas, the Caucasus, New Zealand, the Andes, and Greenland. Cookery follows Jules Gouffé’s Royal Cookery Book of 1869, with its exact quantities. A type, then, is a limited recurrent form; a form descending through generations deserves the name typical, the breeder merely weeding out reversions. Inventions obey the same law: patents are types, subsidiary patents sub-types, and London’s omnibuses, hansoms, and four-wheelers are mechanical types. A polygonal slab model illustrates primary and subordinate stability, tilting back unless pushed over, with a sport arising suddenly at the longest diameter. Sports are stable, as the hansom cab and Sir William Grove’s battery show, while trifling excrescences like moles or extra fingers persist. Mixed types are infertile: no useful blend of four-wheeler and hansom could run on three wheels with the driver halfway up the roof. Evolution need not proceed by minute steps alone; intermediate forms may be unstable varieties afterwards retraced, and inventions are often independently repeated.
Grades, the Median, and Schemes of Distribution
The fourth chapter treats fraternities and populations as units and introduces schemes of distribution and frequency, grades, and the median, M. The great inequality of strength between the sexes is confirmed by Salter’s squeeze instrument: the woman in the 93rd grade matched the man in the 7th, and of 1,657 adult women the strongest squeezed only 86 lbs., about that of a medium man. The shape of a scheme, Galton shows, is independent of the number of observations; samples from one large group, adjusted by horizontal scales, differ little in shape provided the numbers are not too small. The curve is always uncertain at its extreme ends, since the next value may exceed any preceding one; on a chessboard of eight squares the first piece occupies grade 0.5 and the last 7.5, and with 800 pieces the first exceeds grade 0 by half a class-place. Eighteen schemes can be printed in a single line of a table recording measures from grade 5 to 95, and such schemes let each person measured in an anthropometric laboratory find his rank. Schemes may even be built from observations barely exact enough to be called measures: Sir James Paget’s memoir on what becomes of medical students traced 1,000 pupils, and Galton’s redistribution of the classes yields the familiar curve of distribution, with the three professors of anatomy near the top and Palmer the Rugeley murderer at the bottom. The curve of frequency, turned at right angles, expresses the same facts less conveniently, and the regular distribution of faculties is little disturbed by members belonging to different types, as a heavy mass of foliage hides the twigs and branches that grew it.
The Law of Frequency of Error
Normal variability occupies the fifth chapter. Every measure is the median plus or minus a deviation, and the eighteen schemes of deviations show a strong family likeness.
Marriage Selection and the Mid-Parent
Galton turns to whether stature has any bearing on whom people marry. Working from his second problem, he finds the quartile deviation of male stature to be 1.7 inches, and the same for transmuted female statures. Were couples paired at random in this respect, the deviation of summed statures would be √2 times 1.7, or 2.41 inches, so the mean couple stature would show a deviation of 1.20 inch. The figures from his table match this closely—its “Mid-Parent” column standing for an ideal composite person halfway between the father and the transmuted mother. Marriage selection, he concludes, pays no regard to stature worth accounting for.
A rougher test sorted parents into tall, medium, and short groups. Exact equality proved impracticable because statures had been recorded loosely, so he framed rules to govern the sorting. The count gave 32 cases of one short and one tall parent against 27 where both were short or both tall—32 contrasts to 27 likenesses. He sets the difference aside: the numbers are small, and slight shifts in the limiting values would move the result sensibly. Married folk may therefore be treated as though choice were wholly independent of stature, which makes the arithmetic far easier.
Like and Unlike Parents
He next asks whether the children of unlike parents betray that unlikeness, or whether they depend only on the Mid-Parent’s average. Stature blends freely in transmission, and he wants to establish this before tracing the Mid-Parent–Son relationship, since analysing each parent separately would demand far more observations. If children depended on the average alone, fraternities of like and unlike parents should not differ; if children took after one parent rather than the other, the unlike-parent fraternities would be more diverse. Writing statures as M ± D and comparing schemes of deviations, he finds the quartile deviations identical. Across 525 children, those with unlike parents were no more diverse than the rest. Only the Mid-Parent’s stature matters.
Stature suits his purpose well: it is nearly constant in the same adult, frequently measured and recorded, its discussion need not entangle marriage selection, the Mid-Parent suffices, and its variability is Normal, so the law of Frequency of Error can cross-test his conclusions—all of which have borne the test. Its one drawback is small variability: half the population lies within 1.7 inches of the average.
Tables of Sons, Brothers, and Population Constants
He arranged his materials in several ways to guard against rash conclusions. One table records the statures of 928 adult offspring of 205 Mid-Parents, showing how the Sons of each Mid-Parent group are distributed, with the mean of each line calculated chiefly by drawing schemes. Two further tables concern Brothers, drawn from the family records and from special data, and deal only with small or moderate fraternities—larger ones excluded lest their many pairs overwhelm the smaller. They register the difference between every possible pair of brothers: three brothers give three pairs, four give six, five give ten. The larger fraternities are handled separately. Constants derived by more than one method confirm one another well.
The mid-stature of the population, the median P, is deduced from the bottom lines of the three tables: 68.2, 68.5, 68.4. The middle value is a smoothed result—one of only two smoothed values in the whole work—justified because the observed values nearest the fiftieth grade ran out of harmony with the rest of the curve, and a discrepancy of more than 0.15 inch may reasonably be called fortuitous. That series refers to brothers only, a small sample weighted toward a few large families, so less regularity was expected there than in the table fairly based on the whole population. Variability of the population comes out at 1.65, 1.7, and 1.7 inch; his original treatment also gave 1.7, so he accepts 1.7 throughout. The Mid-Parents’ variability is 1.19 inch. Were marriage independent of stature, it should equal 1.7 divided by √2, or 1.21 inch—an excellent agreement with observation.
Co-Fraternities and the Squadron of Statures
All adult Sons and transmuted Daughters of Mid-Parents of the same stature form a Co-Fraternity, one to each line of the table. Co-Fraternals should be more diverse than brothers for three reasons: their Mid-Parents may differ by as much as an inch; their grandparents and remoter ancestors may have differed widely; and their nurture is more various. Brothers in a town family do not seem to differ more than those in a country family, but a mixture of both must show greater diversity.
An unknown brother of a known man carries two tendencies—to resemble the known man, and to resemble his race. The first would make him deviate from P as much as his brother does; the second would make him not deviate at all. The outcome is a compromise. Since the average regression from either parent to the son is twice that from a man to his brother, a man is only half as nearly related to either parent as to his brother. Regression has now been shown from parent to son, son to parent, and brother to brother—the only three lines of kinship—so it must be a universal rule that the unknown kinsman, in any degree, is on average more mediocre than the known man. Let the known man be P ± D and the kinsman P ± D’; it is safe to wager that D’ is less than D.
The Squadron of Statures makes this visible. A million statures divided into a thousand samples of a thousand would yield practically identical schemes, marshalled into a squadron of a thousand statures each way on a square base, divisible into ranks (identical schemes) or files (rectangles of equal breadth but dissimilar heights). A large sample A of a population gives rise to a group of Kinsmen Z so distant as to retain no family likeness to A, yet statistically indistinguishable from the population at large. Provisionally, tall, short, and mediocre parents are supposed to contribute equally to the next generation. Each file of A traced to its Kinsmen in Z yields identical schemes, since every Z scheme contains more measures than the A files—the same kinsmen counted many times over, a man being uncle to many nephews and nephew to many uncles. Z is an exact squadron identical with A in constitution but not in attitude: its ranks derive from A’s files, so the two squadrons stand at right angles, A curved in rank and horizontal in file, Z curved in file and horizontal in rank.
Nearer kinsmen occupy squadrons intermediate between A and Z, somewhat curved both in rank and file. Since the kinsmen of all members of a population, in any degree, are themselves a population with similar characteristics, a law connects the curvatures: calling their quartile deviations r and f, and p that of the general population, r² + f² = p².
Heart Disease Fraternities as a Contrast
Galton rounds off his treatment of consumption by setting beside it nine families in which heart disease runs heavy, offered less for their own sake than to throw the consumptive fraternities into relief. Sixty-nine children across the nine families yield twenty-four deaths from heart disease, with a scattering of ruptured vessels, lung disease, dropsy, apoplexy, suicide and one cancer. Between the diseases of fathers and of mothers he can find no difference beyond what small numbers would explain; the mid-ages at death, seventy and seventy-two, run closely alike.
The Mother’s Superior Influence
The deduction he leaves to medical men to verify: that a consumptive mother has a distinctly greater power than a consumptive father to produce a highly consumptive family. He defines such a fraternity as one where at least half the members have died of consumption or are so stricken that death may be reckoned on, and asks that the fraternities be large, six children and upwards. The proportions drawn from his fourteen families he calls very rude indications indeed. His explanation is summed up in a single word — infection. The malformation may be transmissible equally by either parent, but the child lies in its mother’s arms in infancy and breathes the tainted air of her sheltered rooms, so that contagion reaches it through her.
Consumptivity as a Measurable Quality
Since one person in six or seven dies of consumption, and hereditary diseases intermix through marriage, the whole population must be more or less tainted. Consumptivity may exist without outward sign, and he supposes it normally distributed and measurable. Longevity, marriage and fertility are all affected by it, yet the influences tend to neutralize: consumptives die early but marry earlier, often from great attractiveness, and produce children quickly, so that those dying before middle age leave large families. Taking sixteen per cent of the population as dying of consumption, and applying the law of regression from a deviation of three units in the parent to one in the child, he works through the grades to a consumptive proportion of twenty-seven to thirty-one per cent, against the twenty-six and twenty-eight his observations had given. He warns against stressing the coincidence, but calls the prima facie result successful: the statistical method seems correct, and the law governing other faculties appears to govern consumptivity too, though its constants differ slightly.
A Plea for Insurance Records
Insurance officers, he notes, know far from exactly what constitutes an unsound life. Given the money at stake, the higher-class offices should combine to collect completed cases across two or three generations, anonymous and complete, with no perceptible effect on the future insurances of descendants. Cases must not be picked to support any theory. Vast good material lies at the command of medical officers; combined and accessible, it would give years of work and lead to unexpected results.
Latent Elements and the Tables of Frequency
The chapter on latent elements breaks off at the point where not more than one half of the — and the book turns to its apparatus of tables. Tables 4 to 8 set out how to draw Normal Curves of Frequency and Distribution from the Probability Integral, with the equation of the curve given in terms of the Measure of Precision. Table 5 supplies the integral for the argument t, and at t = ·4769 the entry would be ·50, which makes ·4769 the Probable Error. Table 6 rescales so that the unit of measurement is the Probable Error itself, half of all cases falling within 1.0. Table 7 halves and interpolates these entries into a hundred grades running from 0° to ±50°, and Table 8 modifies the scale so grades run 0° to 100° for drawing Schemes. Table 9 turns to marriage selection in stature, where contrasted heights marry about as often as similar ones, thirty-two cases to twenty-seven; further tables treat eye-colour, the artistic faculty, and the slight effect of differences in parental height on adult children. An appendix lists the author’s memoirs on heredity.
Two Problems in Probable Position
The mathematical problems are then worked through generally. The first, with the angles and probable errors replaced by a and b, yields the ellipses and a relation from which the angle is found by tangent; the probable error of the projection of the whole motion proves independent of the distance of the line of motion from the axis. The second imagines an index moving up and down a bar which itself moves up and down a fixed frame, the two movements independent; given the observed position of the index, the most probable position of the unobservable mean is required. Setting the sum of the squared deviations over their probable errors to a minimum subject to their constant sum, he obtains the most probable position and a probable error that is the same for all values of the observed distance.
Sweet Peas and English Temper
Two appendices carry the argument into the garden and the family record. Sweet peas, chosen and planted as described earlier, show that a difference of ·172 grain in weight corresponds closely to ·01 inch in diameter, and that for each unit increase in the parent seed the filial seed gains only a third of a unit, with mean filial seed resembling parental at about 15·5 hundredths of an inch. Seeds smaller than the mean proved miserable and infertile. On temper, information gathered on 1,981 persons yields fifteen epithets for good temper and forty-six for bad, grouped as mild, docile, fretful, violent and masterful. Though bad epithets are three times as numerous, the persons described under each head are about equal — forty-eight to fifty-two, then forty-seven to fifty-three — with a slight favouring of women. Among 1,361 children of large families, 321 were good-tempered, 705 neutral and 342 bad, nearly one, two, one, exactly what haphazard combination of two equally frequent elements would give. Direct relatives are not treated more tenderly than uncles and aunts, and the marriage pairs show no marked predilection or avoidance between classes, the apparent irregularities dissolving when mildness and docility are combined. Tempers do not readily blend in offspring; some children take after one parent, some another, with threads of ancestral temper occasionally showing.
The Geometric Mean and the Extinction of Surnames
Sociological phenomena, he argues, are generally subject to the condition of the geometric mean, differences arising from size of nation or business and from the influences of circumstance. The ordinary law of Frequency of Error, based on the arithmetic mean, serves statisticians but leads to absurdity at wide deviations: it implies that giants more than double the mean height require dwarfs of less than nothing. A Law of Error based on the geometric mean is therefore worth investigating, and he placed the matter in Mr. Donald Macalister’s hands for a memoir in the Proceedings of the Royal Society.
The closing problem is the extinction of surnames. The decay of families in conspicuous positions has often been remarked, and surnames once common have grown scarce or vanished, prompting the hasty conclusion that comfort and intellect bring diminished fertility and that the population is maintained chiefly through the proletariat. M.
Regression as the Measure of Kinship
The idea that cuts through the whole book is regression, and Galton treats it as something close to a universal rule of life. A father or son stands only half as near in blood as a brother; an uncle or nephew a third as near; a cousin nine times as remote as a brother. Because these are the only possible lines of kinship—descending, ascending, collateral—it follows that the unknown kinsman of any known man is on average more mediocre than he is. Galton turns this into a wager: given a man of stature P±D and an unknown kinsman of stature P±D’, it is safe to bet that D’ is smaller than D.
What makes the concept more than arithmetic is Galton’s insistence that it applies equally to qualities that blend and qualities that are mutually exclusive. Stature blends freely; eye-colour does not, since a child takes one parent’s colour rather than a mixture. Yet the same regression of one-third appears in both, and again in the artistic faculty, where Galton’s predicted proportions of artistic and non-artistic offspring come within a few points of what the family records actually show. He is careful about the difference: a blended heritage gives a child a fifth part of a gifted ancestor’s peculiarity, which is poor, whereas an exclusive heritage gives a one-in-five chance of inheriting the whole, which is prized. The distinction matters for how incipient races form and for how any breeder, human or otherwise, should think about what can be preserved.
Stability, Sports, and the Limits of Prediction
Galton’s account of organic stability gives the book its most concrete images. Newly fertilised ova settle into positions of temporary equilibrium, particles packing as a sphere touches twelve neighbours; tangled strings form knots and rubbish chokes a pipe by arching across it. Stones falling from the ruinous walls of Kenilworth Castle bridged the jambs of an old window and stayed firm for years until a storm shook them down. These recurrent groupings are “temporarily Stable Forms,” fewer than all possible combinations, and Galton finds the same pattern in governments, in the committees that scientific societies invariably establish, in the routes of Alpine guides, and in the exact quantities of a French cookery book.
From this he draws a claim that unsettles any simple gradualism: evolution need not proceed by minute steps alone. A “sport” may arise suddenly at the longest diameter of things and prove perfectly stable, as the hansom cab and Grove’s battery did; intermediate forms may be unstable varieties afterwards retraced, and inventions are often independently repeated. Yet the same chapter insists that petty influences make individual prediction impossible while average results remain certain. That tension—between the fixity of types and the unpredictability of any particular life—runs beneath every table in the book.
What the Book Meant to Do
Galton’s larger ambition surfaces in the appendices and asides: a law of error based on the geometric mean, since the ordinary law implies that giants more than double the mean height require dwarfs of less than nothing; the probable extinction of surnames, worked out by the Rev. H. W. Watson, showing how families of every rank tend to perish and undercutting the hasty conclusion that comfort and intellect necessarily bring diminished fertility; and a plea that insurance offices combine to collect completed cases across two or three generations, since vast good material already lies at the command of medical officers. The book closes its argument in the chapter on latent elements and the summary, having carried its reader from the packing of particles to the fate of family names. Its legacy is the vocabulary it gave later students of heredity—median, grade, regression, co-fraternity—and a method that treated a population, rather than a person, as the proper unit of biological inquiry.
