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NATURAL INHERITANCE

9-

NATURAL INHERITANCE

BY

FRANCIS GALTON, F.R.S.

^

AUTHOR OF
" HEREDITARY GENIUS," " INQUIRIES INTO HUMAN FACULTY," ETC.

CHESTNUT liiLL,AIAS&

MACMILLAN AND CO.

AND LONDON

1894

ITm, Right of Translation and Beprodiiction is Reserved

BOSTON OOLLi^vTi^ ..,.x •.>..' ^
CHKST.NIJT BILL, MASb.

Kkhard Clav and Sons, Limitkd,

LONDON AND BfNGAY.

65941

CONTENTS.

CHAPTER I.

Introductoky

CHAPTER II.

Processes in Heredity

Natural and Acquired Peculiarities, 4. — Transmutation of Female
into Male measures, 5. — Particulate Inheritance, 7. — Family
Likeness and Individual Variation, 9. — Latent Characteristics,
11. — Heritages that Blend, and those that are mutually Ex-
clusive, 12. — Inheritance of Acquired Faculties, 14.— Variety
of Petty Influences, 16.

CHAPTER III.

Organic Stability 18

Incipient Structure, 18. — Filial Relation, 19. — Stable Forms 20. —
Subordinate Positions of Stability, 25. — Model, 27. — Stability
of Sports, 30.— Infertility of Mixed Types, 31.— Evolution
not by Minute Steps only, 32.

CHAPTER IV.

Schemes of Distribution and op Frequency 35

Fraternities and Populations to be treated as units, 35. — Schemes
of Distribution and their Grades, 37. — The Shape of Schemes
is independent of the number of Observations, 44. — Data for
eighteen Schemes, 46. — Application of Schemes to inexact
measures, 47. — Schemes of Frequency, 49.

vi CONTENTS.

CHAPTER V.

PAGE

Normal Variability 51

Scheme of Deviations, 51. — Normal Curve of Distributions, 54. —
Comparison of the Observed with the Normal Curve, 56.— The
value of a single Deviation at a known Grade, determines a
Normal Scheme of Deviations, 60.— Two Measures at known
Grades, determine a Normal Scheme of Measures, 61. The
Charms of Statistics, 62. — Mechanical Illustration of the Cause
of Curve of Frequency, 63.— Order in Apparent Chaos, 66. —
Problems in the Law of Error, 66.

CHAPTER VI.
Data "71

Records of Family Faculties, or R.F.F. data, 72.— Special Data,
78. — Measures at my Anthropometric Laboratory, 79. — Experi-
ments in Sweet Peas, 79.

CHAPTER VII.

Discussion of the Data of Stature 83

Stature as a Subject for Inquiry, 83. — Marriage Selection, 85. —
Issue of Unlike Parents, 88, — Description of the Tables of
Stature, 91. — Mid-Stature of the Population, 92. — Variability
of the Population, 93.' — Variability of Mid-Parents, 93, —
Variability in Co-Fraternities, 94. — Regression, — a, Filial, 95 ;
&, Mid- Parental, 99 ; c, Parental, 100 ; d, Fraternal, 108.—
Squadron of Statures, 110, — Successive Generations of a
People, 115. — Natural Selection, 119. — Variability in Frater-
nities : First Method, 124 ; Second Method, 127 ; Third
Method, 127 ; Fouith Method, 128 ; Trustworthiness of the
Constants, 130 ; General view of Kinship, 132. — Separate Con-
tribution of each Ancestor, 134. — Pedigree Moths, 136.

CHAPTER VIII.

Discussion of the Data of Eye Colour 138

Preliminary Remarks, 138, — Data, 139.— Persistence of Eye
Colour in the Population, 140. — Fundamental E3'-e Colours,
142. — Principles of Calculation, 148. — Results, 152.

CONTENTS. vii

CHAPTER IX.

PAGE

The Artistic Faculty 154

Data, 154. — Sexual Distribution, 156.— Marriage Selection, 157. —
Regression, 158. — Effect of Bias in Marriage, 162.

CHAPTER X.

Disease 164

Preliminary Problem, 165. — Data, 167. — Trustwortbiness of
R.F.F. data, 167. — Mixture of Inberitances, 167. — Consump-
tion : General remarks, 171 ; Distribution of Fraternities,
174 ; Severely Tainted Fraternities, 176 ; Consumptivity, 181.
— Data for Hereditary Diseases, 185.

CHAPTER XI.

Latent Elements 187

Latent Elements not very numerous, 187 ; Pure Breed, 189. —
Simplification of Hereditary Inquiry, 190.

CHAPTER XII.
Summary , . . . 192

viii CONTENTS.

TABLES.

The words by which the various Tables are here described, have been
chosen for the sake of qnick reference ; they are often not identical with
those used in their actual headings.

No. of the Subjects OF THE Tables. ' page

i abies.

1. Strengths of Pull arranged for drawing a Scheme 199

2. Data for Schemes of Distribution for various Qualities and

Faculties 200

3. Evidences of the general applicability of the Law of Frequency

of Error 201

4. Values for the Normal Curve of Frequency (extracted from

the well-known Table) 202

5. Values of the Probability Integral (extracted from the well-

known Table) . . . ." 202

6. A^alues of the Probability Integral when the scale by which

the Errors are measured has the Prob : Error for its Unit . 203

7. Ordinates to the Normal Curve of Distribution, when its 100

Grades run from - 50°, through 0°, to -f 50^ 204

8. Ditto when the Grades run from 0° to lOO"". {This Table is

espeiially adapted for use with Schemes) 205

9. Marriage Selection in respect to Stature 206

9a. Marriage Selection in respect to Eye Colour 206

9Z), Marriages of the Artistic and the Non Artistic 207

10. Issue of Parents who are unlike in Stature 207

11. Statures of adult children born to Mid Parents of Various

Statures 208

1 2. Statures of the Brothers of men of various Statures, fi'om

P.F.F. data 209

CONTENTS. ix

Tables ^"^ Subjects of the Tables. page

13. Ditto from the Special data 210

14. Deviations of Individual brothers from their common Mid-

Fraternal Stature 211

15. Frequency of the different Eye Colours in 4 successive Gene-

rations 212

16. The Descent of Hazel-Eyed families 213

17. Calculated contributions from Parents and from Grandparents,

according as they are Light, Hazel, or Dark eyed . . . . 213

18. Examples of the application of Table 17 214

19. _ Observed and calculated Eye Colours in 16 groups of families 215

20. Ditto in 78 separate families 216

21. Amounts of error in the various calculations of anticipated

Eye Colour 218

22. Inheritance of the Artistic Faculty 218

APPENDICES.

A. Memoirs and Books on Heredity by the Author 219

B. Problems by J. D. Hamilton Dickson 221

C. Experiments on Sweet Peas, bearing on the law of Eegression . . 225

D. Good and bad Temper in English Families 226

E. The Geometric Mean in "Vital and Social Statistics . 238

F. Probable extinction of Families, 214 ; Discussion of the Problem

by the Eev. H. W. Watson, D.Sc 241

G. Orderly arrangement of Hereditary Data 248

Index 257

NATURAL INHERITANCE

NATUKAL INHERITANCE,

CHAPTEE L

INTRODUCTOEY.

I HAVE long been engaged upon certain problems tliat
lie at the base of tlie science of heredity, and during
several years have published technical memoirs concern-
ing them, a list of which is given in Appendix A.
This volume contains the more important of the results,
set forth in an orderly way, w^ith more completeness
than has hitherto been possible, together with a large
amount of new matter.

The inquiry relates to the inheritance of moderately
exceptional qualities by brotherhoods and multitudes
rather than by individuals, and it is carried on by
more refined and searching methods than those usually
employed in hereditary inquiries.

One of the problems to be dealt with refers to the
curious regularity commonly observed in the statistical
peculiarities of great populations during a long series of

B

2 NATURAL INHEHITANCE. [chap.

generations. The large do not always begefc the large,
nor the small the small, and yet the observed propor-
tions between the large and the small in each degree of
size and in every quality, hardly varies from one gener-
ation to another.

A second problem regards the average share con-
tributed to the personal features of the offspring by each
ancestor severally. Though one half of every child
may be said to be derived from either parent, yet he
may receive a heritage from a distant progenitor that
neither of his parents possessed as personal character-
istics. Therefore the child does not on the average
receive so much as one half of his personal qualities
from each parent, but something less than a half. The
question I have to solve, in a reasonable and not merely
in a statistical way, is, how much less ?

The last of the problems that I need mention now,
concerns the nearness of kinship in different degrees.
We are all ag;reed that a brother is nearer akin than a
nephew, and a nephew than a cousin, and so on, but
how much nearer are they in the precise language of
numerical statement ?

These and many other problems are all fundamentally
connected, and I have worked them out to a first degree
of approximation, with some completeness. The con-
clusions cannot however be intelligibly presented in
an introductory chapter. They depend on ideas that
must first be well comprehended, and which are now
novel to the large majority of readers and unfamiliar
to all. But those who care to brace themselves to a

I.] INTRODUCTORY. 3

sustained effort, need not feel much regret that the
road to be travelled over is indirect, and does not
admit of being ma^pped beforehand in a way they can
clearly understand. It is full of interest of its own.
It familiarizes us with the measurement of variability,
and with curious laws of chance that apply to a vast
diversity of social subjects. This part of the inquiry
may be said to run along a road on a high level,
that affords wide views in unexpected directions, and
from w^hich easy descents may be made to totally
different goals to those we have now to reach. I have
a great subject to write upon, but feel keenly my
literary incapacity to make it easily intelligible without
sacrificing accuracy and thoroughness.

r

P> 2

r

CHAPTEE 11.

PROCESSES m HEREDITY.

Natural and Acquired Peculiarities. — Transmutation of Female into Male
Measures. — Particulate Inheritance. — Family Likeness and Individual
Variation. — Latent Characteristics. — Heritages tliat Blend and those
that are Mutually Exclusive. — Inheritance of Acquired Faculties. —
Variety of Petty Influences.

A CONCISE account of the cliief processes in heredity
will be given in this chapter, partly to serve as a
reminder to those to whom the works of Darwdn especi-
ally, and of other writers on the subject, are not
familiar, but principally for the sake of presenting them
under an aspect that best justifies the methods of
investigation about to be employed.

Natural and Acquired Peculiarities. — The peculiari-
ties of men may be roughly sorted into those that
are natural and those that are acquired. It is of the
former that I am about to s|)eak in this book. They
are noticeable in every direction, but are nowhere so
remarkable as in those twins ^ who have been dissimilar

1 See Human Faculty, 237.

CHAP. II.] PROCESSES IN HEIIEDITY. . 5

in features and disposition from tlieir earliest years,
thongli brouo^lit into tlie world under the same condi-
tions and subsequently nurtured in an almost identical
manner. It may be that some natural peculiarity does
not appear till late in life, and yet may justly deserve
to be considered natural, for if it is decidedly exceptional
in its character its origin could hardly be ascribed to
the effects of nurture. If it was also possessed by some
ancestor, it must be considered to be hereditary as
well. But "Natural" is an unfortunate word for
our purpose ; it implies that the moment of birth is
the earliest date from which the effects of surrounding
conditions are to be reckoned, although nurture begins
much earlier than that. I therefore must ask that the
word "Natural" should not be construed too literally,
any more than the analogous phrases of inborn, con-
genital, and innate. This convenient laxity of expres-
sion for the sake of avoiding a pedantic periphrase need
not be accompanied by any laxity of idea.

Transmutation of Female into Male Measures. — We
shall have to deal with the hereditary influence of parents
over their offspring, although the characteristics of the
two sexes are so different that it may seem impossible
to speak of both in the same terms. The phrase of
" Average Stature " may be applied to two men without
fear of mistake in its interpretation ; neither can there
be any mistake when it is applied to two women, but
what meanino^ can we attach to the word " Averas^e "
w^hen it is applied to the stature of two such different

G NATURAL INHERITANCE. [chap.

beings as the Father and the Mother ? How can we
appraise the hereditary contributions of different an-
cestors whether in this or in any other quality, unless
we take into account the sex of each ancestor, in addi-
tion to his or her characteristics ? Again, the same
group of progenitors transmits qualities in different
measure to the sons and to the daughters ; the sons
being on the whole, by virtue of their sex, stronger,
taller, hardier, less emotional, and so forth, than the
daughters. A serious complexity due to sexual differ-
ences seems to await us at every step when investigating
the problems of heredity. Fortunately we are able to
evade it altogether by using an artifice at the outset, else,
looking back as I now can, from the stage which the
reader will reach when he finishes this book, I hardly
know how we should have succeeded in making a
fair start. The artifice is never to deal with female
measures as they are observed, but always to employ
their male equivalents in the place of them. I trans-
mute all the observations of females before taking
them in hand, and thenceforward am able to deal
with them on equal terms with the observed male
values. For example : the statures of women bear to
those of men the proportion of about twelve to thir-
teen. Consequently by adding to each observed female
stature at the rate of one inch for every foot, we are
enabled to compare their statures so increased and trans-
muted, with the observed statures of males, on equal
terms. If the observed stature of a woman is 5 feet,
it will count by this rule as 5 feet -\- 5 inches; if it be

II.] PROCESSES IN HEIIEDITY. , 7

6 feet, as 6 feet + 6 inclies ; if 5-| feet, as 5^ feet +
5^ inches ; that is to say, as 5 feet + Hi inches/

Simihxiiy as regards sons and daughters ; whatever
may be observed or concluded concerning daughters
will, if transmuted, be held true as regarding sons,
and whatever is said concerning sons, will if re-
transrauted, be held true for daughters. We shall see
further on that it is easy to apply this principle to
all measurable qualities.

Particulate Inheritance. — All livino^ beino\s are indi-
viduals in one aspect and composite in another. They
are stable fabrics of an inconceivably large number of
cells, each of which has in some sense a separate life of
its own, ancl which have been combined under influences
tliat are the subjects of much speculation, but are as
yet little understood. We seem to inherit bit by bit,
this element from one progenitor that from another,
under conditions that will be more clearly expressed as
we proceed, \vhile the several bits are themselves liable
to some small change during the process of transmission.
Inheritance may therefore be described as largely if not
wholly " particulate," and as such it will be treated in
these pages. Though this word is good English and
accurately expresses its own meaning, the application

1 .The proportion I use is as 100 to 108 ; that is, I multiply every female
measure by 108, which is a very easy operation to those who possess that
most iisefiil book to statisticians, Crelle's Tables (G. Reimer, Berlin, 1875).
It gives the products of all numbers under 1000, each into each ; so by
referring to the column headed 108 the transmuted values of the female
statures can be read off at once.

8 NATURAL INHERITANCE. [chap.

now made of it will be better understood through an illus-
tration. Thus, many of the modern buildings in Italy
are historically knovv^n to have been built out of the
pillaged structures of older days. Here we may observe
a column or a lintel serving the same purpose for a
second time, and perhaps bearing an inscription that
testifies to its origin, while as to the other stones, though
the mason may have chipped them here and there, and
altered their shapes a little, few, if any, came direct
from the quarry. This simile gives a rude though true
idea of the exact meaning of Particulate Inheritance,
namely, that each piece of the new structure is derived
from a corresponding piece of some older one, as a lintel
was derived from a lintel^ a column from a column, a
piece of wall from a piece of wall.

I will pursue this rough simile just one step further,

which is as much as it will bear. Suppose we were

building a house with seeond-hand materials carted

from a dealer's yard, we should often find considerable

portions of the same old houses to be still grouped

together. Materials derived from various structures

mio^ht have been moved and much shufiled together

in the yard, yet pieces from the same source would

frequently remain in juxtaposition and it may be

entangled They would lie side by side ready to be

carted away at the same time and to be re-erected

together anew. So in the process of transmission by

inheritance, elements derived from the same ancestor

are apt to appear in large groups, just as if they had

clung together in the pre-embryonic stage, as perliaps

II.] PROCESSES IN HEREDITY. 9

they did. They form what is well expressed by the
word " traits," traits of feature and character — that is to
say, continuous features and not isolated points.

We appear, then, to be severally built up out of a
host of minute particles of whose nature we know
nothing, any one of which may be derived from any
one progenitor, but which are usually transmitted in
aggregates, considerable groups being derived from
the same progenitor. It would seem that while the
embryo is developing itself, the particles more or less
qualified for each new post wait as it were in com-
petition, to obtain it. Also that the particle that
succeeds, must owe its success partly to accident of
position and partly to being better qualified than any
equally well placed competitor to gain a lodgment.
Thus the step by step development of the embryo
cannot fail to be influenced by an incalculable number
of small and mostly unknown circumstances.

Family Likeness and Individual Variation. — Natural
peculiarities are apparently due to two broadly difi'erent
causes, the one is Family Likeness and the other is In-
dividual Variation. They seem to be fundamentally
opposed, and to require independent discussion, but this
is not the case altogether, nor indeed in the greater part.
It will soon be understood how the conditions that pro-
duce a general resemblance between the offspring and
their parents, must at the same time give rise to a con-
siderable amount of individual differences. Therefore I
need not discuss Family Likeness and Individual Varia-

10 NATURAL INHERITANCE. [chap.

tion under separate lieads, but as different effects of the
same underlying causes.

The origin of these and other prominent processes
in heredity is best exphiined by illustrations. That
which will be used was suggested by those miniature
gardens, self-made and self-sown, that may be seen
in crevices or other receptacles for drifted earth, on
the otherwise bare faces of quarries and cliffs. I have
frequently studied them through an opera glass, and
have occasionally clambered up to compare more closely
their respective vegetations. Let us then suppose the
aspect of the vegetation, not of one of these detached
little gardens, but of a particular island of substantial
size, to represent the features, bodily and mental, of
some particular parent. Imagine two such islands
floated far away to a desolate sea, and anchored
near together, to represent the two parents. Next
imagine a number of islets, each constructed of earth
that was wholly destitute of seeds, to be reared near to
them. Seeds from both of the islands will gradually
make their way to the islets through the agenc}^ of
winds, currents, and birds. Vegetation will spring up,
and when the islets are covered with it, their several
aspects will represent the features of the several children.
It is almost impossible that the seeds could ever be
distributed equally among the islets, and there must be
slight differences between them in exposure and other
conditions, corresponding to differences in pre-natal
circumstances. All of these would have some influence
upon the vegetation ; hence there would be a corre-

II.] PROCESSES IN HEREDITY. 11

spoiiding variety in the results. In some islets one
plant would prevail, in others another ; nevertheless
there would be many traits of family likeness in the
vegetation of all of them, and no plant would be found
that had not existed in one or other of the islands.

Though family likeness and individual variations are
largely due to a common cause, some variations are so
large and otherwise remarkable, that they seem to
belong to a different class. They are known among
breeders as " sports " ; I will speak of these later on.

Latent Characteristics. — Another fact in heredity
may also be illustrated by the islands and islets ;
namely, that the child often resembles an ancestor in
some feature or character that neither of his parents
personally possessed. AVe are told that buried seeds
may lie dormant for many years, so that when a
plot of ground that was formerly cultivated is again
deeply dug into and upturned, plants that had not been
known to grow on the spot within the memory of man,
will frequently make their appearance. It is easy to
imagine that some of these dormant seeds should find
their way to an islet, through currents that undermined
the island cliffs and drifted away their dehris, after the
cliffs had tumbled into the sea. x\gain, many plants on
the islands may maintain an obscure existence, being
hidden and half smothered by successful rivals ; but
whenever their seeds happened to find their way to any
one of the islets, while those of their rivals did not,
they would sprout freely and assert themselves. This

12 NATURAL INHERITANCE. [chap.

illustration partly covers the analogous fact of diseases
and otlier inheritances skipping a generation, which by
the way I find to be by no means so usual an occurrence
as seems popularly to be imagined.

Heritages that Blend and those that are Mutually
Exclusive. — As regards heritages that blend in the
offspring, let us take the case of human skin colour.
The children of the white and the negro are of a
blended tint ; they are neither wholly white nor
wdioUy black, neither are they piebald, but of a fairly
uniform mulatto brown. The quadroon child of the
mulatto and the w^hite has a quarter tint ; some of
the children ma}' be altogether darker or lighter than
the rest, but they are not j)iebald. Skin-colour is
therefore a good example of wdiat I call blended in-
heritance. It need be none the less '' particulate "
in its origin, but the result may be regarded as a fine
mosaic too minute for its elements to be distinguished
in a oreneral view.

Next as regards heritages that come altogether from
one progenitor to the exclusion of the rest. Eye-colour
is a fairly good illustration of this, the children of a
light- eyed and of a dark-eyed parent being much more
apt to take their eye-colours after the one or the other
than to have intermediate and blended tints.

There are probably no heritages that perfectly blend
or that absolutely exclude one another, but all heritages
have a tendency in one or the other direction, and the
tendency is often a very strong one. This is paralleled

II.] PROCESSES IN HEREDITY. 13

by what we may see in plots of w^ild vegetation, where
two varieties of a plant mix freely, and the general
aspect of the vegetation becomes a blend of the two,
or where individuals of one variety congregate and take
exclusive possession of one place, and those of another
variety congregate in another.

A peculiar interest attaches itself to mutually exclu-
sive heritages, owing to the aid they must afford to the
establishment of incipient races. A solitary peculiarity
that blended freely with the characteristics of the parent
stock, would disappear in hereditary transmission, as
quickly as the white tint imported by a solitary Euro-
pean would disappear in a black population. If the
European mated at all, his spouse must be black, and
therefore in the very first generation the offspring
would be mulattoes, and half of his whiteness would
be lost to them. If these mulattoes did not inter-
breed, the whiteness would be reduced in the second
generation to one quarter ; in a very few more genera-
tions all recognizable trace of it would have gone.
But if the whiteness refused to blend with the black-
ness, some of the offspring of the wdiite man would be
wholly white and the rest wholly black. The same
event would occur in the grandchildren, mostly but
not exclusively in the children of the white offspring,
and so on in subsequent generations. Therefore,
unless the white stock became wholly extinct, some
undiluted specimens of it w^ould make their appear-
ance during an indefinite time, giving it repeated
r

14 NATURAL INHEHITANCE. [chap.

cliaiices of holding its own in tlie struggle for existence,
and of establishing itself if its qualities were superior
to those of the black stock under any one of manj
different conditions.

Inheritance of Acquired Faculties. — I am unpre-
pared to say more than a few words on the obscure,
unsettled, and much discussed subject of the possibility
of transmitting acquired faculties. The main evidence
in its favour is the gradual change of the instincts of
races at large, in conformity with changed habits, and
through their increased adaptation to their surroundings,
otherwise apparently than through the influence of
Natural Selection. There is very little direct evidence
of its influence in the course of a single generation, if
the phrase of Accjuired Faculties is used in perfect
strictness and all inheritance is excluded that could bo
referred to some form of Natural Selection, or of
Infection before birth, or of peculiarities of Nurture
and Eearing. Moreover, a large deduction from the
collection of rare cases must be made on the ground
of their being accidental coincidences. When this
is done, the remaining instances of acquired disease
or faculty, or of any mutilation being transmitted from
parent to child, are very few. Some apparent evidence
of a j)ositive kind, that was formerly relied upon, has
been since found capable of being interpreted in another
way, and is no longer adduced. On the other hand there
exists such a vast mass of distinctly negative evidence,
that every instance offered to prove the transmission

II.] PROCESSES IN HEREDITY. 15

of acquired faculties requires to be closely criticized.
For example, a woman wlio was sober becomes a
drunkard. Her children born during the period of her
sobriety are said to be. quite healthy ; her subsequent chil-
dren are said to be neurotic. The objections to accepting
this as a valid instance in point are many. The woman's
tissues must have been drenched with alcohol, and the
unborn infant alcoholised during all its existence in that
state. The quality of the mother's milk would be bad.
The surroundings of a home under the charge of a
drunken woman would be prejudicial to the health of
a growing child. No wonder that it became neurotic.
Again, a large number of diseases are conveyed by
germs capable of passing from the tissues of the
mother into those of the unborn child otherwise than
through the blood. Moreover it must be recollected
that the connection between the unborn child and the
mother is hardly more intimate than that between some
parasites and the animals on which they live. Not
a single nerve has been traced between them, not a
drop of blood ^ has been found to pass from the mother
to the child. The unborn child together with the
growth to which it is attached, and which is afterwards
thrown off, have their own vascular system to them-
selves, entirely independent of that of the mother.
If in an anatomical preparation the veins of the mother
are injected with a coloured fluid, none of it enters the
veins of the child ; conversely, if the veins of the child

1 See Lectures by William 0. Priestley, M.D. (CluircMll, London, 1860),
pp. 50, 52, 55, 59, and 64.

16 NATURAL INHERITANCE. [chap.

are injected, none of the fluid enters those of the
mother. Again, not only is the unborn child a sepa-
rate animal from its mother, that obtains its air and
nourishment from her purely through soakage, but its
constituent elements are of very much less recent
growth than is popularly supposed. The ovary of
the mother is as old as the mother herself; it was well
developed in her own embryonic state. The ova it con-
tains in her adult life were actually or potentially present
before she was born, and they grew as she grew. There
is more reason to look on them as collateral with the
mother, than as parts of the mother. The same may
be said with little reservation concerning the male
elements. It is therefore extremely difficult to see
how acquired faculties can be inherited by the children.
It would be less difficult to conceive of their inheritance
by the grandchildren. Well devised experiment into
the limits of the power of inheriting acquired faculties
and mutilations, whether in plants or animals, is one of
the present desiderata in hereditary science. Fortunately
for us, our ignorance of the subject will not introduce
any special difficulty in the inquiry on which we are
now engaged.

Variety of Petty Influences.— The mcalculshle number
of petty accidents that concur to produce variability
among brothers, make it impossible to predict the
exact cjualities of any individual from hereditary data.
But we may predict average results with great cer-
tainty, as will be seen further on, and we can also

II.] PROCESSES IN HEREDITY. 17

obtain precise information concerning the penumbra
of uncertainty that attaches itself to single predic-
tions. It would be premature to speak further of
this at present ; what has been said is enough to give
a clue to the chief motive of this chapter. Its
intention has been to show the large part that is always
played by chance in the course of hereditary transmission ,
and to establish the importance of an intelligent use of
the laws of chance and of the statistical methods that
are based upon them, in expressing the conditions
under which heredity acts.

I may here point out that, as the processes of statis-
tics are themselves processes of intimate blendings, their
results are the same, whether the materials had been
partially blended or not, before they were statistically
taken in hand.

CHAPTER III.

ORGIANIC STABILITY.

Incipient Structure. — Filial relation. — Stable Forms. — Subordinate posi-
tions of Stability. — Model. — Stability of Sports. — Infertility of mixed
Types. — Evolution not by minute steps only.

Incipient Structure. — The total heritage of each man
must include a greater variety of material than was
utilised informing his personal structure. The existence
in some latent form of an unused portion is proved by
his power, already alluded to, of transmitting ancestral
characters that he did not personally exhibit. There-
fore the organised structure of each individual should be
viewed as the fulfilment of only one out of an indefinite
number of mutually exclusive possibilities. His struc-
ture is the coherent and more or less stable development
of what is no more than an imperfect sample of a large
variety of elements.

The precise conditions under which each several
element or particle (whatever may be its nature) finds
its way into the sample are, it is needless to repeat,
unknown, but we may provisionally classify them under
one or other of the following three categories, as they

CHAP. III.] ORGANIC STABILITY. 19

apparently exhaust all reasonable possibilities : first, that
in which each element selects its most suitable immediate
neighbourhood, in accordance with the guiding idea in
Darwin's theory of Pangenesis ; secondly, that of more
or less general co-ordination of the influences exerted on
each element, not only by its immediate neighbours, but
by many or most of the others as well ; finally, that of
accident or chance, under which name a group of agen-
cies are to be comprehended, diverse in character
and alike only in the fact that their influence on the
settlement of each particle was not immediately directed
towards that end. In philosophical language we say
that such agencies are not purposive, or that they are
not teleological ; in popular language they are called
accidents or chances.

Filial Relation. — A conviction that inheritance is
mainly particulate and much influenced by chance,
greatly afiects our idea of kinship and makes us con-
sider the parental and filial relation to be curiously
circuitous. It appears that there is no direct hereditary
relation between the personal parents and the personal
child, except perhaps through little-known channels of
secondary importance, but that the main line of
hereditary connection unites the sets of elements out
of which the personal parents had been evolved with
the set out of which the personal child was evolved.
The main line may be rudely likened to the chain of a
necklace, and the personalities to pendants attached to
its links. We are unable to see the particles and

C 2

20 NATURAL INHERITANCE. [chap.

watch their grouping, and we know nothing directly
about them, but we may gain some idea of the various
possible results by noting the differences between the
brothers in any large fraternity (as will be done further
on with much minuteness), whose total heritages must
have been much alike, but whose personal structures
are often very dissimilar. This is why it is so im-
portant in hereditary inquiry to deal with fraternities
rather than with individuals, and with large fraternities
rather than small ones. We ought, for example, to
compare the group containing both parents and all the
uncles and aunts, with that containing all the children.
The relative weight to be assigned to the uncles and
aunts is a question of detail to be discussed in its
proper place further on (see Chap. XL)

Stable Forms. — The changes in the substance of the
newly-fertilised ova of all animals, of which more is
annually becoming known, ^ indicate segregations as
well as aggregations, and it is reasonable to suppose
that repulsions concur with affinities in producing
them. We know nothing as yet of the nature of
these affinities and repulsions, but we may expect them
to act in great numbers and on all sides in a space
of three dimensions, just as the personal likings and dis-

1 A valuable memoir on the state of our knowledge of these matters up
to the end of 1887 is published in Vol. XIX. of the Proceedings of the
Philosophical Society of Glasgow, and reprinted under the title of Tlie
Modern Cell Theory, and Theories as to the Physiological Basis of Heredity^
by Prof. John Gray McKendrick, M.D., F.R.S., &c. (R. Anderson, Glasgow,
1888.)

III.] ORGANIC STABILITY. 21

likings of eaeh indiyidual insect in a flying swarm may
be supposed to determine the position that he occupies
in it. Every particle must have many immediate neigh-
bours. Even a sphere surrounded by other spheres of
equal sizes, like a cannon-ball in the middle of a heap,
when they are piled in the most compact form, is in
actual contact with no less than twelve others. We may
therefore feel assured that the particles which are still
unfixed must be affected by very numerous influences
acting from all sides and varying with slight changes of
place, and that they may occupy many positions of tem-
porary and unsteady equilibrium, and be subject to
repeated unsettlement, before they finally assume the
positions in which they severally remain at rest.

The whimsical eff'ects of chance in producing stable
results are common enough. Tangled strings variously
twitched, soon get themselves into tight knots. Eub-
bish thrown down a sink is pretty sure in time to choke
the pipe ; no one bit may be so large as its bore, but
several bits in their numerous chance encounters will
at length so come into collision as to wedge themselves
into a sort of arch across the tube, and efi'ectually plug
it. Many years ago there was a fall of large stones from
the ruinous walls of Kenilworth Castle. Three of them,
if I recollect rightly, or possibly four, fell into a very
peculiar arrangement, and bridged the interval between
the jambs of an old window. There they stuck fast,
showing clearly against the sky. The oddity of the
structure attracted continual attention, and its stability
was much commented on. These hanging stones, as

22 NATURAL INHERITANCE. [chap.

they were called, remained quite firm for many years ;
at length a storm shook them down.

In every congregation of mutually reacting elements,
some characteristic groupings are usually recognised
that have become familiar through their frequent re-
currence and partial persistence. Being less evanescent
than other combinations, they may be regarded as
temporarily Stable Forms. No demonstration is
needed to show that their number must be greatly
smaller than that of all the possible combinations of
the same elements. I will briefly give as great a
diversity of instances as I can think of, taken from
Grovernments, Crowds, Landscapes, and even from
Cookery, and shall afterwards draw some illustrations
from Mechanical Inventions, to illustrate what is meant
by characteristic and stable groupings. From some
of them it wiU also be gathered that secondary and
other orders of stability exist besides the primary
ones.

In Governments, the primary varieties of stable forms
are very few in number, being such as autocracies, con-
stitutional monarchies, oligarchies, or republics. The
secondary forms are far more numerous ; still it is hard
to meet with an instance of one that cannot be pretty
closely paralleled by another. A curious evidence of
the small variety of possible governments is to be found
in the constitutions of the governing bodies of the
Scientific Societies of London and the Provinces, which
are numerous and independent. Their development
seems to follow a single course that has many stages.

III.] ORGANIC STABILITY. 23

and invariably tends to establish tbe following staff of
officers : President, vice-Presidents, a Council, Honorary
Secretaries, a paid Secretary, Trustees, and a Treasurer.
As Britons are not unfrequently servile to rank, some
seek a purely ornamental Patron as well.

Every variety of Crowd has its own characteristic
features. At a national pageant, an evening party, a
race-course, a marriage, or a funeral, the groupings in
each case recur so habitually that it sometimes appears
to me as if time had no existence, and that the ceremony
in which I am taking part is identical with others at
which I had been present one year, ten years, twenty
years, or any other time ago.

The frequent combination of the same features in
Landscape Scenery, justifies the use of such expressions
as " true to nature," when applied to a pictorial com-
position or to the descriptions of a novel writer. The
experiences of travel in one part of the world may
curiously resemble those in another. Thus the military
expedition by boats up the Nile was planned from
experiences gained on the Eed Eiver of North America,
and was carried out with, the aid of Canadian voyageurs.
The snow mountains all over the world present the
same peculiar difficulties to the climber, so that Swiss
experiences and in many cases Swiss guides have been
used for the exploration of the Himalayas, the Caucasus,
the lofty mountains of New Zealand, the Andes, and
Greenland. Whenever the general conditions of a
new country resemble our own, we recognise character-
istic and familiar features at every turn, whether we

24 NATURAL INHERITANCE. [chap.

are walking by the brookside, along the seashore, in
the woods, or on the hills.

Even in Cookery it seems difficult to invent a new
and good dish, though the current recipes are few, and
the proportions of the flour, sugar, butter, eggs, &c.,
used in making them might be indefinitely varied and
be still eatable. I consulted cookery books to learn the
facts authoritatively, and found the following passage :
" I have constantly kept in view the leading principles
of this work, namely, to give in these domestic recipes
the most exact quantities. ... I maintain that one
cannot be too careful ; it is the only way to put an end
to those approximations and doubts which will beset the
steps of the inexperienced, and which account for so
many people eating indifierent meals at home." ^

It is the triteness of these experiences that makes
the most varied life monotonous after a time, and many
old men as well as Solomon have frequent occasion to
lament that there is nothing new under the sun.

The object of these diverse illustrations is to impress
the meaning I wish to convey, by the phrase of stable
forms or groupings, which, however uncertain it may be
in outline, is perfectly distinct in substance.

Every one of the meanings that have been attached
by writers to the vague but convenient word '' type " has
for its central idea the existence of a limited number

^ The Royal Coohery Book By Jules GoufF^, Clief de Cuisine of the Paris
Jockey Club ; translated by Alphonse Gouffe, Head Pastry Cook to H.M.
the Queen. Sampson Low. 1869. Introduction, p. 9.

III.] ORGANIC STABILITY. 25

of frequently recurrent forms. The word etymologically
compares these forms to the identical medals that may
be struck by one or other of a set of dies. The central
idea on which the phrase " stable forms " is based is of
the same kind, while the phrase further accounts for
their origin, vaguely it may be, but still significantly,
by showing that though we know little or nothing of
details, the result of organic groupings is analogous to
much that we notice elsewhere on every side.

Siihordwate positions of Stability. — Of course there
are different degrees of stability. If the same structural
form recurs in successively descending generations, its
stability must be great, otherwise it could not have
withstood the effects of the admixture of equal doses of
alien elements in successive generations. Such a form
well deserves to be called typical. A breeder would
always be able to establish it. It tends of itself to
become a new and stable variety ; therefore all the
breeder has to attend to is to give fair play to its
tendency, by weeding out from among its offspring such
reversions to other forms as may crop up from time to
time, and by preserving the breed from rival admixtures
until it has become confirmed, and adapted in every
minute particular to its surroundings.

Personal Forms may be compared to Human Inven-
tions, as these also may be divided iuto types, sub-types,
and deviations from them. Every important inven-
tion is a new type, and of such a definite kind as to
admit of clear verbal description, and so of becoming

26 NATURAL INHERITANCE. [chap.

the subject of patent rights ; at the same time it need
not be so minutely defined as to exclude the possibility
of small improvements or of deviations from the main
design, any of which may be freely adopted by the in-
ventor without losing the protection of his patent. But
the range of protection is by no means sharply distinct,
as most inventors know to their cost. Some other man,
who may or may not be a plagiarist, applies for a sepa-
rate patent for himself, on the ground that he has intro-
duced modifications of a fundamental character ; in other
words, that he has created a fresh type. His application
is opposed, and the question whether his plea be valid
or not, becomes a subject for legal decision.

Whenever a patent is granted subsidiary to another,
and lawful to be used only by those who have acquired
rights to w^ork the primary invention, then we should
rank the new patent as a secondary and not as a
primary type. Thus we see that mechanical inventions
ofi'er good examples of types, sub-types, and mere
deviations.

The three kinds of public carriages that characterise
the streets of London ; namely, omnibuses, hansoms,
and four-wheelers, are specific and excellent illustra-
tions of what I wish to express by mechanical types,
as distinguished from sub -types. Attempted improve-
ments in each of them are yearly seen, but none have as
yet superseded the old familiar patterns, which cannot,
as it thus far appears, be changed with advantage, taking
the circumstances of London as they are. Yet there
have been numerous subsidiary and patented contriv-

III.]

ORGANIC STABILITY.

27

ances, each a distinct step in the improvement of one
or other of the three primary types, and there are or
may be in each of the three an indefinite number
of varieties in details, too unimportant to be subjects
of patent rights.

The broad classes, of primary or subordinate types,
and of mere deviations from them, are separated by no
well-defined frontiers. Still the distinction is very ser-
viceable, so much so that the whole of the laws of patent
and copyright depend upon it, and it forms the only
foundation for the title to a vast amount of valuable
property. Corresponding forms of classification must
be equally appropriate to the organic structure of all
living things.

Model. — The distinction between primary and sub-
ordinate positions of stability will be made clearer by the

riG.T

help of Fig 1, which is drawn from a model I made. The
model has more sides, but Fig. 1 suffices for illustration.
It is a polygonal slab that can be made to stand on any
one of its edges when set upon a level table, and is

28 NATURAL INHERITANCE. [cbap.

intended to illustrate tlie meaning of primary and sub-
ordinate stability in organic structures, although the
conditions of these must be far more complex than
anything we have wits to imagine. The model and the
organic structure have the cardinal fact in common, that
if either is disturbed without transgressing the range of
its stability, it will tend to re-establish itself, but if the
range is overpassed it will topple over into a new
position ; also that both of them are more likely to
topple over towards the position of primary stability,
than away from it.

The ultimate point to be illustrated is this. Though a
long established race habitually breeds true to its kind,
subject to small unstable deviations, yet every now and
then the offspring of these deviations do not tend to
revert, but possess some small stability of their own.
They therefore have the character of sub-types, always,
however, with a reserved tendency under strained con-
ditions, to revert to the earlier type. The model further
illustrates the fact that sometimes a sport may occur of
such marked peculiarity and stability as to rank as a
new type, capable of becoming the origin of a new race
with very little assistance on the part of natural selection.
Also, that a new type may be reached without any large
single stride, but through a fortunate and rapid succession
of many small ones.

The model is a polygonal slab, the polygon being one
that might have been described within an oval, and it is
so shaped as to stand on any one of its edges. When the
slab rests as in Fig. 1, on the edge A B, corresponding to

III.] ORGANIC STABILITY. 29

the shorter diameter of the oval, it stands in its most
stable position, and in one from which it is equally diffi-
cult to dislodge it by a tilt either forwards or backwards.
So long as it is merely tilted it will fall back on being
left alone, and its position when merely tilted corre-
sponds to a simple deviation. But when it is pushed
with sufficient force, it will tumble on to the next
edge, B c, into a new position of stability. It will
rest there, but less securely than in its first position ;
moreover its range of stability will no longer be dis-
posed symmetrically. A comparatively slight push from
the front will suffice to make it tumble back, a com-
paratively heavy push from behind is needed to make
it tumble forward. If it be tumbled over into a
third position (not shown in the Fig.), the process
just described may recur with exaggerated effect, and
similarly for many subsequent ones. If, however, the
slab is at length brought to rest on the edge c d,
most nearly corresponding to its longest diameter, the
next onward push, which may be very slight, will suffice
to topple it over into an entirely new system of stability ;
in other words, a ''sport" comes suddenly into exist-
ence. Or the figure might have been drawn with its
longest diameter passing into a projecting spur, so that
a push of extreme strength would be required to topple
it entirely over.

If the first position, A B, is taken to represent a type,
the other portions will represent sub-types. All the
stable positions on the same side of the longer diameter
are subordinate to the first position. On whichever of

30 NATURAL INHERITANCE. [chap.

of them the polygon may stand, its principal tendency
on being seriously disturbed will be to fall back towards
the first position ; yet each position is stable within
certain limits.

Consequently the model illustrates how the following
conditions may co- exist : (1) Variability within narrow
limits without prejudice to the purity of the breed.
(2) Partly stable sub-types. (3) Tendency, when much
disturbed, to revert from a sub-type to an earlier form.
(4) Occasional sports which may give rise to new types.

Stability of Sports. — Experience does not show that
those wide varieties which are called ^' sports " are
unstable. On the contrary, they are often transmitted
to successive generations with curious persistence.
Neither is there any reason for expecting otherwise.
While we can well understand that a strained modi-
fication of a type would not be so stable as one that
approximates more nearly to the typical centre, the
variety may be so wide that it falls into difi*erent condi-
tions of stability, and ceases to be a strained modification
of the original type.

The hansom cab was originally a marvellous novelty.
In the language of breeders it was a sudden and re-
markable " sport," yet the suddenness of its appearance
has been no bar to its unchanging hold on popular
favour. It is not a monstrous anomaly of incongruous
parts, and therefore unstable, but quite the contrary.
Many other instances of very novel and yet stable
inventions could be quoted. One of the earliest

III.] ORGANIC STABILITY. 31

electrical batteries was that wliicli is still known as a
Grove battery, being the invention of Sir William Grove.
Its principle was quite new at the time, and it continues
in use without alteration.

The persistence in inheritance of trifling characteristics,
such as a mole, a white tuft of hair, or multiple fingers,
has often been remarked. The reason of it is, I presume,
that such characteristics have inconsiderable influence
upon the general organic stability ; they are mere
excrescences, that may be associated with very different
types, and are therefore inheritable without let or
hindrance.

It seems to me that stability of type, about which we
as yet know very little, must be an important factor in
the general theory of heredity, when the theory is
applied to cases of high breeding. It will be shown
later on, at what point a separate allowance requires
to be made for it. But in the earlier and principal
part of the inquiry, which deals with the inheritance of
qualities that are only exceptional in a small degree, a
separate allowance does not appear to be required.

Infertility of Mixed Types. — It is not difficult to see
in a general way why very different types should refuse
to. coalesce, and it is scarcely possible to explain the
reason why, more clearly than by an illustration. Thus
a useful blend between a four-wheeler and a hansom
would be impossible ; it would have to run on three
wheels and the half-way position for the driver would
be upon its roof A blend would be equally impossible

32 NATURAL INHERITANCE. [chap.

between an omnibus and a hansom, and it would be
difficult between an omnibus and a four-wheeler.

Evolution not hy Minute Steps Only. — The theory
of Natural Selection might dispense wdth a restriction,
for which it is difficult to see either the need or the
justification, namely, that the course of evolution always
proceeds by steps that are severally minute, and that
become effective only through accumulation. That
the steps may be small and that they '}nust be small are
very different views ; it is only to the latter that I
object, and only when the indefinite word *^ small " is used
in the sense of " barely discernible," or as small com-
pared with such large sports as are known to have been
the origins of new races. An apparent ground for the
common belief is founded on the fact that whenever
search is made for intermediate forms between widely
divergent varieties, whether they be of plants or of
animals, of weapons or utensils, of customs, religion or
language, or of any other product of evolution, a long
and orderly series can usually be made out, each member
of which differs in an almost imperceptible degree from
the adjacent specimens. But it does not at all follow
because these intermediate forms have been found to
exist, that they are the very stages that w^ere passed
through in the course of evolution. Counter evidence
exists in abundance, not only of the appearance of con-
siderable sports, but of their remarkable stability in
hereditary transmission. Many of the specimens of
intermediate forms may have been unstable varieties,

III.] ORGANIC STABILITY. 33

whose descendants had reverted ; they might be looked
upon as tentative and faltering steps taken along parallel
courses of evolution, and afterwards retraced. Affiliation
from each generation to the next requires to be proved
before any apparent line of descent can be accepted
as the true one. The history of inventions fully illus-
trates this view. It is a most common experience that
what an inventor knew to be original, and believed to
be new, had been invented independently by others
many times before, but had never become established.
Even when it has new features, the inventor usually
finds, on consulting lists of patents, that other inventions
closely border on his own. Yet we know that inventors
often proceed by strides, their ideas originating in some
sudden happy thought suggested by a chance occurrence,
though their crude ideas may have to be laboriously
worked out afterwards. If, however, all the varieties of
any machine that had ever been invented, were collected
and arranged in a Museum in the apparent order of
their Evolution, each would differ so little from its
neighbour as to suggest the fallacious inference that the
successive inventors of that machine had progressed by
means of a very large number of hardly discernible
steps.

The object of this and of the preceding chapter has
been first to dwell on the fact of inheritance beinof
"particulate," secondly to show how this fact is com-
patible with the existence of various types, some of
which are subordinate to others, and thirdly to argue

34 NATURAL INHERITANCE. [chap. hi.

that Evolution need not proceed by small steps only. I
have largely used metaphor and illustratioD to explain
the facts, wishing to avoid entanglements with theory
as far as possible, inasmuch as no complete theory of
inheritance has yet been propounded that meets with
general acceptation.

CHAPTEK TV,

SCHEMES OF DISTEIBUTION AIN'D OF FEEQUENCY.

Fraternities and Populations to be treated as Units. — Scliemes of Distribu-
tion and their Grades. — The Shape of Schemes is independent of the
number of observations. — Data for Eighteen Schemes. — Application
of the method of Schemes to inexact Measures. — Schemes of Fre-
quency,

Fraternities and Populations to he Treated as Units. —
The science of heredity is concerned with Fraternities
and large Populations rather than with individnals, and
mnst treat them as units. A compendious method is
therefore requisite by which we may express the dis-
tribution of each faculty among the members of any
large group, whether it be a Fraternity or an entire
Population.

The knowledge of an average value is a meagre piece
of information. How little is conveyed by the bald
statement that the average income of English families is
100^. a year, compared with what we should learn if w^e
were told how English incomes were distributed ; what
proportion of our countrymen had just and only just
enough means to ward off starvation, and what were the

D 2

36 NATURAL INHERITANCE. [ohap.

proportions of those who had incomes in each and every
other degree, up to the huge annual receipts of a few
great speculators, manufacturers, and landed proprietors.
So in respect to the distribution of any human quality
or faculty, a knowledge of mere averages tells but little ;
we want to learn how the quality is distributed among
the various members of the Fraternity or of the Popula-
tion, and to express what we know in so compact a
form that it can be easily grasped and dealt with.
A parade of great accuracy is foolish, because precision
is unattainable in biological and social statistics ; their
results being never strictly constant. Over-minuteness
is mischievous, because it overwhelms the mind with
more details than can be compressed into a single
view. We require no more than a fairly just and
comprehensive method of expressing the way in which
each measurable quality is distributed among the
members of any group, whether the group consists
of brothers or of members of any particular social,
local, or other body of persons, or whether it is co-
extensive with an entire nation or race.

A knowledge of the distribution of any quality en-
ables us to ascertain the Eank that each man holds
among his fellows, in respect to that quality. This is
a valuable piece of knowledge in this struggling and
competitive world, where success is to the foremost, and
failure to the hindmost, irrespective of absolute efficiency.
A blurred vision would be above all price to an in-
dividual man in a nation of blind men, though it would
hardly enable him to earn his bread elsewhere. When

IV.] SCHEMES OF DISTRIBUTION AND OF FREQUENCY. 37

tlie distribution of any faculty has been ascertained, we
can tell from the measurement, say of our child, how he
ranks among other children in respect to that faculty,
whether it be a physical gift, or one of health, or of
intellect, or of morals. As the years go by, we may
learn by the same means whether he is making his way
towards the front, whether he just holds his place, or
whether he is falling back towards the rear. Similarly
as regards the position of our class, or of our nation,
among other classes and other nations.

Schemes of Distribution and their Grades. — I shall
best explain my graphical method of expressing Dis-
tribution, which I like the more, the more I use it,
and which I have latterly much developed, by showing
how to determine the Grrade of an individual among his
fellows in respect to any particular faculty. Suppose
that we have already put on record the measures of
many men in respect to Strength, exerted as by an
archer in pulling his bow, and tested by one of Salter's
well-known dial instruments with a movable index.
Some men will have been found strong and others weak ;
how can we picture in a compendious diagram, or how
can we define by figures, the distribution of this faculty
of Strength throughout the group ? How shall we
determine and specify the Grade that any particular
person would occupy in the group ? The first step is
to marshal our measures in the orderly way familiar to
statisticians, which is shown in Table I. I usually work
to about twice its degree of minuteness, but enough

38

NATURAL INHERITANCE.

[chap.

has been entered in the Table for the purpose of
illnstration, while its small size makes it all the more
intellioible.

The fourth column of the Table headed " Percentages "
of " Sums from the beginning," is pictorially translated
into Fig. 2, and the third column headed " Percentages "
of " No. of cases observed," into Fis^. 3. The scale of

FIG. 2.

Us

100

80

-GO

40

•''-20

MiO

FIG. 3.

91

W41

kjil||l|W|i||in

|i'i:nj!iIiiimiI

4D

— r-
20

Ths.

100

so

60

-40

'20

i-0

lbs. is given at the side of both Figs. : and the com-
partments a to g, that are shaded with hrohen lines,
have the same meaning in both, but they are differently
disposed in the two Figs. We will now consider Fig. 2
only, which is the one that principally concerns us.
The percentages in the last column of Table I. have
been marked off on the bottom line of Fig. 2, where
they are called (centesimal) Grades. The number of
lbs. found in the first column of the Table determines

IV.] SCHEMES OF DISTRIBUTION AND OF FREQUENCY. 39

the height of the vertical lines to be erected at the
corresponding Grades when we are engaged in con-
structing the Figure.

Let us bemn with the third line in the Table for
illustration : it tells us that 37 per cent, of the group
had Strengths less than 70 lbs. Therefore, when drawing
the figure, a perpendicular must be raised at the 37th
grade to a height corresponding to that of 70 lbs. on
the side scale. The fourth line in the Table tells us
that 70 per cent, of the group had Strengths less than
80 lbs. ; therefore a perpendicular must be raised at the
70th Grade to a height corresponding to 80 lbs. We
proceed in the same way with respect to the remaining
figures, then we join the tops of these perpendiculars
by straight lines.

As these observations of Strength have been sorted
into only 7 groups, the trace formed by the lines that
connect the tops of the few perpendiculars difi'ers sensibly
from a flowing curve, but when working with double
minuteness, as mentioned above, the connecting lines
difi"er little to the eye from the dotted curve. The
dotted curve may then be accepted as that which would
result if a separate perpendicular had been drawn for
every observation, and if permission had been given
to slightly smooth their irregularities. I call the figure
that is bounded by such a curve as this, a Scheme of
Distribution ; the perpendiculars that formed the scaf-
folding by which it was constructed having been first
rubbed out. (See Fig 4, next page.)

A Scheme enables us in a moment to find the Grade

40

NATURAL INHERITANCE.

[chap.

of Eank (on a scale reckoned from 0° to 100°) of any
person in the gronp to which he belongs. The measured
strength of the person is to be looked for in the side
scale of the Scheme ; a horizontal line is thence drawn
until it meets the curve ; from the point of meeting
a perpendicular is dropped upon the scale of Grades
at the base ; then the G-rade on which it falls is

FIG

.4. 1

y^

-

/

•

100

FIG. 5.

50

£0°

100

IDO"

100*

the one required. For example : let us suppose the
Strength of Pull of a man to have been 74 lbs.,
and that we wish to determine his Eank in Strength
among the large group of men who were measured
at the Health Exhibition in 1884. We find by Fig.
4 that his centesimal Grade is 50°; in other words,
that 50 per cent, of the group will be weaker than
he is, and 50 per cent, will be stronger. His

IV.] SCHEMES OF DISTRIBUTION AND OF FREQUENCY. 41

position will be exactly Middlemost, after tlie Strengths
of all the men in the gronp have been marshalled in
the order of their magnitudes. In other words, he is
of mediocre strength. The accepted term to express
the value that occupies the Middlemost position is
" Median," which may be used either as an adjective or
as a substantive, but it will be usually replaced in this
book by the abbreviated form M. I also use the word
" Mid " in a few combinations, such as " Mid-Fraternity,"
to express the same thing. The Median, M, has three
properties. The first follows immediately from its con-
struction, namely, that the chance is an equal one, of
any previously unknown measure in the group exceeding
or falling short of M. The second is, that the most
probable value of any previously unknown measure in
the group is M. Thus if N be any one of the measures,
and u be the value of the unit in which the measure is
recorded, such as an inch, tenth of an inch, &c., then
the number of measures that fall between (N - ^u) and
(N -\r^u), is greatest when N=: IVI. Mediocrity is always
the commonest condition, for reasons that will become
apparent later on. The third property is that whenever
the curve of the Scheme is symmetrically disposed on
either side of M, except that one half of it is turned
upwards, and the other half downwards, then M is
identical with the ordinary Arithmetic Mean or Average.
This is closely the condition of all the curves I have to
discuss. The reader may look on the Median and on
the Mean as being practically the same things, throughout
this book.

42 NATURAL INHERITANCE. [chap.

It must be understood that M, like the Mean or the
Average, is almost always an interpolated value, corre-
sponding to no real measure. If the observations were
infinitely numerous its position would not differ more
than infinitesimally from that of some one of them ;
even in a series of one or two hundred in number, the
difference is insignificant.

Now let us make our Scheme answer another question.
Suppose we want to know the percentage of men in the
group of which we have been speaking, whose Strength
lies between any two specified limits, as between 74 lbs.
and 64 lbs. We draw horizontal lines (Fig. 4) from
points on the side scale corresponding to either limit,
and drop perpendiculars upon the base, from the points
where those lines meet the curve. Then the number of
Grades in the intercept is the answer. The Fig. shows
that the number in the present case is 30 ; therefore
30 per cent, of the group. have Strengths of Pull ranging
between 74 and 64 lbs.

We learn how to transmute female measures of any
characteristic into male ones, by comparing their respec-
tive schemes, and devising a formula that will change
the one into the other. In the case of Stature, the
simple multiple of 1*08 was found to do this with
sufficient precision.

If we wish to compare the average Strengths of two
different groups of persons, say one consisting of men
and the other of women, we have simply to comjDare
the values at the 50th Grades in the two schemes. For
even if the Medians difi'cr considerably from the Means,

IV.] SCHEMES OF DISTRIBUTION AND OF FREQUENCY. 43

both the ratios and the differences between either pair of
values would be sensibly the same.

A different way of comparing two Schemes is some-
times useful. It is to draw them in opposed directions,
as in Fig. 5, p. 40. Their curves will then cut each
other at some point, whose Grade when referred to
either of the two Schemes (whichever of them may be
preferred), determines the point at which the same
values are to be found. In Fig. 5, the Grade in the
one Scheme is 20° ; therefore in the other Scheme it is
100°- 20°, or 80°. In respect to the Strength of Pull
of men and women, it appears that the woman who
occupies the Grade of 96° in her Scheme, has the same
strength as the man who occupies the Grade of 4° in his
Scheme.

I should add that this great inequality in Strength
between the sexes, is confirmed by other measure-
ments made at the same time in respect to the
Strength of their Squeeze, as tested by another of
Salter's instruments. Then the woman in the 93rd and
the man in the 7th Grade of their resective Schemes,
proved to be of equal strength. In my paper ^ on the
results obtained at the laboratory, I remarked : " Yery
powerful women exist, but happily perhaps for the
repose of the other sex such gifted women are rare.
Out of 1,657 adult women of all ages measured at the
laboratory, the strongest could only exert a squeeze of
86 lbs., or about that of a medium man."

1 Journ. Anthropol. Inst. 1885. Mem. : There is a blunder in the para-
graph, p. 23, headed "Height Sitting and Standing." The paragraph
should be struck out.

44 NATURAL INHERITANCE. [chap.

The Shape of Schemes is Independent of the Number
of Observations. — When Schemes are drawn from dif-
ferent samples of the same large group of measurements,
though the number in the several samples may differ
greatly, we can always so adjust the horizontal scales
that the breadth of the several Schemes shall be uniform.
Then the shaj)es of the Schemes drawn from different
samples will be little affected by the number of observa-
tions used in each, supposing of course that the numbers
are never too small for ordinary statistical purposes.
The only recognisable differences between the Schemes
will be, that, if the number of observations in the
sample is very large, the upper margin of the Scheme
will fall into a more regular curve, especially towards
either of its limits. Some irregularity will be found in
the above curve of the Strength of Pull ; but if the
observations had been ten times more numerous, it is
probable, judging from much experience of such curves,
that the irregularity would have been less consjoicuous,
and perhaps would have disappeared altogether.

However numerous the observations may be, the
curve will always be uncertain and incomplete at its
extreme ends, because the next value may happen to be
greater or less than any one of those that preceded it.
Again, the position of the first and the last observation,
supposing each observation to have been laid down sepa-
rately, can never coincide with the adjacent limit. The
more numerous the observations, and therefore the closer
the perpendiculars by which they are represented, the
nearer will the two extreme perpendiculars approach the

IV] SCHEiMES OF DISTRIBUTION AND OF FREQUENCY. 45

limits, but they will never actually touch them. A chess
board has eight squares in a row, and eight pieces may be
arranged in order on any one row, each piece occupying
the centre of a square. Let the divisions in the row be
graduated, calling the boundary to the extreme left,
0°. Then the successive divisions between the squares
will be 1°, 2°, 3°, up to 7°, and the boundary to the
extreme right will be 8°. It is clear that the position of
the first piece lies half-way between the grades (in a
scale of eight grades) of 0° and 1° ; therefore the grade
occupied by the first piece would be counted on that
scale as 0*5°; also the grade of the last piece as 7 '5°.
Or again, if we had 800 pieces, and the same number
of class-places, the grade of the first piece, in a scale
of 800 grades, would exceed the grade 0°, by an amount
equal to the width of one half-place on that scale,
while the last of them would fall short of the 800th
grade by an equal amount. This half-place has to be
attended to and allowed for when schemes are con-
structed from comparatively few observations, and
always when values that are very near to either of the
centesimal grades 0° or 100° are under observation ;
but between the centesimal grades of 5° and 95° the
influence of a half class-place upon the value of the
corresponding observation is insignificant, and may be
disregarded. It will not henceforth be necessary to
repeat the word centesimal. It will be always implied
when nothing is said to the contrary, and nothing
henceforth will be said to the contrary. The word will
be used for the last time in the next paragraph.

46 NATURAL INHERITANCE. [chap.

Data for Eighteen Schemes. — Sufficient data for re-
constructing any Scheme, witli niucli correctness, may
be printed in a single line of a Table, and according to
a uniform plan tbat is suitable for any kind of values.
The measures to be recorded are those at a few definite
G-rades, beginning say at 5°, ending at 95°, and including
every intermediate tenth Grade from 10° to 90°. It is
convenient to add those at the Grades 25° and 75°, if
space permits. The former values are given for eighteen
different Schemes, in Table 2. In the memoir from
which that table is reprinted, the values at what I now
call (centesimal) Grades, were termed Percentiles. Thus
the values at the Grades 5° and 10° would be respectively
the 5th and the 10th percentile. It still seems to me
that the word percentile is a useful and expressive
abbreviation, but it will not be necessary to employ it
in the present book. It is of course unadvisable to use
more technical words than is absolutely necessary, and
it will be possible to get on without it, by the help of
the new and more important word " Grade."

A series of Schemes that express the distribution of
various faculties, is valuable in an anthropometric labora-
tory, for they enable every person who is measured to
find his Rank or Grade in each of them.

Diagrams may also be constructed by drawing parallel
lines, each divided into 100 Grades, and entering each
round number of inches, lbs., &c., at their proper places.
A diagram of this kind is very convenient for reference,
but it does not admit of being printed ; it must be
drawn or lithographed. I have constructed one of these

IV.] SCHEMES OF DISTRIBUTION AND OF FREQUENCY. 47

from tlie 18 Schemes, and find it is easily understood
and mucli used at my laboratory.

Application of Schemes to Inexact Measures. — Schemes
of Distribution may be constructed from observations
that are barely exact enough to deserve to be called
measures.

I will illustrate the method of doing so by marshalling
the data contained in a singularly interesting little
memoir written by Sir James Paget, into the form of
such a Scheme. The memoir is published in vol. v. of St.
Bartholomew's Hospital Eeports, and is entitled " What
Becomes of Medical Students." He traced with great
painstaking the career of no less than 1,000 pupils who
had attended his classes at that Hospital during various
periods and up to a date 15 years previous to that at
which his memoir was written. He thus did for St.
Bartholomew's Hospital what has never yet been done,
so far as I am aware, for any University or Public
School, whose historians count the successes and are
silent as to the failures, giving to inquirers no adequate
data for ascertaining the real value of those institutions
in English Education. Sir J. Paget divides the successes
of his pupils in their profession into fiYQ grades, all of
which he carefully defines ; they are distinguished ;
considerable ; moderate ; very limited success ; and
failures. Several of the students had left the profes-
sion either before or after taking their degrees, usually
owing to their unfitness to succeed, so after analysing
the accounts of them given in the memoir, I drafted

48 NATURAL INHERITANCE. [chap.

several into the list of failures and distributed the rest,
with the result that the number of cases in the successive
classes, amounting now to the full total of 1,000, became
28, 80, 616, 151, and 125. This differs, I should say,
a Kttle from the inferences of the author, but the matter
is here of small importance, so I need not go further into
details.

If a Scheme is drawn from these figures, in the way
described in page 39, it will be found to have the
characteristic shape of our familiar curve of Distribution.
If we wished to convey the utmost information that this
Scheme is capable of giving, we might record in much
detail the career of two or three of the men who are
clustered about each of a few selected Grades, such as
those that are used in Table 11. , or fewer of them. I
adopted this method when estimating the variability of
the Visualising Power (Inquiries into Human Faculty).
My data were very lax, but this method of treatment
got all the good out of them that they possessed. In
the present case, it appears that towards the foremost
of the successful men within fifteen years of taking
their degrees, stood the three Professors of Anatomy
at Oxford, Cambridge, and Edinburgh ; that towards
the bottom of the failures, lay two men who committed
suicide under circumstances of great disgrace, and lowest
of all Palmer, the Rugeley murderer, who was hanged.

We are able to compare any two such Schemes as the
above, with numerical precision. The want of exactness
in the data from which they are drawn, will of course
cling to the result, but no new error will l^e introduced

IV.] SCHEMES OF DISTRIBUTION AND OF FREQUENCY. 49

by the process of comparison. Suppose the second
Scheme to refer to the successes of students from another
hospital, we should draw the two Schemes in opposed
directions, just as was done in the Strength of Pull of
Males and Females, Fig. 5, and determine the Grrade
in either of the Schemes at which success was equal.

Schemes of Frequency. — The method of arranging
observations in an orderly manner that is generally
employed by statisticians, is shown in Fig. 3, page 38,
which expresses the same facts as Fig. 2 under a different
aspect, and so gives rise to the well-known Curve of
"Frequency of Error," though in Fig. 3 the curve is
turned at right angles to the position in which it is
usually drawn. It is so placed in order to show more
clearly its relation to the Curve of Distribution. The
Curve of Frequency is far less convenient than that of
Distribution, for the purposes just described and for
most of those to be hereafter spoken of. But the Curve
of Frequency has other uses, of which advantage will
be taken later on, and to which it is unnecessary now
to refer.

A Scheme as explained thus far, is nothing more than
a compendium of a mass of observations which, on being
marshalled in an orderly manner, fall into a diagram
whose contour is so regular, simple, and bold, as to
admit of being described by a few numerals (Table 2),
from which it can at any time be drawn afresh. The
regular distribution of the several faculties among a
large population is little disturbed by the fact that its

E

50 NATURAL INHERITANCE. [chap. iv.

members are varieties of different types and sub-types.
So the distribution of a heavy mass of foliage gives little
indication of its growth from separate twigs, of separate
branches, of separate trees.

The application of theory to Schemes, their approxi-
mate description by only two values, and the properties
of their bounding Curves, will be described in the next
chapter.

CHAPTER y.

NOEMAL VAEIABILITY.

Schemes of Deviations. — Normal Curve of Distribution. — Comparison of
the observed with the Normal Curve. — Tlie value of a single Devia-
tion at a known Grade determines a Normal Scheme of Deviations. —
Two Measures at two known Grades determine a Normal Scheme
of Measures. — The Charms of Statistics. — Mechanical illustration of
the Cause of the Curve of Frequency. — Order in apparent Chaos. —
Problems in the Law of Error.

Schemes of Deviations. — We have now seen how easy
it is to represent the distribution of any qnality among a
multitude of men, either by a simple diagram or by a line
containing a few figures. In this chapter it will be shown
that a considerably briefer description is approximately
sufficient.

Every measure in a Scheme is equal to its Middlemost,
or Median value, or ^,plus or minus a certain Devia-
tion from M. The Deviation, or "Error" as it is
technically called, is plus for all grades above 50°, zero
for 50°, and minus for all grades below 50°. Thus if
(±D) be the deviation from IVI in any particular case,
every measure in a Scheme may be expressed in the

E 2

52 NATURAL INHERITANCE. [chap.

form of IV1 + (±D). If IVI = 0, or if it is subtracted
from every measure, the residues wliicli are tlie different
values of ( ± D) will form a Scheme by themselves.
Schemes may therefore be made of Deviations as well as
of Measures, and one of the former is seen in the
upper part of Fig. 6, page 40. It is merely the upper
portion of the corresponding Scheme of Measures, in
which the axis of the curve plays the part of the base.

A strong family likeness runs between the 1 8 different
Schemes of Deviations that may be respectively derived
from the data in the 18 lines of Table 2. If the slope
of the curve in one Scheme is steeper than that of
another, we need only to fore-shorten the steeper
Scheme, by inclining it away from the line of sight, in
order to reduce its apparent steepness and to make it
look almost identical with the other. Or, better still,
we may select appropriate vertical scales that will enable
all the Schemes to be drawn afresh with a uniform slope,
and be made strictly comparable.

Suppose that we have only two Schemes, A. and b.,
that we wish to compare. Let L.i, L.2 be the lengths of
the perpendiculars at two specified grades in Scheme A.,
and K.i K.2 the lengths of those at the same grades in
Scheme b. ; then if every one of the data from which

Scheme b. was drawn be multiplied by ^^ ^'^' , a

series of transmuted data will be obtained for drawing
a new Scheme b'., on such a vertical scale that its
general slope between the selected grades shall be the
same as in Scheme A. For practical convenience the

v.] NORMAL VARIABILITY. 53

selected Grades will be always those of 25° and 75°.
They stand at the first and third quarterly divisions of
the base, and are therefore easily found by a pair of
compasses. They are also well placed to afford a fair
criterion of the general slope of the Curve. If we call
the perpendicular at 25°, Q.i ; and that at 75°, Q.2,
then the unit by which every Scheme will be defined
is its value of -^(0.2- Q-i), and will be called its
Q. As the M measures the Average Height of the
curved boundary of a Scheme, so the Q measures its
general slope. When we wish to transform many difi'er-
ent Schemes, numbered I., II., III., &c., whose respective
values of Q are qi, q^, q^, Sec, to others whose values of Q
are in each case equal to qo, then all the data from which

Scheme I. was drawn, must be multiplied by ^ ; those

from which Scheme II. was drawn, by ^, and so on, and

new Schemes have to be constructed from these trans-
muted values.

Our Q has the further merit of being practically the
same as the value which mathematicians call the
" Probable Error," of which we shall speak further on.

Want of space in Table 2 prevented the insertion of
the measures at the Grades 25° and 75°, but those at
20° and 30° are given on the one hand, and those at 70**
and 80° on the other, whose respective averages diff'er
but little from the values at 25° and 75°. I therefore
will use those four measures to obtain a value for our
unit, which we will call Q^, to distinguish it from Q.

54 NATURAL INHERITANCE. [chap.

These are not identical in value, because the outline of
the Scheme is a curved and not a straight line, but the
difference between them is small, and is approximately
the same in all Schemes. It will shortly be seen that
Q'= 1*015 xQ approximately; therefore a series of De-
viations measured in terms of the large unit Q' are
numerically smaller than if they had been measured in
terms of the small unit (for the same reason that the
numerals in 2, 3, kQ.^feet are smaller than those in the
corresponding values of 24, 36, &c., inches), and they
must be multiplied by 1.015 when it is desired to
change them into a series having the smaller value of Q
for their unit.

All the 18 Schemes of Deviation that can be derived
from Table 2 have been treated on these principles, and
the results are given in Table 3. Their general accord-
ance with one another, and still more with the mean of
all of them, is obvious.

Normal Curve of Distribution. — The values in the
bottom line of Table 3, which is headed " Normal Values
when Q = 1," and which correspond with minute pre-
cision to those in the line immediately above them, are
not derived from observations at all, but from the well-
known Tables of the " Probability Integral " in a way
that mathematicians will easily understand by comparing
the Tables 4 to 8 inclusive. I need hardly remind the
reader that the Law of Error upon which these Normal
Values are based, was excogitated for the use of astro-
nomers and others who are concerned with extreme

v.] NORMAL VARIABILITY. 55

accuracy of measurement, and without tlie slightest idea
until the time of Quetelet that they might be applicable
to human measures. But Errors, Differences, Deviations,
Divergencies, Dispersions, and individual Variations, all
spring from the same kind of causes. Objects that bear
the same name, or can be described by the same phrase,
are thereby acknowledged to have common points of
resemblance, and to rank as members of the same species,
class, or whatever else we may please to call the group.
On the other hand, every object has Differences peculiar
to itself, by which it is distinguished from others.

This general statement is applicable to thousands of
instances. The Law of Error finds a footing wherever
the individual peculiarities are wholly due to the com-
bined influence of a multitude of " accidents," in the
sense in which that word has already been defined.
All persons conversant with statistics are aware that
this supposition brings Variability within the grasp
of the laws of Chance, with the result that the
relative frequency of Deviations of different amounts
admits of being calculated, when those amounts are
measured in terms of any self-contained unit of varia-
bility, such as our Q. The Tables 4 to 8 give the
results of these purely mathematical calculations, and
the Curves based upon them may with propriety be
distinguished as '' Normal." Tables 7 and 8 are based
upon the familiar Table of the Probability Integral,
given in Table 5, via that in Table 6, in which the unit
of variability is taken to be the " Probable Error " or
our Q, and not the "Modulus." Then I turn Table 6

56 NATURAL INHERITANCE. [chap.

inside out, as it were, deriving the " arguments " for
Tables 7 and 8 from tlie entries in the body of Table 6,
and making other easily intelligible alterations.

Comparison of the Observed ivith the Normal Curve.
— I confess to having been amazed at the extraordinary
coincidence between the two bottom lines of Table 3,
considering the great variety of faculties contained in
the 1 8 Schemes ; namely, three kinds of linear measure-
ment, besides one of weight, one of capacity, two of
strength, one of vision, and one of swiftness. It is
obvious that weight cannot really vary at the same rate
as height, even allowing for the fact that tall men are
often lanky, but the theoretical impossibility is of the
less practical importance, as the variations in weight are
small compared to the weight itself. Thus we see from
the value of Q in the first column of Table 3, that half
of the persons deviated from their M by no more than
10 or 11 lbs., which is about one-twelfth part of the
value of IVI. Although the several series in Table 3 run
fairly well together, I should not have dared to hope
that their irregularities would have balanced one another
so beautifully as they have done. It has been objected
to some of my former work, especially in Hereditary
Genius, that I pushed the applications of the Law of
Frequency of Error somewhat too far. I may have done
so, rather by incautious phrases than in reality ; but
I am sure that, with the evidence now before us, the
applicability of that law is more than justified within
the reasonable limits asked for in the present book. I

v.] NORMAL VARIABILITY. 57

am satisfied to claim that the Normal Curve is a fair
average representation of the Observed Curves during
nine-tenths of their course ; that is, for so much of
them as lies between the grades of 5° and 95°. In
particular, the agreement of the Curve of Stature with
the Normal Curve is very fair, and forms a mainstay of
my inquiry into the laws of Natural Inheritance.

It has already been said that mathematicians laboured
at the law of Error for one set of purposes, and we
are entering into the fruits of their labours for another.
Hence there is no ground for surprise that their Nomen-
clature is often cumbrous and out of place, when applied
to problems in heredity. This is especially the case
with regard to their term of " Probable Error," by which
they mean the value that one half of the Errors exceed
and the other half fall short of This is practically the
same as our Q.-^ It is strictly the same whenever the
two halves of the Scheme of Deviations to which it
applies are symmetrically disposed about their common
axis.

The term Probable Error, in its plain English inter-
pretation of the most Probable Error, is quite mis-
leading, for it is not that. The most Probable Error
(as Dr. Venn has pointed out, in his Logic of Chance)

1 The following little Table may be of service : —

Values of the different Constants when the Proh. Error is tahen as unity, and

their corresponding Grades.

Prob. Error I'OOO

Modulus 2-097

Mean Error 1-183

Error of Mean Squares 1-483

corresponding Grades 25°-0, 75° -0

r-9, 92°-l
„ „ 21°-2, 78°-8

16°-0, 84°-0

58 NATURAL INHERITANCE. [chap.

is zero. This results from what was said a few pages
back about the most probable measure in a Scheme
being its IVI. In a Scheme of Errors the M is equal to
0, therefore the most Probable Error in such a Scheme
is 0 also. It is astonishing that mathematicians, who
are the most precise and perspicacious of men, have not
long since revolted against this cumbrous, slip-shod,
and misleading phrase. They really mean what I
should call the Mid-Error, but their phrase is too firmly
established for me to uproot it. I shall however always
write the word Probable when used in this sense, in the
form of " Prob. " ; thus " Prob. Error," as a continual
protest against its illegitimate use, and as some slight
safeguard against its misinterpretation. Moreover the
term Probable Error is absurd when applied to the
subjects now in hand, such as Stature, Eye-colour,
Artistic Faculty, or Disease. I shall therefore usually
speak of Prob. Deviation.

Though the value of our Q is the same as that of
the Prob. Deviation, Q is not a convertible term with
Prob. Deviation. We shall often have to speak of the
one without immediate reference to the other, just as
we speak of the diameter of the circle without reference
to any of its properties, such as, if lines are drawn from
its ends to any point in the circumference, they will
meet at a right angle. The Q of a Scheme is as de-
finite a phrase as the Diameter of a Circle, but we
cannot replace Q in that phrase by the words Prob.
Deviation, and speak of the Prob. Deviation of a
Scheme, without doing some violence to lanoaiao^e. We

v.] NORMAL VARIABILITY. 59

should have to express ourselves from another point of
view, and at much greater length, and say "the Prob.
Deviation of any, as yet unknown measure in the Scheme,
from the Mean of all the measures from which the
Scheme was constructed."

The primary idea of Q has no reference to the existence
of a Mean value from which Deviations take place. It
is half the difference between the measures found at the
25th and 75th Centesimal Grades. In this definition
there is not the slightest allusion, direct or indirect, to
the measure at the 50th Grade, which is the value of M.
It is perfectly true that the measure at Grade 25° is
IVI — Q, and that at Grade 75° is IVI + Q, but all this is
superimposed upon the primary conception. Q stands
essentially on its own basis, and has nothing to do with
IVI. It will often happen that we shall have to deal
with Prob : Deviations, but that is no reason why we
should not use Q whenever it suits our purposes better,
especially as statistical statements tend to be so cum-
brous that every abbreviation is welcome.

The stage to which we have now arrived is this. It
has been shown that the distribution of very different
human qualities and faculties is approximately Normal,
and it is inferred that with reasonable precautions we
may treat them as if they were wholly so, in order to
obtain approximate results. We shall thus deal with an
entire Scheme of Deviations in terms of its Q, and with
an entire Scheme of Measures in terms of its IVI and Q,
just as we deal with an entire Circle in terms of its

60 NATURAL INHERITANCE. [chap.

radius, or with an entire Ellipse in terms of its major
and minor axes. We can also apply tlie various beau-
tiful properties of the Law of Frequency of Error to
the observed values of Q. In doing so, we act like
woodsmen who roughly calculate the cubic contents of
the trunk of a tree, by measuring its length, and its girth
at either end, and submitting their measures to formulae
that have been deduced from the properties of ideally
perfect straight lines and circles. Their results prove
serviceable, although the trunk is only rudely straight
and circular. I trust that my results will be yet closer
approximations to the truth than those usually arrived
at by the woodsmen.

The value of a single Deviation at a known Grade
determines a Normal Scheme of Deviations, — When
Normal Curves of Distribution are drawn within the
same limits, they differ from each other only in their
general slope ; and the slope is determined if the value
of the Deviation is given at any one specified G-rade.
It must be borne in mind that the width of the limits
between which the Scheme is drawn, has no influence on
the values of the Deviations at the various Grades,
because the latter are proportionate parts of the base.
As the limits vary in width, so do the intervals between
the Grades. When measuring the Deviation at a speci-
fied Grade for the purpose of determining the whole
Curve, it is of course convenient to adhere to the same
Grade in all cases. It will be recollected that when
dealing with the observed curves a few pages back, I

v.] NORMAL VARIABILITY. 61

used not one Grade but two Grades for the purpose,
namely 25° and 75° ; but in tbe Normal Curve, the
plus and minus Deviations are equal in amount at all
pairs of symmetrical distances on either side of grade
50° ; therefore the Deviation at either of the Grades 25°
or 75° is equal to Q, and suffices to define the entire
Curve.

The reason why a certain value Q' was stated a few
pages back to be equal to 1'015 Q, is that the Normal
Deviations at 20° and at 30°, (whose average we called
Q') are found in Table 8, to be 1*25 and 078; and
similarly those at 70° and 60°. The average of 1*25
and 0"78 is 1'015, whereas the Deviation at 25° or at
75° is 1-000.

Tivo Measures at known Grades determine a Normal
Scheme of Measures. — If we know the value of IVI as
well as that of Q we know the entire Scheme. IVI ex-
presses the mean value of all the objects contained in
the group, and Q defines their variability. But if we
know the Measures at any two specified Grades, we can
deduce IVI and Q from them, and so determine the entire
Scheme. The method of doing this is explained in the
foot-note.^

1 The following is a fuller description of the propositions in this and
in the preceding paragraph : —

(1) In any Normal Scheme, and therefore approximately in an observed
one, if the value of the Deviation is given at any one specified Grade the
whole Curve is determined. Let D he the given Deviation, and d the
tabular Deviation at the same Grade, as found in Table 8 ; then multiply

every entry in Table 8 ^J—r. As the tabular value of |J is 1, it will become

changed into _.
^ d

62 NATURAL INHERITANCE. [chap.

The Charms of Statistics. — It is difficult to under-
stand why statisticians commonly limit their inquiries
to Averages, and do not revel in more comprehensive
views. Their souls seem as dull to the charm of variety
as that of the native of one of our flat English counties,
whose retrospect of Switzerland was that, if its moun-
tains could be thrown into its lakes, two nuisances
would be got rid of at once. An Average is but a
solitary fact, whereas if a single other fact be added to
it,, an entire Normal Scheme, which nearly corresponds
to the observed one, starts potentially into existence.

Some people hate the very name of statistics, but I
find them full of beauty and interest. Whenever they
are not brutalised, but delicately handled by the higher
methods, and are warily interpreted, their power of
dealing with complicated phenomena is extraordinary.
They are the only tools by which an opening can be cut

(2) If the Measures at any two specified Grades are given, the whole
Scheme of Measures is thereby determined. Let ^, 5 be the two given
Measures of which A is the larger, and let a, h be the values of the tabular
Deviations for the same Grades, as found in Table 8, not omitting their
signs of jplus or minus as the case may be.

A —B

Then the (J of the Scheme = ± j . (The sign of |J is not to be re-
garded ; it is merely a magnitude.)

\^ = A - a^; ot\^ = B - h[^.

Example : A^ situated at Grade 55°, = 14*38
B, situated at Grade 5", = 9*12
The corresponding tabular Deviations are : — a = -j-0'19; h — — 2 •44.

Therefore R = '^'^^ " ^^'^ =^^= 2-0
^ 0-19 H- 2-44 2-63

M = 14.38 - 0-19 X 2 = 14-0
or = 9-12 + 2-44 X 2 = 14*0

v.]

NORMAL VARIABILITY.

63

through the formidable thicket of difficulties that bars
the path of those who pursue the Science of man.

Mechanical Illustration of the Cause of the Curve of
Frequency. — The Curve of Frequency, and that of Dis-
tribution, are convertible : therefore if the genesis of either
of them can be made clear, that of the other becomes
also intelligible. I shall now illustrate the origin of the
Curve of Frequency, by means of an apparatus shown in
Fig. 7, that mimics in a very pretty way the conditions

FIG.T.

/

^

V

\

•

•

/

/

1

•

N

15

FIG .8.

A

B

FIG .9.

A

B

r

1

V

>

(

c

/

/

ft
•

/

f

on which Deviation depends. It is a frame glazed in
front, leaving a depth of about a quarter of an inch be-
hind the glass. Strips are placed in the upper part to act
as a funnel. Below the outlet of the funnel stand a

64 NATURAL INHERITANCE. [chap.

succession of rows of pins stuck squarely into tlie back-
board, and below these again are a series of vertical
compartments. A charge of small sliot is inclosed.
When the frame is held topsy-turvy, all the shot runs
to the upper end ; then, when it is turned back into
its working position, the desired action commences.
Lateral strips, shown in the diagram, have the effect of
directing all the shot that had collected at the upper
end of the frame to run into the wide mouth of the
funnel. The shot passes through the funnel and issuing
from its narrow end, scampers deviously down through
the pins in a curious and interesting way ; each of them
darting a step to the right or left, as the case may be,
every time it strikes a pin. The pins are disposed in a
quincunx fashion, so that every descending shot strikes
against a pin in each successive row. The cascade
issuing from the funnel broadens as it descends, and, at
length, every shot finds itself caught in a compartment
immediately after freeing itself from the last row of
pins. The outline of the columns of shot that accumulate
in the successive compartments approximates to the
Curve of Frequency (Fig. 3, p. 38), and is closely of
the same shape however often the experiment is re-
peated. The outline of the columns would become more
nearly identical with the Normal Curve of Frequency,
if the rows of pins were much more numerous, the shot
smaller, and the compartments narrower ; also if a larger
quantity of shot w^as used.

The principle on which the action of the apparatus
depends is, that a number of small and independent

v.] NORMAL VARIABILITY. 65

accidents befall each sliot in its career. In rare cases,
a long run of luck continues to favour the course of
a particular shot towards either outside place, but in
the large majority of instances the number of accidents
that cause De^dation to the right, balance in a greater
or less degree those that cause Deviation to the left.
Therefore most of the shot finds its way into the com-
partments that are situated near to a perpendicular line
drawn from the outlet of the funnel, and the Frequency
with which shots stray to different distances to the right
or left of that line diminishes in a much faster ratio
than those distances increase. This illustrates and
explains the reason why mediocrity is so common.

If a larger quantity of shot is put inside the apparatus,
the resulting curve will be more humped, but one half
of the shot win stiU faU within the same distance as
before, reckoning to the right and left of the perpen-
dicular line that passes through the mouth of the
funnel. This distance, which does not vary with the
quantity of the shot, is the " Prob : Error," or " Prob :
Deviation," of any single shot, and has the same value
as our Q. But a Scheme of Frequency is unsuitable
for finding the values of either IVI or Q. To do so, we
must divide its strangely shaped area into four equal
parts by vertical lines, which is hardly to be efi'ected
except by a tedious process of " Trial and Error." On
the other hand iVI and Q can be derived from Schemes
of Distribution with no more trouble than is needed to
divide a line into four equal parts.

F

66 NATURAL INHERITANCE. [chap.

Order in Apparent Chaos. — I know of scarcely any-
thing so apt to impress tlie imagination as the wonderful
form of cosmic order expressed by the " Law of Fre-
c|iiency of Error." The law would have been personified
by the Greeks and deified, if they had known of it. It
reigns v/ith serenity and in complete self-effacement
amidst the wildest confusion. The huger the mob, and
the greater the apparent anarchy, the more perfect is its
sway. It is the supreme law of Unreason. Whenever
a large sample of chaotic elements are taken in hand
and marshalled in the order of their magnitude, an un-
suspected and most beautiful form of regularity proves
to have been latent all along. The tops of the mar-
shalled row form a flowing curve of invariable pro-
portions ; and each element, as it is sorted into place,
finds, as it were, a pre-ordained niche, accurately
adapted to fit it. If the measurement at any two
specified Grades- in the row are known, those that will
be found at every other Grade, except towards the
extreme ends, can be predicted in the way already
explained, and with much precision.

Prohlems in the Lain of Brror. — All the properties of
the Law of Frequency of Error can he expressed in
terms of Q, or of the Prob: Error, just as those of a
circle can be expressed in terms of its radius. The
visible Schemes are not, however, to be removed too
soon from our imagination. It is always well to retain
a clear geometric view of the facts when we are dealing
with statistical problems, which abound with dangerous

v.] NORMAL VARIABILITY. G7

pitfalls, easily overlooked by the unwary, while they are
cantering gaily along upon their arithmetic. The Laws
of Error are beautiful in themselves and exceedingly
fascinating to inquirers, owing to the thoroughness and
simplicity with which they deal with masses of materials
that appear at first sight to be entanglements on the
largest scale, and of a hopelessly confused description.
I will mention five of the laws.

(1) The following is a mechanical illustration of the
first of them. In the apparatus already described, let q
stand for the Prob: Error of any one of the shots
that are dispersed among the compartments BB at its
base. Now cut the apparatus in two parts, horizontally
through the rows of pins. Separate the parts and interpose
a row of vertical compartments A A, as in Fig. 8, p. 63,
where the bottom compartments, BB, corresponding to
those shown in Fig. 7, are reduced to half their depth, in
order to bring the whole figure within the same sized
outline as before. The compartments BB are still deep
enough for their purpose. It is clear that the inter-
polation of the AA compartments can have no ultimate
efi'ect on the final dispersion of the shot into those at
BB. Now close the bottoms of all the AA compart-
ments ; then the shot that falls from the funnel will be
retained in them, and will be comparatively little dis-
persed. Let the Prob: Error of a shot in the AA com-
partments be called a. Next, open the bottom of any
one of the AA compartments ; then the shot it contains
will cascade downwards and disperse themselves among
the BB compartments on either side of the per|)endicu-

F 2

08 NATURAL INHERITANCE. [chap

lar line drawn from its starting point, and each sliot
will liave a Prob: Error tliat we will call h. Do this
for all the AA compartments in turn ; h will be the
same for all of them, and the final result must be to re-
produce the identically same system in the BB com-
partments that was shown in Fig. 7, and in which each
shot had a Prob: Error of q.

The dispersion of the shot at BB may therefore be
looked upon as compounded of two superimposed and
independent systems of dispersion. In the one, when
acting singly, each shot has a Prob: Error of a ; in
the other, when acting singly, each shot has a Prob:
Error of h, and the result of the two acting together is
that each shot has a Prob: Error of q. What is the
relation between a, h, and q ? Calculation shows that
q^ = a^-\- h^. In other words, q corresponds to the hypo-
thenuse of a right-angled triangle of which the other two
sides are a and h respectively.

(2) It is a coroUary of the foregoing that a system Z,
in which each element is the Sum of a couple of inde-
pendent Errors, of which one has been taken at random
from a Normal system A and the other from a Normal
system B, will itself be Normal.^ Calling the Q of the Z
system q, and the Q of the A and B systems respectively,
a and h, then g^ = a^ + h^.

1 We may see tlie rationale of this corollary if we invert part of the
statement of the problem. Instead of saying that an a element deviates
from its m, and that a b element also deviates independently from its m, we
may phrase it thus : An a element deviates from its M, and its M deviates
from the b element. Therefore the deviation of the b element from the
A element is compounded of two independent deviations, as in Prohlem 1.

v.] NORMAL VARIABILITY. 69

(3) Suppose that a row of compartments, whose upper
openings are situated like those in Fig. 7, page 63, arc
made first to converge towards some given point below,
but that before reaching it their sloping course is
checked and they are thenceforward allowed to drop
vertically as in Fig. 9. The effect of this will be to
compress the heaj) of shot laterally ; its outline will still
be a Curve of Frequency, but its Prob: Error will be
diminished.

The foregoing three proj)erties of the Law of Error are
well known to mathematicians and require no demon-
stration here, but two other properties that are not
familiar will be of use also ; proofs of them by ISir. J.
Hamilton Dickson are given in Appendix B. They are
as follows. I purposely select a different illustration to
that used in the Appendix, for the sake of presenting
the same general problem under more than one of its
applications.

(4) Bullets are fired by a man who aims at the centre
of a target, which we will call its M, and we will suppose
the marks that the bullets make to be painted red, for
the sake of distinction. The system of lateral deviations
of these red marks from the centre IVI will be approxi-
mately Normal, whose Q we will call c. Then another
man takes aim, not at the centre of the target, but at
one or other of the red marks, selecting these at random.
We will suppose his shots to be painted green. The
lateral distance of any green shot from the red mark
at which it was aimed will have a Prob: Error that we

70 NATURAL INHERITANCE. [chap. v.

will call h. Now, if the lateral distance of a particular
green mark from IVI is given, what is the most prohahle
distance from IVI of the red mark at which it was aimed ?

(5) What is the Prob: Error of this determination ?

In other words, if estimates have been made for a great

many distances founded upon the formula in (4), they

would be correct on the average, though erroneous in

particular cases. The errors thus made would form a

normal system whose Q it is desired to determine. Its

1 • he
value IS -—— ^

Vip' + c^)

By the help of these five problems the statistics of
heredity become perfectly manageable. It will be
found that they enable us to deal with Fraternities,
Populations, or other Groups, just as if they were units.
The largeness of the number of individuals in any of
our groups is so far from scaring us, that they are actu-
ally welcomed as making the calculations more sure
and none the less simple.

CHAPTEE VI.

DATA.

EecorJs of rainilj Faculties, or E. F. F. data. — Special Data. — Measures
at my AntLropometric Laboratory. — Experiments on Sweet Peas.

I HAD to collect all my data for myself, as nothing
existed, so far as I know, that would satisfy even my
primary requirement. This was to obtain records of at
least two successive generations of some population of
considerable size. They must have lived under con-
ditions that were of a usual kind, and in which no great
varieties of nurture were to be found. Natural selection
must have had little influence on the characteristics
that were to be examined. These must be measurable,
variable, and fairly constant in the same individual.
The result of numerous inquiries, made of the most
competent persons, was that I began my experiments
many years ago on the seeds of sweet peas, and that
at the present time I am breeding moths, as will be
explained in a later chapter, but this book refers to
a human population, which, take it all in all, is the
easiest to work with when the data are once ol:>tained,

72 NATURAL INHERITANCE. [chap.

to say notliing of its being more interesting by far than
one of sweet peas or of moths.

Record of Family Faculties, or R.F.F. Data. — The
source from which the larger part of my data is derived
consists of a valuable collection of " Kecords of Family
Faculties," obtained through the offer of prizes. They
have been much tested and cross-tested, and have borne
the ordeal very fairly, so far as it has been applied. It
is well to reprint the terms of the published offer, in
order to give a just idea of the conditions under which
they were compiled. It was as follows :

'' Mr. Francis Galton offers 500^. in prizes to those
British Subjects resident in the United Kingdom who
shall furnish him before May 15, 1884, with the best
Extracts from theii* own Family Eecords.

" These Extracts will be treated as confidential docu-
ments, to be used for statistical purposes only, the
insertion of names of persons and places being required
solely as a guarantee of authenticity and to enable Mr.
Galton to communicate with the writers in cases where
further question may be necessary.

" The value of the Extracts will be estimated by the
degree in which they seem likely to facilitate the scien-
tific investigations described in the preface to the
'Eecord of Family Faculties.'

" More especially :

" (a) By including every direct ancestor who stands
within the limits of kinship there specified.

" (6) By including brief notices of the brothers and

vl] data. 73

sisters (if any) of each of tliose ancestors. (Importance
will be attached both to the completeness with which
each family of brothers and sisters is described, and also
to the number of persons so described.)

" (c) By the character of the evidence upon which the
information is based.

" (d) By the clearness and conciseness with Y/hich the
statements and remarks are made.

" The Extracts must be legibly entered either in the
tabular forms contained in the copy of the ' Record of
Family Faculties ' (into which, if more space is wanted,
additional pages may be stitched), or they may be
written in any other book with pages of the same size
as those of the Record, provided that the information be
arranged in the same tabular form and order. (It will
be obvious that uniformity in the arrangement of docu-
ments is of primary importance to those who examine
and collate a large number of them.)

" Each competitor must furnish the name and address
of a referee of good social standing (magistrate, clergy-
man, lawyer, medical practitioner, &c.), who is personally
acquainted with his family, and of whom inquiry may
be made, if desired, as to the general trustworthiness of
the competitor.

" The Extracts must be sent prepaid and by post,
addressed to Francis Galton, 42 Rutland Gate, London,
S.W. It will be convenient if the letters ' R.F.F.'
(Record of Family Faculties) be written in the left-
hand corner of the parcel, below the address.

74 NATURAL INHERITANCE. [chap.

" The examination will be conducted by tlie donor of
tlie prizes, aided by competent examiners.

" The value of the individual prizes cannot be fixed
beforehand. No prize will, however, exceed 5.0/., nor be
less than 5l., and 500/. will on the whole be awarded.

'' A list of the gainers of the prizes will be posted
to each of them. It will be published in one or more
of the daily newspapers, also in at least one clerical, and
one medical Journal."

The number of Family Eecords sent in reply to this
offer, that deserved to be seriously considered before
adjudging the prizes, barely reached 150 ; 70 of these
being contributed by males, 80 by females. The re-
mainder were imperfect, or they were marked " not for
competition," but at least 10 of these have been to some
degree utilised. The 150 Records were contributed
by persons of very various ranks. After classing the
female writers according to the profession of their
husbands, if they were married, or according to that of
their fathers, if they were unmarried, I found that each
of the following 7 classes had 20 or somewhat fewer
representatives : (l) Titled persons and landed gentry ;
(2) Army and Navy ; (3) Church (various denomina-
tions) ; (4) Law ; (5) Medicine ; (6) Commerce, higher
class ; (7) Commerce, lower class. This accounts for
nearly 130 of the writers of the Eecords ; the remainder
are land agents, farmers, artisans, literary men, school-
masters, clerks, students, and one domestic servant in a
family of position.

VI.] DATA. 75

Three cases occurred in which the Records sent by
different contributors overlapped. The details are
complicated, and need not be described here, but the
result is that five persons have been adjudged smaller
prizes than they individually deserved.

Every one of the replies refers to a very large number
of persons, as will easily be understood if the fact is
borne in mind that each individual has 2 parents, 4
grandparents, and 8 great parents; also that he and
each of those 14 progenitors had usually brothers and
sisters, who were included in the incjuiry. The replies
were unequal in merit, as might have been expected, but
many were of so high an order that I could not justly
select a few as recipients of large prizes to the exclusion
of the rest. Therefore I divided the sum into two
considerable groups of small prizes, all of which were
well deserved, regretting much that I had none left to
award to a few others of nearly ecjual merit to some
of those who had been successful. The list of winners
is reproduced below, the four years that have elapsed
have of course made not a few changes in the addresses,
which are not noticed here.

LIST OF AWAEDS.

A Prize of £1 was awarded to each op the 40 following

Contributors.

Amphlett, Jolin, Clent, Stourbridge ; Batchelor, Mrs. Jacobstow Kectory,
Stratton, N. Devon ; Bathnrst, Miss K., Vicarage, Biggleswade, Bedford-
sliire ; Beane, Mrs. C. F., 3 Portland Place, Venner Eoad, Sydenham ;
Berisford, Samuel, Park Villas, Park Lane, Macclesfield ; Carruthers, Mrs.,
Briglitside, North Finchley ; Carter, Miss Jessie E., Hazelwood, The Park,
Cheltenham ; Cay, Mrs., Eden House, Holyhead ; Clark, J. Edmund,

76 NATURAL INHERITANCE. [chap.

I'eversham Terrace, York ; Oust, Lady Elizabetli, 13 Eccleston Square, S.W. ;
Fry, Edward, Portsmouth, 5 The Grove, Highgate, N. ; Gibson, G. A., M D.,
1 Eandolph Cliff, Edinburgh ; Gidley, B. Conrtenay, 17 Ribblesdale Road,
Hornsey, N. ; Gillespie, Franklin, M.D., 1 The Grove, Aldershot ; Griffith-
Boscawen, Mrs., Trevalyn Hall, AVrexham ; Hard castle, Henry, 38 Eaton
Square, S.W. ; Harrison, Miss Edith, 68 Gloucester Place, Portman Square,
W. ; Hobhouse, Mrs. 4 Kensington Square, W. ; Holland, INIiss, Ivynieath,
Snodland, Kent ; Ilollis, George, Dartmouth House, Dartmouth Park Hill,
N. ; Ingram, Mrs. Ades, Chailey, Lewis, Sussex ; Johnstone, Miss C. L.,
3 Clarendon Place, Leamington ; Lane-Poole, Stanley, 6 Park Villas East,
Richmond, Middlesex ; Leathley, D. W. B., 59 Lincoln's Inn Fields (in
trast for a competitor who desires her name not to be published) ; Lewin,
Lieutenant-Colonel T. H., Colway Lodge, Lyme Regis ; Lipscomb, R. H.,
East Buclleigh, Budleigh Salterton, Devon ; Maiden, Henry C, Wincllesham
House, Brighton ; Maiden, Henry Elliot, Kitland, Holmwood, Surrey ;
McCall, Hardy Bertram, 5 St. Augustine's Road, Edgbaston, Birmingham ;
Moore, Miss Georgina M., 45 Chepstow Place, Bayswaler, AV. ; Newlands,
Mrs., Raeden, near Aberdeen ; Pearson, David R., M.D., 23 Upper Phili-
more Place, Kensington, W. ; Pearson, Mrs., The Garth, Woodside Park,
North Finchley : Pechell, Hervey Charles, 6 West Chapel Street, Curzon
Street, W. ; Roberts, Samuel, 21 Roland Gardens, S.W. ; Smith, Mrs.
Archibald, Riverbank, Putney, S.W. ; Strachey, Mrs. Fowey Lodge,
Clapham Common, S.W. ; Sturge, Miss Mary C, Chilliswood, Tyndall's
Park, Bristol ; Sturge, Mrs. R. F., 101 Pembroke Road, Clifton ; Wilson,
Edward T., M.D., Westall, Cheltenham.

A Prize of £b was awarded to each of the 44 following

Contributors.

Allan, Francis J., M.D., 1 Dock Street, E. ; Atkinson, Mrs., Clare College
Lodge, Cambridge ; Bevan, Mrs , Plumpton House, Bury St. Edmunds ;
Browne, Miss, Maidenwell House, Louth, Lincolnshire ; Cash, Frederick
Goodall, Gloucester ; Chisholm, Mrs., Church Lane House, Haslemere,
Surrey ; Collier, Mrs. R., 7 Thames Embankment, Chelsea ; Croft, Sir
Herbert G. D., Lugwardine Court, Hereford ; Davis, Mrs. (care of Israel
Davis, 6 King's Bench Walk, Temple, E.G.) ; Drake, Henry H., The
Firs, Lee, Kent; Ercke, J. J. G., 13, Brownhill Road, Catford, S.E. ;
Flint, Fenner Ludd, 83 Brecknock Eoad, N. ; Ford, William, 4 South
Square, Gray's Inn, W.C. ; Foster, Rev. A. J., The Vicarage, Wootton,
Bedford ; Glanville-Richards, AV. V. S., 23 Endsleigh Place, Plymouth ;
Hale, C. D. Bowditch, 8 Sussex Gardens, Hyde Park, W. ; Horder, Mrs.
Mark, Rothenwood, Ellen Grove, Salisbury ; Jackson, Edwin, 79 Withington
Road, Whalley Range, Manchester ; Jackson, George, 1 St. George's Terrace,
Plymouth ; Kesteven, W. H., 401 Holloway Road, N. ; Lawrence, Mrs.

VI.] DATA. 77

Alfred, 16 Suffolk Square, Cheltenham ; Lawrie, Mrs., 1 Chesham Place,
S.W. ; Leveson-Gower, G. W. G., Titsey Place, Limpsfield, Surrey ; Lobb,
H. W., 66 Eussell Square, W. ; McConnell, Miss M. A. Brooklands,
Prestwich, Manchester ; Marshall, Mrs., Fenton Hall, Stoke-upon-Trent ;
Meyer, Mrs., 1 Rodney Place, Clifton, Bristol; Milman, Mrs., The Governor's
House, H.M. Prison, Camden Road ; Olding, Mrs. W. 4 Brunswick Road,
Brighton, Sussex ; Passingham, Mrs., Milton, Cambridge ; Pringle, Mrs.
Fairnalie, Fox Grove Road, Beckenham, Kent ; Reeve, Miss, Foxholes,
Christchurch, Hants ; Scarlett, Mrs., Boscorab Manor, Bournemouth ;
Shand, William, 57 Caledonian Road, N. ; Shaw, Cecil E., Wellington
Park, Belfast ; Sizer, Miss Kate T., Moorlands, Great Huntley, Colchester ;
Smith, Miss A. M. Carter, Thistleworth, Stevenage ; Smith, Rev. Edward S.,
Yiney Hall Vicarage, Blakeney, Gloucestershire ; Smith, Mrs. F, P., Cliffe
House, Sheffield ; Staveley, Edw. S. R., Mill Hill School, N.W. ; Slurge,
Miss Mary W., 17 Frederick Road, Eclgbaston, Birmingham ; Terry, Mrs.,
Tostock, Bury St. Edmunds, Suffolk; Utley, W, H. Alliance Hotel,
Cathedral Gates, Manchester ; Weston, Mrs. Ensleigh, Lansdown, Bath ;
Wodehouse, Mrs. E. R. 50 Chester Square, S.W.

The material in these Eecords is sufficiently varied to
be of service in many inquiries. The chief subjects to
which allusion will be made in this book concern
Statnre, Eye-Colonr, Temper, the Artistic Faculty, and
some forms of Disease, but others are utilized that refer
to Marriage Selection and Fertility.

The following remarks in this Chapter refer almost
wholly to the data of Stature.

The data derived from the Eecords of Family Faculties
will be hereafter distinguished by the letters R.F.F. I
was able to extract from them the statures of 205 couples
of parents, with those of an aggregate of 930 of their
adult children of both sexes. I must repeat that when
dealing with the female statures, I transmuted them to
their male equivalents ; and treated them when thus
transmuted, on equal terms with the measures of males.

78 NATURAL INHERITANCE. [chap.

except where otherwise expressed. The factor I used
was 1*08, which is equivalent to adding a little less than
one-twelfth to each female height. It differs slightly
from the factors employed by other anthropologists,
who, moreover, differ a trifle between themselves ; any-
how, it suits my data better than 1*07 or 1*09. I can
say confidently that the final result is not of a kind to
be sensibly affected by these minute details, because it
happened that owing to a mistaken direction, the com-
puter to whom I first entrusted the figures used a
somewhat different factor, yet the final results came out
closely the same. These E.F.F. data have by no means
the precision of the observations to be spoken of in the
next paragraph. In many cases there remains consider-
able doubt whether the measurement refers to the height
with the shoes on or off; not a few of the entries are, I
fear, only estimates, and the heights are commonly given
only to the nearest inch. StiU, speaking from a know-
ledge of many of the contributors, I am satisfied that a
fair share of these returns are undoubtedly careful and
thoroughly trustworthy, and as there is no sign or sus-
picion of bias, I have reason to place confidence in the
values of the Means that are derived, from them. They
bear the internal tests that have been appHed better
than might have been expected, and when checked by
the data described in the next paragraph, and cautiously
treated, they are very valuable.

Special Data. — A second set of data, distinguished
by the name of " Sj^ecial observations," concern the

VI.] DATA. 79

variations in stature amona; Brothers. I circulated cards
of inquiry among trusted correspondents, stating that I
wanted records of the heights of brothers who were more
than 24 and less than 60 years of age ; that it was
not necessary to send the statures of all of the brothers
of the same family, but only of as many of them as
could be easily and accurately measured, and that the
height of even two brothers would be acceptable. The
blank forms sent to be filled, were ruled vertically in
three parallel columns : (a) family name of each set of
brothers ; (b) order of birth in each set ; (c) height
without shoes, in feet and inches. A place was reserved
at the bottom for the name and address of the sender.
The circle of inquirers widened, but I was satisfied when
I had obtained returns of 295 families, containing in
the aggregate 783 brothers, some few of whom also
appear in the E.F.F. data. Though these two sets of
returns overlap to a trifling extent, they are practically
independent. I look upon the " Special Observations "
as being quite as trustworthy as could be expected in any
such returns. They bear every internal test that I can
apply to them in a very satisfactory manner. The mea-
sures are commonly recorded to quarter or half inches.

Measures at my Anthropometric Laboratory. — A
third set of data have been incidentally of service.
They are the large lists of measures, nearly 10,000 in
number, made at my Anthropometric Laboratory in the
International Health Exhibition of 1884.

4. Experiments on Sweet Peas. — The last of the data

80 NATURAL INHERITANCE. [chap.

that I need specify were the very first that I used ; they
refer to the sizes of seeds, which are equivalent to the
Statures of seeds. I both measured and weighed them,
but after assuring myself of the equivalence of the
two methods (see Appendix C), confined myself to
ascertaining the weights, as they were much more
easily ascertained than the measures. It is more
than 10 years since I procured these data. They
were the result of an extensive series of experiments
on the produce of seeds of difi'erent sizes, . but of
the same species, conducted for the following reasons.
I had endeavoured to find a population possessed
of some measurable characteristic that was suitable
for investigating the causes of the statistical similarity
between successive generations of a people, as will here-
after be discussed in Chapter YIII. At last I determined
to experiment on seeds, and after much inquiry of very
competent advisers, selected sweet-peas for the purpose.
They do not cross-fertilize, which is a very exceptional
condition among plants ; they are hardy, prolific, of a
convenient size to handle, and nearly spherical ; their
weight does not alter perceptibly when the air changes
from damp to dry, and the little pea at the end of the
pod, so characteristic of ordinary peas, is absent in sweet-
peas. I began by weighing thousands of them individ-
ually, and treating them as a census ofiicer would treat
a large population. Then I selected with great pains
several sets for planting. Each set contained seven
little packets, numbered K, L, M, N, 0, P, and Q,
each of the seven packets contained ten seeds of almost

VI.] DATA. 81

exactly the same weight ; those in K being the heaviest,
L the next heaviest, and so down to Q, which was the
lightest. The precise weights are given in Appendix C,
together with the corresponding diameters, which I
ascertained by laying 100 peas of the same weight in a
row. The weights^ rim in an arithmetic series, ha^dng a
common average difference of 0*172 grain. I do not of
course profess to work to thousandths of a grain, though
I did work to somewhat less than one hundredth of a
grain ; therefore the third decimal place represents little
more than an arithmetical working value which has to be
regarded in multiplications, lest an error of sensible im-
portance should be introduced by its neglect. Curiously
enough, the diameters were found also to run approxi-
mately in an arithmetic series, owing, I suppose, to the
misshape and corrugations of the smaller seeds, which
gave them a larger diameter than if they had been
plumped out into spheres. AH this is shown in the
Appendix, where it will be seen that T was justified
in sorting the seeds by the convenient method of the
balance and weights, and of accepting the weights as
directly proportional to the mean diameters.

In each experiment, seven beds were prepared in
parallel rows ; each was 1^ feet wide and 5 feet
long. Ten holes of 1 inch deep were dibbled at equal
distances apart along each bed, and a single seed was
put into each hole. The beds were then bushed over to
keep off the birds. Minute instructions were given to
ensure uniformity, which I need not repeat here. The
end of all was that the seeds as they became ripe were

G

82 NATURAL INHERITANCE. [chap. vi.

collected from time to time and put into bags that I
had sent, lettered from K to Q, the same letters having
been stuck at the ends of the beds. When the crop was
coming to an end, the whole remaining produce of each
bed, including the foliage, was torn up, tied together,
labelled, and sent to me. Many friends and acquaint-
ances had each undertaken the planting and culture of
a complete set, so that I had simultaneous experiments
going on in various parts of the United Kingdom from
Nairn in the North to Cornwall in the South. Two
proved failures, but the final result was that I obtained
the more or less complete produce of seven sets ; that is
to say, the produce of 7x7x10, or of 490 carefully
weighed parent seeds. Some additional account of the
results is given in Appendix C.

It would be wholly out of place to enter here into
further details of the experiments, or to narrate the
numerous little difiiculties and imperfections I had to
contend with, and how I balanced doubtful cases ; how
I divided returns into groups to see if they confirmed
one another, or how I conducted any other w^ell-known
statistical operation. Sufiice it to say that I took im-
mense pains, which, if I had understood the general
conditions of the ^^I'o^^lem as clearly as I do now, I
should not perhaps have cared to bestow. The results
were most satisfactory. They gave me two data, which
were all that I wanted in order to understand in its
simplest approximate form, the way in which one
generation of a people is descended from a previous one ;
and thus I got at the heart of the problem at once.

CHAPTER YIL

DISCUSSION OF THE DATA OF STATUTE.

Stature as a subject for inquiry, — Marriage Selection. — Issue of unlike
Parents. — Description of the Tables of Stature. Mid-Stature of tbe
Population. — Variability of the Population. — Variability of Mid-
Parents. — Variability in Co-Fraternities. — Regression : «, Filial ;
6, Mid-Parental ; c, Parental ; d^ Fraternal. — Squadrons of Statures. —
Successive Generations of a People. — Natural Selection. — Variability
in Fraternities. — Trustworthiness of tlie Constants. — General view of
Kinship. — Separate Contribution from each Ancestor. — Pedigree
Lloths.

Stature as a Subject for Inquiry. — The first of these
inquiries into the laws of human heredity deals with
hereditary Stature, which is an excellent subject for
statistics. Some of its merits are obvious enough, such
as the ease and frequency with which it may be measured,
its practical constancy during thirty-five or forty years
of middle life, its comparatively small dependence upon
clifi'erences of bringing up, and its inconsiderable influ-
ence on the rate of mortalitv. Other advantaQ;es which
are not equally obvious are equally great. One of these
is due to the fact that human stature is not a simple
element, but a sum of the accumidated lengths or

G 2

Si NATURAL INHERITANCE. [chap.

thicknesses of more than a hnndred iDoclily parts, each
so distinct from the rest as to have earned a name by
which it can be s|)ecified. The list includes about fifty
separate bones, situated in the skull, the spine, the
pelvis, the two legs, and in the two ankles and feet.
The bones in both the lower limbs have to be counted,
because the Stature depends upon their average length.
The two cartilages interposed between adjacent bones,
wherever there is a movable joint, and the single
cartilage in other cases, are rather more numerous than
the bones themselves. The fleshy parts of the scalp
of the head and of the soles of the feet conclude the
list Account should also be taken of the shape and
set of the many bones which conduce to a more or less
arched instep, straight back, or high head. I noticed
in the skeleton of O'Brien, the Irish giant, at the College
of Surgeons, which is the tallest skeleton in any English
museum, that his great stature of about 7 feet 7 inches
would have been a trifle increased if the faces of his
dorsal vertebrae had been more parallel than they are,
and his back consequently straighter.

This multiplicity of elements, whose variations are to
some degree independent of one another, some tending
to lengthen the total stature, others to shorten it,
corresponds to an equal number of sets of rows of
pins in the apparatus Fig. 7, p. 63, by which the cause
of variability was illustrated. The larger the number of
these variable elements, the more nearly does the varia-
bility of their sum assume a "Normal" character, though
the approximation increases only as the sc[uare root of

VII.J DISCUSSION OF THE DATA OF STATURE. 85

their number. The beautiful regularity in the Statures of
a population, whenever they are statistically marshalled
in the order of their heights, is due to the number
of variable and quasi-independent elements of which
Stature is the sum.

Mai^riage Selection. — Whatever may be the sexual
preferences for similarity or for contrast, I find little
indication in the average results obtained from a fairly
large number of cases, of any single measurable personal
peculiarity, whether it be stature, temper, eye-colour,
or artistic tastes, in influencing marriage selection to
a notable degree. Nor is this extraordinary, for though
people may fall in love for trifles, marriage is a serious
act, usually determined by the concurrence of numerous
motives. Therefore we could hardly expect either
shortness or tallness, darkness or lightness in com-
plexion, or any other single quality, to have in the
long run a large separate influence.

I was certainly surprised to find how imperceptible
was the influence that even good and bad Temper
seemed to exert on marriage selection. A list was made
(see Appendix D) of the observed frequency of marriages
between persons of each of the various classes of Temper,
in a group of 111 couples, and I calculated what would
have been the relative frequency of intermarriages be-
tween persons of the various classes, if the same number
of males and females had been paired at random. The
result showed that the observed list agreed closely with
the calculated list, and therefore that these observations

86 NATURAL INHERITANCE. [chap.

gave no evidence of discriminative selection in respect
to Temper. The good-tempered husbands were 46 per
cent, in number, and, between them, they married 22
good-tempered and 24 bad-tempered wives ; whereas
calculation, having regard to the relative proportions
of good and bad TemjDer in the two sexes, gave the
numbers as 25 and 21. Again, the bad-tempered hus-
bands, who were 54 per cent, in number, married 31
good-tempered and 23 bad-tempered wives, whereas
calculation gave the number as 30 and 24. This rough
summary is a just expression of the results arrived at
by a more minute analysis, which is described in the
Appendix, and need not be repeated here.

Similarly as regards Eye-Colour. If we analyse the
marriages between the 78 couples whose eye-colours are
described in Chapter YIIL, and compare the observed
results with those calculated on the supposition that
Eye-Colour has no influence whatever in marriage
selection, the two lists will be found to be much alike.
Thus where both of the parents have eyes of the same
colour, whether they be light, or hazel, or dark, the
percentage results are almost identical, being 37, 3, and
8 as observed, against 37, 2, and 7 calculated. Where
one parent is hazel-eyed and the other dark-eyed, the
marriages are as 5 observed against 7 calculated. But
the results run much less well together in the other two
possible combinations, for where one parent is light and
the other hazel-eyed, they give 23 observed against 15
calculated ; and where one parent is light and the other
dark-eyed, they give 24 observed against 32 calculated.

VII.] DISCUSSION OF THE DATA OF STATURE. 87

The effect of Artistic Taste on marriage selection is
discussed in Chapter X., and this also is shown to be
small. The influence on the race of Bias in Marriage
Selection will be discussed in that chapter.

I have taken much trouble at different times to
determine whether Stature plays any sensible part in
marriage selection. I am not yet prepared to offer
complete results, but shall confine my remarks for the
present to the particular cases with which we are now
concerned. The shrewdest test is to proceed under the
guidance of Problem 2, page 68. I find the Q of
Stature among the male population to be 1*7 inch,
and similarly for the transmuted statures of the female
population. Consequently if the men and (transmuted)
women married at random so far as stature was con-
cerned, the Q in a group of couples, each couple
consisting of a pair of summed statures, would be
\/2i X 1"7 inches ==2*41 inches. Therefore the Q in a
group of which each element is the mean stature of a
couple, would be half that amount, or 1'20 inch. This
closely corresponds to what I derived from the data
contained in the first and in the last column but one
of Table 11. The word " Mid-Parent," in the headings
to those columns, expresses an ideal person of composite
sex, whose Stature is half way between the Stature of
the father and the transmuted Stature of the mother. I
therefore conclude that marriage selection does not pay
such regard to Stature, as deserves being taken into
account in the cases with which we are concerned.

I tried the question in another but ruder way, l^y

88 NATURAL INHERITANCE. [chap.

dividing (see Table 9) the male and female parents re-
spectively into three nearly equal groups, of tall, medium,
and short. It was impracticable to make them precisely
equal, on account of the roughness with Avhich the
measurements were recorded, so I framed rules that
seemed best adapted to the case. Consequently the
numbers of the tall and short proved to be only ap-
proximately and not exactly equal, and the two together
were only approximately equal to the medium cases.
The final results were : — 32 instances where one parent
was short and the other tall, and 27 where both were
short or both were tall. In other words, there were 32
cases of contrast in marriage, to 27 cases of likeness.
I do not regard this difference as of consequence,
because the numbers are small, and because a slight
change in the limiting values assigned to shortness and
tallness, would have a sensible effect upon the result.
I am therefore content to ignore it, and to regard the
Statures of married folk just as if their choice in mar-
riage had been wholly independent of stature. The
importance of this supposition in facilitating calculation
will be appreciated as we proceed.

Issue of Unlike Parents. — AVe will next discuss the
question whether the Stature of the issue of unlike
parents betrays any notable evidence of their unlikeness,
or whether the peculiarities of the children do not rather
depend on the average of two values ; one the Stature
of the father, and the other the transmuted Stature
of the mother ; in other words, on the Stature of

VII.] DISCLTSICN CF THE DATA OF STATURE. 89

that ideal personage to wliom we have akeady been
introduced under the name of a Mid- Parent. Stature
has already been spoken of as a well-marked instance
of the heritages that blend freely in the course of
hereditary transmission. It now becomes necessary to
substantiate the statement, because it is proposed to
trace the relationship between the Mid-Parent and the
Son. It would not be possible to discuss the relationship
between either parent singly, and the son, in a trust-
w^orthy way, without the help of a much larger number
of observations than are now at my disposal. They
ought to be numerous enough to give good assurance that
the casea of tall and short, among the unknown parents,
shall neutralise one another ; otherwise the uncertainty
of the stature of the unknown parent would make the re-
sults uncertain to a serious degree. I am heartily glad
that I shall be able fully to justify the method of deal-
ing with Mid-Parentages instead of with single Parents.
The evidence is as follows : — If the Stature of children
depends only upon the average Stature of their two
Parents, that of the mother having been first trans-
muted, it will make no difi'erence in a Fraternity whether
one of the Parents was tall and the other short, or
whether they were alike in Stature. But if some children
resemble one Parent in Stature and others resemble the
other, the Fraternity will be more diverse when their
Parents had differed in Stature than when they were
alike. We easily acquaint ourselves with the facts by
separating a considerable number of Fraternities into
two contrasted groups : (a) those who are the progeny

90 NATURAL INHERITANCE. ^cnAP.

of Like Parents ; (b) those who are tlie progeny of
Unlike Parents. Next we write tlie statures of the
individuals in eacli Fraternity under the form of
M + (dzD) (see page 51), where M is the mean stature
of the Fraternity, and D is the deviation of any one of
its members from M. Then we marshal all the values
of D that belong to the group a, into one Scheme of
de^dations, and all those that belong to the group h
into another Scheme, and we find the Q of each. If it
should be the same, then there is no greater diversity
in the a Grroup than there is in the b Group, and such
proves to be the case. I applied the test (see Table 10)
to a total of 525 children, and found that they were no
more diverse in the one case than in the other. I
therefore conclude that we have only to look to the
Stature of the Mid-Parent, and need not care whether
the Parents are or are not unlike one another.

The advantages of Stature as a subject from which the
simple laws of heredity may be studied, will now be
well appreciated. It is nearly constant in the same
adult, it is frequently measured and recorded ; its dis-
cussion need not be entangled with considerations of
marriage selection. It is sufficient to consider the Stature
of the Mid-Parent and not those of the two Parents
separately. Its variability is Normal, so that much use
may be made of the curious properties of the law of
Frequency of Error in cross-testing the several con-
clusions, and I may add that in all cases they have
borne the test successfully.

VII.] DISCUSSION OF THE DATA OF STATURE. 91

The only drawback to tlie use of Stature in statistical
inquiries, is its small variability, one balf of tbe popula-
tion differing less than 1'7 inch, from the average of all
of tliem. In other words, its Q is only 1'7 inch.

Description of the ToMes of Stature. — I have arranged
and discussed my materials in a great variety of ways, to
guard against rash conclusions, but do not think it
necessary to trouble the reader with more than a few
Tables, which afford sufficient material to determine
the more important constants in the formulae that will
be used.

Table 11, E.F.F., refers to the relation between the
Mid-Parent and his (or should we say its ?) Sons and
Transmuted Daughters, and it records the Statures of
928 adult offspring of 205 Mid-Parents. It shows the
distribution of Stature among the Sons of each succes-
sive group of Mid-Parents, in which ^ the latter are all
~of the same Stature, reckoning to the nearest inch. I
have calculated the M of each line, chiefly by drawing
Schemes from the entries in it. Their values are printed
at the ends of the lines and they form the right-hand
column of the Table.

Tables 12 and 13 refer to the relation between Brothers.
The one is derived frcm the E.F.F. and the other from
the Special data. They both deal with small or moder-
ately sized Fraternities, excluding the larger ones for
reasons that will be explained directly, but the E.F.F.
Table is the least restricted in this respect, as it only
excludes families of 6 brothers and upwards. The data

92 NATURAL INHERITANCE. [chap.

were so few in number tliat I could not well afford to lop
off more. These Tables were constructed by registering
the differences between each possible pair of brothers in
each family : thus if there were three brothers, A, B,
and C, in a particular family, I entered the differences
of stature between A and B, A and C, and B and C,
four brothers gave rise to 6 entries, and five brothers to
10 entries. The larger Fraternities were omitted, as the
very large number of different pairs in them would
have overwhelmed the influence of the smaller Frater-
nities. Large Fraternities are separately dealt with in
Table 14.

We can derive some of the constants by more than
one method ; and it is gratifying to find how well the
results of different methods confirm one another.

Mid-Stature of the Population. — The Median, Mid-
Stature, or M of 'the general Population is a value of
primary importance in this inquiry. Its value will be
always designated by the symbol P, and it may be
deduced from the bottom lines of any one of the three
Tables. I obtain from them respectively the values
6 8 '2, 68 '5, 68 '4, but the middle of these, which is
printed in italics, is a smoothed result. It is one of the
only two smoothed values in the whole of my work, and
was justifiably corrected, because the observed values
that happen to lie nearest to the Grade of 50° ran out of
harmony with the rest of the curve. It is therefore
reasonable to consider its discrepancy as fortuitous,
althouQ-h it amounts to more than 0'15 inch. The

VII.] DISCUSSION OF THE DATA OF STATURE. 93

series in question refers to E.F.F. brothers, wlio, owing
to the principle on whicli the Table is constructed, are
only a comparatively small sample taken out of the
E.F.F. Population, and on a principle that gave greater
weight to a few large families than to all the rest.
Therefore it could not be expected to give rise to so
regular a Scheme for the general E.F.F. Population
as Table 11, which was fairly based upon the whole
of it. Less accuracy was undoubtedly to have been
expected in this group than in either of the others.

Variahility of the Population. — The value of Q in
the Statures of the general Population is to be deduced
from the bottom lines of any one of the Tables 11, 12,
and 13. The three values of it that I so obtain, are
1'65, 1*7, and 1'7 inch. I should mention that the
method of the treatment originally adopted, happened
also to make the first of these values 1 '7 inch, so I have
no hesitation in accepting 1*7 as the value for all my
ciaLa.

Variability of Mid-Parents. — The value of Q in a
Scheme drawn from the Statures of the E.F.F. Mid-
Parents according to the data in Table 11, is 1'19
inches. Now it has already been shown that if marriage
selection is independent of stature, the value of Q in the
Scheme of Mid-parental Statures would be ec[ual to its
value in that of the general Population (which we have
just seen to be 1*7 inch), divided by the square root of
2 ; that is by 1'45. This calculation makes it to be

94 NATURAL INHERITANCE. . [chap.

1*21 iiicli, which agrees excellently with the observed
value/

Variahilky in Co- Fraternities. — As all the Adult
Sons and Transmuted Daughters of the same Mid-
Parent, form what is called a Fraternity, so all the Adult
Sons and Transmuted Daughters of a group of Mid-
Parents who have the same Stature (reckoned to the
nearest inch) will be termed a Co-Fraternity. Each
line in Table 11 refers to a separate Co-Fraternity and
expresses the distribution of Stature among them.
There are three reasons why Co-Fraternals should be
more diverse among themselves than brothers. First,
because their Mid-Parents are not of identical height,
but may differ even as much as one inch. Secondly,
because their grandparents, great-grandparents, and so
on indefinitely backwards, may have difi'ered widely.
Thirdly, because the nurture or rearing of Co-Fraternals
is more various than that of Fraternals. The brothers
in a Fraternity of townsfolk do not seem to difi'er more
among themselves than those in a Fraternity of country-
folk, but a mixture of Fraternities derived indiscrimi-
nately from the two sources, must show greater diversity
than either of them taken by themselves. The large
difi'erences between town and country-folk, and those
between persons of difi'erent social classes, are con-
spicuous in the data contained in the Report of the

'^ In all my values referring to liuman stature, tlie second decimal is
rudely approximate. I am obliged to use it, because if I worked only to
tentlis of an incli, sensible errors might creep in entirely owing to aritli-
metical operations.

vii.] DISCUSSION OF THE DATA OF STATURE. 95

Anthropological Committee to the British Association
in 1880, and published in its Journal.

I concluded after carefully studying the chart upon
which each of the individual observations from which
Table 11 was constructed, had been entered separately
in their appropriate places, and not clubbed into groups
as in the Tables, that the value of Q in each Co-
Fraternal group was roughly the same, whatever their
Mid-Parental value might have been. It was not cjuite
the same, being a trifle larger when the Mid-Parents
were tall than when they were short. This justifies
what will be said in Appendix E about the G-eometric
Mean ; it also justifies neglect in the present inquiry of
the method founded upon it, because the improvement
in the results to which it might lead, would be insignifi-
cant, while its use would have added to the difiiculty
of explanation, and introduced extra trouble throuo-h-
out, to the reader more than to myself. The value that
I adopt for Q in every Co-Fraternal group, is 1*5 inch.

Regression. — a. Filial : However paradoxical it may
appear at first sight, it is theoretically a necessary fact,
and one that is clearly confirmed by observation, that
the Stature of the adult ofi*spring must on the whole,
be more mediocre than the stature of their Parents ;
that is to say, more near to the IVI of the general
Population. Table 11 enables us to compare the
values of the IVI in difi'erent Co-Fraternal groups
with the Statures of their respective Mid-Parents.
Fig. 10 is a graphical representation of the meaning of

96

NATURAL INHERITANCE.

[chap.

the Table so far as it now concerns ns. The horizontal
dotted lines and the graduations at their sides, cor-
respond to the similarly placed lines of figures and
graduations in Table 11. The dot on each line shows
the point where its IVI falls. The value of its M is to
be read on the graduations along the top, and is the
same as that which is given in the last column of
Table 11. It will be perceived that the line drawn

FIG.EO.

through the centres of the dots, admits of being inter-
preted by the straight line C D, with but a small
amount of give and take ; and the fairness of this
interpretation is confirmed by a study of the MS. chart
above mentioned, in which the individual observations
were plotted in their right places.

Now if we draw a line A B through every point where
the graduations along the top of Fig. 10, are the same
as those along the sides, the line will be straight and.
will run diagonally. It represents what the Mid-

VII.] DISCUSSION OF THE DATA OF STATURE. 97

Statures of the Sons would be, if tliey were on tlie
average identical with those of their Mid-Parents.
Most obviously A B does not agree with C D ; therefore
Sons do not, on the average, resemble their Mid-
Parents. On examining these lines more closely, it
will be observed that A B cuts C D at a point M that
fairly corresponds to the value of 685- inches, whether
its value be read on the scale at the top or on that at
the side. This is the value of P, the Mid-Stature of
the population. Therefore it is only when the Parents
are mediocre, that their Sons on the average resemble
them.

Next draw a vertical line, E M F, through M, and
let EGA be any horizontal line cutting ME at E, MC
at E, and MA at A. Then it is obvious that the ratio of
EA to EC is constant, whatever may be the position of
E C A. This is true whether E C A be drawn above or
like F D B, below M. In other words, the proportion
between the Mid-Filial and the Mid-Parental deviation
is constant, whatever the Mid-Parental stature may be.
I reckon this ratio to be as 2 to 3 : that is to say, the
Filial deviation from P is on the average only two-
thirds as wide as the Mid-Parental Deviation. I call
this ratio of 2 to 3 the ratio of " Filial Eegression." It
is the proportion in which the Son is, on the average,
less exceptional than his Mid-Parent.

My first estimate of the average proportion between
the Mid-Filial and the Mid-Parental deviations, was
made from a study of the MS. chart, and I then
reckoned it as 3 to 5. The value given above was

H

98 NATURAL INHERITANCE. [chap.

afterwards substituted, because the data seemed to
admit of that interpretation also, in which case the
fraction of two-thirds was preferable as being the more
simple expression. I am now inclined to think the
latter may be a trifle too small, but it is not worth
while to make alterations until a new, larger, and more
accurate series of observations can be discussed, and the
whole work revised. The present doubt only ranges
between nine-fifteenths in the first case and ten-
fifteenths in the second.

This value of two-thirds will therefore be accepted as
the amount of Eegression, on the average of many
cases, from the Mid-Parental to the Mid-Filial stature,
whatever the Mid-Parental stature may be.

As the two Parents contribute equally, the contribu-
tion of either of them can be only one half of that
of the two jointly ; in other words, only one half of that
of the Mid-Parent. Therefore the average Eegression
from the Parental to the Mid-Filial Stature must be the
one half of two-thirds, or one-third. I am unable to
test this conclusion in a satisfactory manner by direct
observation. The data are barely numerous enough for
dealing even with questions referring to Mid- Parentages ;
they are quite insufficient to deal with those that involve
the additional large uncertainty introduced owing to an
ignorance of the Stature of one of the parents. I have
entered the Uni-Parental and the Filial data on a
MS. chart, each in its appropriate place, but they are
too scattered and irregular to make it useful to give

VII.] DISCUSSION OF THE DATA OF STATURE. 99

the results in detail. They seem to show a Eegression
of about two-fifths, which differs from that of one-third
in the ratio of 6 to 5. This direct observation is so
inferior in value to the inferred result, that I disregard
it, and am satisfied to adopt the value given by the
latter, that is to say, of one-third, to express the
averag^e Recession from either of the Parents to the
Son.

h. Mid-Parental : The converse relation to that which
we have just discussed, namely the relation between
the unknown stature of the Mid-Parent and the known
Stature of the Son, is expressed by a fraction that is
very far from being the converse of two-thirds. Though
the Son deviates on the average from P only f as
widely as his Mid-parent, it does not in the least follow
that the Mid-parent should deviate on the average from
P, 1^ or 1-J-, as widely as the Son. The Mid-Parent is
not likely to be more exceptional than the son, but
quite the contrary. The number of individuals who
are nearly mediocre is so preponderant, that an ex-
ceptional man is more frequently found to be the
exceptional son of mediocre parents than the average
son of very exceptional parents. This is clearly shown
by Table 1 1 , where the very same observations which give
the average value of Filial Regression when it is read
in one way, gives that of the Mid-Parental Regression
when it is read in another way, namely down the vertical
columns, instead of along the horizontal lines. It then
shows that the Mid-Parent of a man deviates on the

H 2

100 NATURAL INHERITANCE. [chap.

average from P, only one-third as much, as tlie man
himself. This value of -^ is four and a half times
smaller than the numerical converse of f , since A^, or
f, being multiplied into ^, is equal to f .

c. Parental : As a Mid-Parental deviation is equal
to one-half of the two Parental deviations, it follows
that the Mid-Parental Eegression must be ecjual to
one-half of the sum of the two Parental Regressions.
As the latter are equal to one another it follows that
all three must have the same value. In other words,
the average Mid-Parental Regression being ^, the
average Parental Regression must be -J- also.

As there was much appearance of paradox in the
above strongly contrasted results, I looked carefully
into the run of the figures in Table 11. They were
deduced, as already said, from a MS. chart on which
the stature of every Son and the transmuted Stature of
every Daughter is entered opposite to that of the Mid-
Parent, the transmuted Statures being reckoned to the
nearest tenth of an inch, and the position of the other
entries being in every respect exactly as they were
recorded. Then the number of entries in each square
inch were counted, and copied in the form in which
they ajDpear in the Table. I found it hard at first
to catch the full significance of the entries, though 1
soon discovered curious and apparently very interesting
relations between them. These came out distinctly
after I had '' smoothed " the entries by writing at
each intersection between a horizontal line and a ver-

VII.]

DISCUSSION OF THE DATA OF STATURE.

101

tical one, tlie sum of the entries in the four adjacent
squares. I then noticed (see Fig. 11) that lines drawn
through entries of the same value formed a series of
concentric and similar ellipses. Their common centre
lay at the intersection of those vertical and horizontal
lines which correspond to the value of 68 J inches, as
read on both the top and on the side scales. Their
axes were similarly inclined. The points where each
successive ellipse was touched by a horizontal tangent,
lay in a straight line that was inclined to the vertical in

FIG. II.

A

Y

\

'N

/

'-"/P J^\

m:

k

^

^

the ratio of f, and those where the ellipses were touched
by a vertical tangent, lay in a straight line inclined to
the horizontal in the ratio of \. It will be obvious
on studying Fig. 11 that the point where each suc-
cessive horizontal line touches an ellipse is the point
at which the greatest value in the line will be found.
The same is true in respect to the successive vertical lines.
Therefore these ratios confirm the values of the Eatios
of Eegression, already obtained by a different method,
namely those of f from Mid-Parent to Son, and of

102 NATURAL INHERITANCE. [chip.

^- from Son to Mid-Parent. These and other re-
lations were evidently a subject for matliematical
analysis and verification. It seemed clear to me that
they all depended on three elementary measures, sup-
posing the law of Frequency of Error to be applicable
throughout ; namely (l) the value of Q in the General
Population, which was found to be 17 inch; (2) the
value of Q in any Co-Fraternity, which was found to be
1*5 inch; (3) the Average Eegression of the Stature of
the Son from that of the Mid-Parent, which was found
to be f . I wrote down these values, and phrasing the
problem in abstract terms, disentangled from all refer-
ence to heredity, submitted it to Mr. J. T>, Hamilton
Dickson, Tutor of St. Peter's College, Cambridge (see
Appendix B). I asked him kindly to investigate for
me the Surface of Frequency of Error that would result
from these three data, and the various shapes and other
particulars of its sections that were made by horizontal
planes, inasmuch as they ought to form the ellipses of
which I spoke.

The problem may not be difficult to an accomplished
mathematician, but I certainly never felt such a glow
of loyalty and respect towards the sovereignty and wide
sway of mathematical analysis as when his answer arrived,
confirming, by purely mathematical reasoning, my vari-
ous and laborious statistical conclusions with far more
minuteness than I had dared to hope, because the data
ran somewhat roughly, and I had to smooth them with
tender caution. His calculation corrected my observed
value of Mid- Parental Eegression from ^ to yf tt '> ^^^^

VII.] DISCUSSION OF THE DATA OF STATURE. 103

relation between the major and minor axis of the
ellipses was changed 3 per cent. ; and their inclination
to one another was changed less than 2°.^

It is obvious from this close accord of calculation
with observation, that the law of Error holds through-
out with sufficient precision to be of real service, and
that the various results of my statistics are not
casual and disconnected determinations, but strictly
interdependent.

I trust it will have become clear even to the most
non-mathematical reader, that the law of Eegression
in Stature refers primarily to Deviations, that is, to
measurements made from the level of -mediocrity to the

1 The following is a more detailed comparison between tlie calculated
and tlie observed results. The latter are enclosed in brackets. The letters
refer to Fig. 11 : —
Given —

The "Probable Error" of each system of Mid- Parentages = 1-22
inch. (This was an earlier determination of its value ; as already said,
the second decimal is to be considered only as approximate.)
Eatio of mean filial regression = f .
" Prob. Error" of each Co-Fraternity = 1*50 inch.

Sections of surface of frequency parallel to XY are true ellipses.

(Obs. — Apparently true ellipses.)
MX : YO = 6 : 17*5, or nearly 1:3.

(Obs.— 1 : 3.)
Major axes to minor axes = ^ 1 '. ^^2 = 10: 5*35.

(Obs.— 10 : 5-1.)
Inclination of major axes to OX = 26° 36'.

(Obs. 25°. )
Section of surface parallel to XZ is a true Curve of Frequency.

(Obs. — Apparently so.)
" Prob. Error ", the Q of that curve, = 1.07 inch.

(Obs.— 1 '00, or a little more.)

104 NATURAL INHERITANCE. [chap.

crown of the liead, upwards or downwards as the case
may be, and not from the ground to the crown of the
head. (In the po23ulation with which I am now dealing,
the level of mediocrity is 68 J inches (without shoes).)
The law of Regression in respect to Stature may be
phrased as follows ; namely, that the Deviation of the
Sons from P are, on the average, equal to one-third of
the deviation of the Parent from P, and in the same
direction. Or more briefly still : — If P -1- (zt D) be the
Stature of the Parent, the Stature of the offspring will
on the average be P + (zb |- D).

If this remarkable law of Regression had been based
only on those experiments with seeds, in which I first
observed it, it might weU be distrusted until otherwise
confirmed. If it had been corroborated by a compara-
tively small number of observations on human stature,
some hesitation might be expected before its truth could
be recognised in opposition to the current belief that the
child tends to resemble its parents. But more can be
urged than this. It is easily to be shown that we ought
to expect Filial Regression, and that it ought to amount
to some constant fractional part of the value of the Mid-
Parental deviation. All of this will be made clear in a
subsequent section, when we shall discuss the cause of
the curious statistical constancy in successive generations
of a large population. In the meantime, two different
reasons may be given for the occurrence of Regression ;
the one is connected with our notions of stability of
type, and of which no more need now be . said ; the
other is as follows : — The child inherits partly from his

VII.] DISCUSSION OF THE DATA OF STATURE. 105

parents, partly from liis ancestry. In every population
tliat intermarries freely, wlien the genealogy of any man
is traced far backwards, liis ancestry will be found to
consist of such varied elements that they are indistin-
guishable from a sample taken at haphazard from the
general Population. The Mid- Stature IVI of the remote
ancestry of such a man will become identical with P ;
in other words, it will be mediocre. To put the same
conclusion into another form, the most probable value
of the Deviation from P, of his Mid- Ancestors in any
remote generation, is zero.

For the moment let us confine our attention to some
one generation in the remote ancestry on the one hand,
and to the Mid-Parent on the other, and ignore all
other generations. The combination of the zero Devia-
tion of the one with the observed Deviation of the other
is the combination of nothing with something. Its
efi'ect resembles that of pouring a measure of water
into a vessel of wine. The wine is diluted to a con-
stant fraction of its alcoholic strength, whatever that
strength may have been.

Similarly with regard to every other generation.
The Mid-Deviation in any near generation of the
ancestors will have a value intermediate between that
of the zero Deviation of the remote ancestry, and of the
observed Deviation of the Mid-Parent. Its combination
with the Mid-Parental Deviation will be as if a mixture
of wine and water in some definite proportion, and not
pure water, had been poured into the wine. The process
throughout is one of proportionate dilutions, and the

106 NATURAL INHERITANCE. [chap.

joint effect of all of tliem is to weaken the original
alcoholic strength in a constant ratio.

The law of Eegression tells heavily against the full
hereditary transmission of any gift. Only a few out of
many children would be likely to differ from mediocrity
so widely as their Mid-Parent, and still fewer would
differ as widely as the more exceptional of the two
Parents. The more bountifully the Parent is gifted
by nature, the more rare will be his good fortune
if he begets a son who is as richly endowed as himself,
and still more so if he has a son who is endowed yet
more largely. But the law is even-handed ; it levies an
equal succession-tax on the transmission of badness as of
goodness. If it discourages the extravagant hopes of a
gifted parent that his children will inherit all his powers ;
it no less discountenances extravagant fears that they
will inherit all his weakness and disease.

It must be clearly understood that there is nothing in
these statements to invalidate the general doctrine that
the children of a gifted pair are much more likely to be
gifted than the children of a mediocre pair. They
merely express the fact that the ablest of all the
children of a few gifted pairs is not likely to be as
gifted as the ablest of all the children of a very great
many mediocre pairs.

The constancy of the ratio of Eegression, whatever
may be the amount of the Mid-Parental Deviation, is
now seen to be a reasonable law which might have been
foreseen. It is so simple in its relations that I have

VII.]

DISCUSSION OF THE DATA OF STATURE.

107

FIG .12.

contrived more than one form of apparatus by which
the probable stature of the children of known parents
can be mechanically reckoned. Fig. 12 is a representation
of one of them, that is worked with pulleys and weights.
A, B, and C are three thin wheels with grooves round
their edges. They are screwed
together so as to form a single
piece that turns easily on its
axis. The weights M and F are
attached to either end of a thread
that passes over the movable
pulley D. The pulley itself hangs
from a thread which is wrapped
two or three times round the
groove of B and is then secured
to the wheel. The weight SD
hangs from a thread that is
wrapped two or three times round
the groove of A, and is then
secured to the wheel. The dia-
meter of A is to that of B as 2
to 3. Lastly, a thread is wrapped
in the opposite direction round
the wheel C, which may have
any convenient diameter, and is
attached to a counterpoise. M refers to the male statures,
F to the female ones, S to the Sons, D to the Daughters.
The scale of Female Statures differs from that of the
Males, each Female height being laid down in the
position which would be occupied by its male equivalent.

108 NATURAL INHERITANCE. [chap.

Tims 56 is written in the position of 60*48 inches, wliich
is equal to 56x1*08. Similarly, 60 is written in the
position of 64*80, which is equal to 60 x 1*08.

It is obvious that raising M will cause F to fall, and
vice versa, without affecting the wheel AB, and there-
fore without affecting SD ; that is to say, the Parental
Differences may be varied indefinitely without affecting
the Stature of the children, so long as the Mid-Parental
Stature is unchanged. But if the Mid-Parental Stature
is changed to any specified amount, then that of SD
will be changed to f of that amount.

The weights M and F have to be set opposite to the
heights of the mother and father on their respective
scales ; then the weight SD will show the most probable
heights of a Son and of a Daughter on the corresponding
scales. In every one of these cases, it is the fiducial
mark in the middle of each weight by which the reading
is to be made. But, in addition to this, the length of
the weight SD is so arranged that it is an equal chance
(an even bet) that the height of each Son or each
Daughter will lie within the range defined by the upper
and lower edge of the weight, on their respective scales.
The length of SD is 3 inches, which is twice the Q of
the Co-Fraternity ; that is, 2 x 1*50 inch.

d. Fraternal : In seeking for the value of Fraternal
Regression, it is better to confine ourselves to the
Special data given in Table 13, as they are much
more trustworthy than the R.F.F. data in Table 12.
By treating them in the way shown in Fig. 13, which
is constructed on the same principle as Fig. 10, page 96,

VII.]

DISCUSSION OF THE DxiTA OF STATURE.

109

2. .
3 '

I obtained the value for Fraternal Eegression of
that is to say, the unknown brother of a known man is
probably only two-thirds as exceptional in Stature as
he is. This is the same value as that obtained for the
Regression from Mid-Parent to Son. However para-
doxical the fact may seem at first, of there being such
a thing as Fraternal Regression, a little reflection will
show its reasonableness, which will become much clearer
later on. In the meantime, we may recollect that the

F\Cr A3.

FRATERNAL REGRESSION

R.F.F.

64 6S 6S 70 72

SPECfALS

64 €6 68 70 73

' I ' J .1.1

7B

70
6S
66
64

-

e / /
1* /

72,
70

68

€6

6^

*/ /

/ /'

1 1 I 1

1 1 1 1 \

1 I 1 I—

unknown brother has two different tendencies, the one
to resemble the known man, and the other to resemble
his race. The one tendency is to deviate from P as
much as his brother, and the other tendency is not
to deviate at all. The result is a compromise.

As the average Regression from either Parent to the
Son is twice as great as that from a man to his Brother,
a man is, generally speaking, only half as nearly related

110 NATURAL INHERITANCE. [cuap.

to either of his Parents as he is to his Brother. In
other words, the Parental kinship is only half as close
as the Fraternal.

We have now seen that there is Eegression from the
Parent to his Son, from the Son to his Parent, and from
the Brother to his Brother. As these are the only three
possible lines of kinship, namely, descending, ascending,
and collateral, it must be a universal rule that the un-
known Kinsman, in any degree, of a known Man, is on
the average more mediocre than he. Let PitD be the
stature of the known man, and PdzP)' the stature of his
as yet unknown kinsman, then it is safe to wager, in
the absence of all other knowledge, that D^ is less
than D.

Squadron of Statures.— It is an axiom of statistics,
as I need hardly repeat, that every large sample taken
at random out of any still larger group, may be con-
sidered as identical in its composition, in such inquiries
as these in which we are now engaged, where minute
accuracy is not desired and where highly exceptional
cases are not regarded. Suppose our larger group to
consist of a million, that is of 1000 x 1000 statures, and
that we had divided it at random into 1000 samples
each containing 1000 statures, and made Schemes of
each of them. The 1000 Schemes would be practically
identical, and we mioiit marshal them one behind the
other in successive ranks, and thereby form a " Squad-
ron," numbering 1000 statures each way, and standing

VII.]

DISCUSSION OF THE DATA OF STATURE.

Ill

upon a square base. Our Squadron may be divided
either into 1000 ranks or into 1000 files. The ranks
will form a series of 1000 identical Schemes, the files
will form a series of 1000 rectangles, that are of the
same breadth, but of dissimilar heights. (See Fig. 14.)
It is easy by this illustration to give a general idea,
to be developed as we proceed, of the way in which any
large sample, A, of a Population gives rise to a group
of Kinsmen, Z, so distant as to retain no family likeness

FIG. 14

to A, but to be statistically undistinguishable from the
Population generally, as regards the distribution of their
statures. In this case the samples A and Z would form
similar Schemes. I must suppose provisionally, for the
purpose of easily arriving at an approximate theory,
that tall, short, and mediocre Parents contribute equally
to the next generation though this may not strictly
be the case.^

1 Oddly enough, the shortest couple on my list have the largest family,
namely, sixteen children, of whom fourteen were measured.

112 NATUIIAL INHERITANCE. [chap.

Tlirow A into the form of a Squadron and not of a
Scheme, and let us begin by confining our attention
to the men who form any two of the rectangular files
of A, that we please to select. Then let us trace
their connections with their respective Kinsmen in Z.
As the number of the Z Kinsmen to each of the A files
is considered to be the same, and as their respective
Stature-Schemes are supposed to be identical with that
of the general Population, it follows that the two Schemes
in Z derived from the two difi'erent rectangular files in
A, will be identical with one another. Every other
rectangular file in A will be similarly represented by
another identical Scheme in Z. Therefore the 1,000
difi'erent rectangular files in A will produce 1,000 iden-
tical Schemes in Z, arranged as in Fig. 14.

Though all the Schemes in Z, contain the same
number of measures, each will contain many more
measures than were contained in the files of A, because
the same kinsmen would usually be counted many
times over. Thus a man may be counted as uncle to
many nephews, and as nephew to many uncles. We
will therefore (though it is hardly necessary to do so)
suppose each of the files in Z to have been constructed
from only a sample consisting of 1,000 persons, taken at
random out of the more numerous measures to which it
refers. By this treatment Z becomes an exact Squadron,
consisting of 1,000 elements, both in rank and in file,
and it is identical with A in its constitution, though
not in its attitude. The ranks of Z, which are Schemes,
have been derived from the files of A, which arc rect-

VII.]

DISCUSSION OF THE DATA OF STATURE.

113

angles, therefore the two Squadrons must stand at right
angles to one another, as in Fig. 14. The upper surface
of A is curved in rank, and horizontal in file ; that of
Z is curved in file and horizontal in rank.

The Kinsmen in nearer degrees than Z will be re-
presented by Squadrons whose forms are intermediate
between A and Z. Front views of these are shown in

i

FiG .15.

i yi I

J\ ! 11

pi

—

vy^

Tr.

T

•¥2

-S-1

-1

tis

1

•f-

C 1^

Fig. 15. Consequently they will be somewhat curved
both in rank and in file. Also as the Kinsmen of all
the members of a Population, in any degree, are them-
selves a Population having similar characteristics to
those of the Population of w^hich they are part, it
follows that the elements of every intermediate Squadron
when they are broken up and sorted afresh into ordinary
Schemes, would form identical Schemes. Therefore, it
is clear that a law exists that connects the curvatures in
rank and in file, of any Squadron. Both of the cur-
vatures are Curves of Distribution; let us call their
Q values respectively r and /. Then if p be the Q of

I

114 NATURAL INHERITANCE. [c'Hap.

the general Population, we arrive at a general equation
tliat is true for all degrees of Kinship ; namely —

r^+/^=p^ (1)

but r, tlie curvature in rank, is a regressed value of p,
and may be written icp, iv being the value of the
Eegression. Therefore the above equation may be put
in the form of

%D''^''^P^f (2)

in which f is the Q of the Co-kinsmen in the given
degree.

It will be found that the intersection of the surfaces
of the Squadrons by a horizontal plane, whose height is
equal to P, forms in each case a line, whose general in-
clination to the ranks of A increases as the Kinship
becomes more remote, until it becomes a right angle in
Z. The progressive change of inclination is shown in
the small squares drawn at the base of Fig. 13, in which
the lines are the projections of contours drawn on the
upper surfaces of the Squadrons, to correspond with the
multiples there stated of values of jy.

It will be understood from the front views of the
four different Squadrons, which form the upper part of
Fig. 13, how the Mid-Statures of the Kinsmen to the
Men in each of the files of A, gradually become more
mediocre in the successive stages of kinship until they
all reach absolute mediocrity in Z. This figure aff*ords
an excellent diagramatic representation, true to scale,-
of the action of the law of Eegression in Descent. I
should like to have given in addition, a perspective
view of the Squadrons, but fiiilcd to draw them

VII.] DISCUSSION OF THE DATA OF STATURE. 115

clearly, after making many attempts. Their curvatures
are so delicate and peculiar tliat tlie eye can liardly
appreciate them even in a model, without turning it
about in different lights and aspects. A plaster model
of an intermediate form was exhibited at the Eoyal
Society by Mr. J. D. H. Dickson, when my paper on
Hereditary Stature was read, together with his solutions
of the problems that are given in the Appendix. I also
exhibited arrangements of files and ranks that were
made of pasteboard. Mr. Dixon mentioned that the
mathematical properties of a Surface of Frequency
showed that no strictly straight line could be drawn
upon it.

Successive Oenerations of a People. — We are far too
apt to regard common events as matters of course, that
require no explanation, whereas they may be problems
of much interest and of some difficulty, and still await
solution.

Why is it, when we compare two large groups of
persons selected at random from the same race, but
belonging to different generations, that they are usually
found to be closely alike ? There may be some
small statistical dissimilarity due to well understood
differences in the general conditions of their lives, but
with this I am not concerned. The present question
is as to the origin of that statistical resemblance between
successive generations which is due to the strict pro-
cesses of heredity, and which is commonly observed in
all forms of life.

T 2

116 NATURAL INHERITANCE. [chap.

In eacli generation, individuals are found to be tall
and short, heavy and light, strong and weak, dark
and pale ; and the proportions of those who present
these several characteristics in their various degrees,
tend to be constant. The records of geological history
afford striking evidences of this statistical similarity.
Fossil remains of plants and animals may be dug out of
strata at such different levels, that thousands of genera-
tions must have intervened between the periods at which
they lived ; yet in large samples of such fossils we may
seek in vain for peculiarities that distinguish one
generation from another, the different sizes, marks, and
variations of every kind, occurring with equal frequency
in all.

If any are inclined to reply that there is no wonder
in the matter, because each individual tends to leave his
like behind him, and therefore each generation must, as
a matter of course, resemble the one preceding, the
patent fact of Eegression shows that they utterly
misunderstand the case.

We have now reached a stage at which it has
become possible to discuss the problem with some
exactness, and I will do so by giving mathematical
expression to what actually took place in the Statures
of that sample of our Population whose life-histories
are recorded in the E.F.F. data.

The Males and Females in Generation I. whose M has
the value of P (viz., GSj inches), and whose Q is 17
inch, were found to group themselves as it were at
random, into couples, and then to form a system of

VII.] DISCUSSION OF THE DATA OF STATURE. 117

Mid-Parents. This system had of course the same IVI
as the general Population, but its Q was reduced to
^^xl'7 inch, or to 1*2 inch. It was next found
w^hen the Statures of the Mid-Parents, expressed in tlie
form of P-h(=tD), were sorted into groups in which
D w^as the same (reckoning to the nearest inch), that a
Co-fraternity sprang from each group, and that its IVI
had the value of P-l-(zizfD). The system in which
each element is a Mid- Co-Fraternity, must have the
same M as before, of 6 8|^ inches, but its Q will be again
reduced, namely from 1 '2 inch to f x 1 *2 inch, or to
0'8 inch. Lastly, the individual Co-Fraternals were
seen to be dispersed from their respective Mid-Co-
Fraternities, with a Q equal in each case to 1*5 inch.
The sum of all of the Co-Fraternals forms the Popula-
tion of Generation 11. Consequently the members of
Generation II. constitute a system that has an IVI of
68^ inches and a Q equal to ^ [(0-8)'-|- (1'5)'], = 17
inch. These values are identical with those in Genera-
tion I. ; so the cause of their statistical similarity is
tracked out.

There ought to be no misunderstanding as to the
character of the evidence or of the reasoning upon
which this analysis is based. A small but fair sample
of the Population in two successive Generations has been
taken, and its conditions as regards Stature have been
strictly discussed. It was found that the distribution
of Stature was sufficiently Normal to justify our ignoring
any shortcomings in that respect. The transmutation

118 NATURAL INHERITANCE. [chap

of female lieigiits to tlieir male equivalents was justified
by the fact that when the individual Statures of a group
of females are raised in the proportion of 100 to 108,
the Scheme drawn from them fairly coincides with that
drawn from male Statures. Marriage selection was found
to take no sufiicient notice of Stature to be worth con-
sideration ; neither was the number of children in
Fraternities found to be sensibly afi^ected by the
Statures of their Parents. Again, it was seen to be
of no consecj^uence when dealing statistically with the
offspring, whether their Parents were alike in stature or
not, the only datum deserving consideration being the
Stature of the Mid-Parent, that is to say, the average
value of (l) the Stature of the Father, and of (2) the
Transmuted Stature of the Mother. I fully grant that
not one of these deductions may be strictly exact, but
the error introduced into the conclusions by supposing
them to be correct proves not to be worth taking into
account in a first approximation.

Precisely the same may be said of the ulterior steps
in this analysis. Every one of them is based on the
properties of an ideally perfect curve, but in no case
has there been need to make any sensible departure
from the observed results, except in assigning a uniform
value to Q in the difi"erent Co-Fraternities. Strictly
speaking, that value was found to slightly rise or fall as
the Mid-Stature of the Co-Fraternity rose or fell. This
suggested the advisability of treating the whole inquiry
on the principle of the Geometric Mean, Appendix G.
I tried that principle in what seemed to be the most

VII.] DISCUSSION OF THE DATA OF STATURE. . 119

hopeful case among my 18 schemes, but found the gain,
if any, to be so small, that I did not care to go on
with the experiment. It did not seem to deserve the
additional trouble, and I was indisposed to do anything
that was not really necessary, which might further
confuse the reader. But had I possessed better data,
I should have tried the Geometric Mean throughout.
In doing so, every measure would be replaced by its
logarithm, and these logarithms would be treated just
as if they had been the observed values. The conclusions
to which they might lead would then be re-transmuted
to the numbers of which they were the logarithmic
equivalents.

In short, we have dealt mathematically with an ideal
population which has similar characteristics to those of
a real population, and have seen how closely the'
behaviour of the ideal population corresponds in every
stage to that of the real one. Therefore we have
arrived at a closely approximate solution of the problem
of statistical constancy, though numerous refinements
have been neglected.

Natural Selection. — This hardly falls within the
scope of our incjuiry into Natural Inheritance, but it
will be appropriate to consider briefly the way in
which the action of Natural Selection may harmonise
with that of pure heredity, and work together with it
in such a manner as not to compromise the normal
distribution of faculty. To do this, we must deal
with the case that best represents the various possible

120 NATURAL INHERITANCE. [chap.

occurrences, namely tliat in wliicli tlie mediocre members
of a population are those tliat are most nearly in
harmony with their circumstances. The harmony ought
to concern the aggregate of their faculties, combined
on the principle adopted in Table 3, after weighting
them in the order of their importance. We may deal
with any faculty separately, to serve as an example, if
its mediocre value happens to be that which is most
preservative of life under the majority of circumstances.
Such is Stature, in a rudely approximate degree, inas-
much as exceptionally tall or exceptionally short persons
have less chance of life than those of moderate size.

It will give more definiteness to the reasoning to
take a definite example, even though it be in part an
imaginary one. Suppose then, that we are considering
the stature of some animal that is liable to be hunted
by certain beasts of prey in a particular country. So
far as he is big of his kind, he would be better able
than the mediocrities to crush through thick grass and
foliage whenever he was scampering for his life, to jump
over obstacles, and possibly to run somewhat faster
than they. So far as he is small of his kind, he would
be better able to run through narrow openings, to
make quick turns, and to hide himself. Under the
general circumstances, it would be found that animals
of some particular stature had on the whole a better
chance of escape than any other, and if their race is
closely adapted to their circumstances in respect to
stature, the most favoured stature would be identical
with the M of the race. AVe already know that if we

VII.] DISCUSSION OF THE DATA OF STATURE. 121

call this value P, and write each stature under the
form of P + o^ (in which x includes its sign), and if the
number of times with which any value P + cc occurs,
compared to the number of times in which P occurs,
be called y, then x and y are connected by the law
of Frequency of Error.

Though the impediments to flight are less unfavour-
able, on the average, to the stature P than to any other,
they will differ in different experiences. The course of
one animal may chance to pass through denser foliage
than usual, or the obstacles in his way may be higher.
In that case an animal whose stature exceeded P would
have an advantage over mediocrities. Conversely, the
circumstances might be more favourable to a small
animal.

Each particular line of escape w^ould be most favour-
able to some particular stature, and whatever the value
of X might be, it is possible that the stature V-{-x
might in some cases be more favoured than any other.
But the accidents of foliage and soil in a country are
characteristic and persistent, and may fairly be con-
sidered as approximately of a typical kind. Therefore
those that most favour the animals whose stature is
P will be more frequently met with than those that
favour any other stature P-l-x, and the frequency
of the latter occurrence will diminish rapidly as x
increases. If the number of times with which any
particular value oiV-\-x is most favoured, as compared
with the number of times in which P is most favoured,
be called y\ we may fairly assume that y^ and x are

122 NATURAL INHERITANCE. [chap.

connected by the law of Frequency of Error. But
though the system of y values and that of if values
may be both subject to the law, it is not for a moment
to be supposed that their Q values are necessarily
the same.

We have now to show how a large population of
animals becomes reduced by the action of natural
selection to a smaller one, in which the M value of the
statures is unchanged, while the Q value is decreased.

To do this we must first consider the population to
have grown up entirely shielded from causes of pre-
mature mortality ; call their number N. Then suppose
them to be assailed by all the lethal influences that have
no reference to stature. These would reduce their
number to W, but by the hypothesis, the values of
M and of Q would remain unaffected. Next let the
influences that act selectively on stature, further reduce
the numbers to S ; these being the final survivors.
We have seen that : —

^=:the number of individuals who have the stature
Pzh^, counting those who have the stature P, as 1.

?/' = the number of times in which Pzb^ is the most
favoured stature, counting those in which P is the
most favoured, as 1.

Then yij — t]iQ number of times that individuals of
the stature Pzba^ are selected, counting those in which
individuals of the stature P are selected, as 1.

As the relation between y and x, and between y' and
X are severally governed by the law of Frequency of
Error, it follows directly from the formula by which

VII.] DISCUSSION OF THE DATA OF STATURE. 123

that law is expressed, that the relation between yy^ and
X is also governed by it. The value of P of course
remains the same throughout, but the Q in the system
of yy' values is necessarily less than that in the system
of y values.

It might well be that natural selection would favour
the indefinite increase of numerous separate faculties, if
their improvement could be effected without detriment
to the rest ; then, mediocrity in that faculty would
not be the safest condition. Thus an increase of
fleetness would be a clear gain to an animal liable to
be hunted by beasts of prey, if no other useful faculty
was thereby diminished.

But a too free use of this *Mf" would show a
jaunty disregard of a real difficulty. Organisms are
so knit together that change in one direction involves
change in many others ; these may not attract atten-
tion, but they are none the less existent. Organisms are
like ships of war constructed for a particular purpose
in warfare, as cruisers, line of battle ships, &c., on the
principle of obtaining the utmost efficiency for their
special purpose. The result is a compromise between
a variety of conflicting desiderata, such as cost, speed,
accommodation, stability, weight of guns, thickness of
armour, quick steering power, and so on. It is hardly
possible in a ship of any long established type to make
an improvement in any one of these respects, without a
sacrifice in other directions. If the fleetuess is increased,
the engines must be larger, and more space must be
given up to coal, and this diminishes the remaining

124 NATURAL INHERITANCE. [chap.

accommoda,tion. Evolution may produce an altogether
new type of vessel that shall be more efficient than the
old one, but when a particular type of vessel has become
adapted to its functions through long experience it is not
possible to produce a mere variety of its type that shall
have increased efficiency in some one particular without
detriment to the rest. So it is with animals.

Variability in Fraternities. — Human Fraternities are
far too small to admit of their Q being satisfactorily
measured by the direct method. We are obliged to
have recourse to indirect methods, of which no less than
four are available. I shall ajoply each of them to both
the Special and to the E.F.F. data ; this mil give 8
separate estimates of its value, which in the meantime
will be called h. The four methods are as follow :

First method ; by Fraternities each containing the
same nnmber of persons : — Let me begin by saying that
I had already found in the large Fraternities of Sweet
Peas, that the sizes of individuals of whom they con-
sisted were normally distributed, and that their Q was
independent of the size, or of the Stature as we may
phrase it, of the Mid- Fraternity. We have also seen
that the Q is practically the same in all Co-fraternities
of men. Therefore it is reasonable to expect that it
will also be found to be the same in all their Fraternities,
though owing to their small size we cannot assure our-
selves of the fact by direct evidence. We will assume
this to be the case for the present ; it will be seen that
the results justify the assumption.

VII.] DISCUSSION OF THE DATA OF STATURE. 125

The value of the IVI of a small Fraternity may be
much affected by the addition or subtraction even of
a single member, it may therefore be called the apparent
M, to be distinguished from the triie ^, from which its
members would be found to be dispersed, if there had
been many more of them. The apparent M approxi-
mates towards the true M as the Fraternity increases
in size, though at a much slower rate. We have now
somehow to get at this true M. For distinction and
for brevity let us call the apparent IV! of any small
Fraternity (MF^), and that of the corresponding true
IVI (MF). Then (MF) may be deduced from (MF') as
follows : —

We will begin by allowing ourselves for the moment
to imagine the existence of an exceedingly large Frater-
nity, far more numerous than is physiologically possible,
and to suppose that its members vary among themselves
just as widely, neither more nor less so, than in the
small Fraternities of real life. The (MF^) of our large
ideal Fraternity will therefore be identical with its (MF),
and its Q will be the same as h. Next, take at random
out of this huge ideal Fraternity a large number of small
samples, each consisting of the same number, n, of
brothers, and call the apparent Mid- values in the several
samples, (MF^i), (MF^s)? &c. It can easily be shown
that (MF^i), (MF^g)? &c., will be so distributed about the
common centre of (MF), that the Prob. Deviation of
any one of them from it, that is to say, the Q of their
system will = 7> x ^. If n = 1 , then the Prob. Devia-
tion becomes 6, as it should. If n = 2, the Prob.

126 NATURAL INHERITANCE. [chap.

Deviation is determined by tlie same problem as tbat
wliich concerned tbe Q of the Mid-Parentages (page 87),
where it was shown to be h x ~^. By similar reasoning,
when 72 = 3, the Prob. Deviation becomes ^ x -^, and
so on. When n is infinitely large, the Prob. Deviation
is 0 ; that is to say, the (MF^) values do not differ at
all from their common (MF).

Now if we make a collection of human Fraternities,
each consisting of the same number, n, of brothers, and
note the differences between the (MF^) in each frater-
nity and the individual brothers, we shall obtain a
system of values. By drawing a Scheme from these in
the usual way, we are able to find their Q ; let us call
it d. We then determine h in terms of d, as follows : —
The (MF^) values are distributed about their common
(MF), each with the Prob. Deviation of h x ^^^, and the
Statures of the individual Brothers are distributed
about their respective (MF^) values, each with the Prob.
Deviation d. The compound result is the same as
if the statures of the individual brothers had been
distributed about the common (MF), each with the
Prob. Deviation h,

consequently 5^ = (i^ -}- — , or lf= d^.

^ ^ n' n-1

I determined d by observation for four different
values of n, having taken four groups of Fraternities,
consisting respectively of 4, 5, 6, and 7 brothers, as
shown in Table 14. Substituting these four observed
values in turns for d in the above formula, I obtained

VII.] DISCUSSION OF THE DATA OF STATURE. 127

four independent values of h, wliich are respectively
I'Ol, 1-01, 1'20, and I'OS ; tlie mean of these is 1'07.

Second Method ; from the mean value of Fraternal
Eegression : — We may look on the Population as com-
posed of a system of Fraternities. Call their respective
true centres (see last paragraph) (MFi), (MFg), &c.
These will be distributed about P with an as yet un-
known Prob. Deviation, that we will call c. The
individual members of each Fraternity will of course
be distributed from their own (MF) with a Q equal to h.
Then {l'7Y = c' + ¥ (l)

Let P-l-(dzF„) be the stature of any individual, and
let P+(dzMF,,) be that of the M of his Fraternity,
then Problem 4 (page 69) shows us that : —

, , , , ^ (MFJ . c' , ,

the most probable value oi —^ — - is ^^,2 , 2 (2)

This is also the value of Fraternal Eegression, and
therefore equal to -f. Substituting in (2), and replacing
c by the value given by (l), we obtain 6=: 0*9 8
inch.

Third Method ; by the Variability in the value of
individual cases of Fraternal Eegression : — The figures
in each line of Table 13 are found to have a Q equal to
1 '24 inch, and they are the results of two independent
systems of variation. First, the several (MF) values (see
last paragraph) are dispersed from the M of all of
them with a Q that we will call v. Secondly the

128 NATURAL INHERITANCE. [chap.

individiial brotliers in each Fraternity are dispersed
from their own (MF) with a Q equal to h.
Hence {l'24.Y==v'-]-h\

he

But it is shown Problem 5 that v = ,/,2 , — 2\ J

7 2 2

therefore (1-24)^ = 6^ + 5^.

Substituting for c^ its value of (17)^ — 6^ (see last para-
graph), we obtain 5 = 0*98 inch.

Fourth Method ; from differences between pairs of
brothers taken at random : — In the fourth method,
Pairs of Brothers are taken at random, and the Differ-
ences between the statures in each pair are noted ; then,
under the following reservation, any one of these
differences would have the Prob. value of \/ 2 x 5. The
reservation is, that only as many Differences should be
taken out of each Fraternity as are independent. A
Fraternity of n brothers admits of '-^^^ possible pairs,
and the same number of Differences ; but as no more
than n—1 of these are independent, that number only
of the Differences should be taken. I did not appre-
ciate this necessity at first, and selected pairs of brothers
on an arbitrary system, which had at all events the
merit of not taking more than four sets of Differences
from any one Fraternity however large it might be.
It was faulty in taking three Differences instead of only
two, out of a Fraternity of three brothers, and four
Differences, instead of only three, from a Fraternity of

VII.]

DISCUSSION OF THE DATA OF STATURE.

129

four brothers, and therefore givang an increased weight
to those Fraternities, but in other respects the system
was hardly objectionable. The introduced error must
be so slight as to make it scarcely worth while now to
go over the work again. By the system adopted, I
found the Prob. Difference to be 1'55, which divided
by \^ 2 gives h =1'10 inch.

Thus far we have dealt with the special data only.
The less trustworthy R.F.F. give larger values of b in
every case. An epitome of all the results appears in
the following table : —

Methods and data.

Values of h obtained by different methods
and from different data.

From Special Data.

From R.F.F. data.l

(1) From Fraternities each
containing the same number of
persons

1-07
0-98
MO
MO

1-38
1-31
M4
1-35

(2) From the mean value of
Fraternal Regression

(3) From the Variability cf
Fraternal Regression

(4) From Pairs of Brothers
taken at random

Mean.

1-06

The data used in the four methods are somewhat
different. In (1) I could not deal with small Fraterni-

1 The E.F.F. results were obtained from brothers only and not from
transmuted sisters, except in method (2), where the paucity of the data
compelled me to include them,

K

130 NATURAL INHERITANCE. [ciiAr.

ties, so all were disregarded tliat contained fewer tlian
four individuals. In (2) and (3) I could, not with,
safety use large Fraternities. In (4) the method of
selection was, as we have seen, quite indifferent. This
makes the accordance of the results derived from the
Special data all the more gratifying. Those from the
E.F.F. data accord less well together. The E.F.F.
measures are not sufficiently exact for use in these
delicate calculations. Their results, being compounded
of b and of their tendency to deviate from exactness,
are necessarily too high, and should be discarded. I
gather from all this that we may safely consider the
value of h to be less than 1'06, and that allowing for
some want of precision in the Special data, the very
convenient value of 1*00 inch may reasonably be
adopted.

Trustivorthiness of the Constants. — There is difficulty
in correcting the results obtained from the E.F.F. data,
though we can make some estimate of their general
inaccuracy as compared with the Special data. The
reason of the difficulty is that the inaccuracy cannot
be ascribed to an uncertainty of equal ± amount in
every entry, such as might be due to a doubt of
"shoes off" or ''shoes on." If it were so, the Prob.
Error of a single value of the E.F.F. would be greater
than that of one of the Specials, whereas it proves to
be the same. It is likely that the inaccuracy is a com-
pound first of the uncertainty above mentioned, whose
effect would be to increase the value of the Prob. Error,

VII ] DISCUSSION OF THE DATA OF STATURE. 131

and secondly of a tendency on tlie part of my corre-
spondents to record medium statures when they were
in doubt, whose effect would be to reduce the value of
the Prob. Error, The E.F.R data in Table 12 run so
irregularly that I cannot interpret them with aDy
assurance. The value they give for Fraternal Eegression
certainly does not exceed ^, and therefore a correction,
amounting to no less than ^ of its amount, is required
to bring it to a parity with that derived from the
Special data (because i- + ^ x -J- = f). Hence it
might be argued, that the value of Eegression from
Mid-Parent to Son, which the E.F.F. data gave as f,
ought to receive a similar correction. If so, it would
be raised to |- -i- -| = f ; but I cannot believe this
high value to be correct. My first estimate made
from the E.F.F. data, was f , as already mentioned. If
this be adopted, the corrected value would be f , or ^
instead of f , which might possibly pass. Curiously
enough, this value of ^ for Eegression from Mid-Parent
to Son, coincides with the value of f for Eegression
from a single Parent to Son, which the direct observa-
tions showed (see page 99), but which owing to their
paucity and to the irregularity of the way in which
they ran, I rejected and still reject, at least for the
present. While sincerely desirous of obtaining a
revised value of average Filial Eegression from entirely
different and more accurate groups of data, the pro-
visional value already adopted of f from Mid- Parent
to Son may be accepted as being near enough for the
present. It is impossible to revise one datum in the

k2

132 NATURAL INHERITANCE. [chap.

E.F.F. series without revising all, as they hang together
and support one another.

General View of Kinship. — We are now able to deal
with the distribution of statures among the Kinsmen in
every near degree, of persons whose statures we know,
but whose ancestral statures we either do hot know, or
do not care to take into account. We are able to calcu-
late Tables for every near degree of Kinship on the form
of Table 11, and to reconstruct that same Table in a
shape free from irregularities. We must first find the
Regression, which we may call w, appropriate to the
degree of Kinship in question. Then we calculate a
value f for each line of a Table corresponding in form to
that of Table 11, in which/* was found to be equal to
1*50 inch. We deduce the value of y from that of w by
means of the general equation pV-{-f^=p^, p being
equal to 1*7 inch. The values to be inserted in the
several lines are then calculated from the ordinary table
(Table 5) of the "probability integral."

As an example of the first part of the process, let us
suppose we are about to construct a table of Uncles and
their Nephews, we find w and f as follows : A Nephew
is the son of a Brother, therefore in this case we have
t(;r=ixf=:f ; whence /= 1*66.

The Regression, which we call lu, is a convenient and
correct measure of family likeness. If the resemblance
of the Kinsman to the Man, was on the average as
perfect as that of the Man to his own Self, there would
be no Regression at all, and the value of lo would be 1.

VII.J

DISCUSSION OF THE DxVTA OF STATURE.

133

Table of Data for calculating Tables of Distribution of
Stature among the Kinsmen of Persons whose Stature is

KNOWN.

From group of persons of the same Stature,
to their Kinsmen in various near degrees.

Mean
regression=w.

Q = f

= PXV(1-W2).

Mid-parents to Sons

2/3
2/3

1/3

2/9

1/9

2/27

1-27
1-27

1-60

1-66

^ Practically
J that of Popu-
) lation, or
( 1'7 inch.

Brothers to Brothers

Fathers or Sons to "1

Sons or Fathers j

Uncles or Nephews to )
Nephews or Uncles j

Grandsons to Grandparents...
Cousins to Cousins

On the other hand, if the Kinsmen were on the average
no more like the Man than if they had been a group
picked at random out of the general Population, then
the Eegression to P would be complete. The IVI of the
Kinsmen, which is expressed by P + t(^(dzD), would in
that case become P, whatever might have been the value
of D ; therefore w must = 0. We see by the preceding
Table that as a general rule. Fathers or Sons should be
held to be only one-half as near in blood as Brothers,
and Uncles and Nephews to be one- third as near in
blood as Brothers. Cousins are 4-|^ times as remote as
Fathers or as Sons, and 9 times as remote as Brothers.
I do not extend the table further, because considera-
tions would have to be taken into account that will be
discussed in the next Section.

The remarks made in a previous chapter about

134 NATURAL INHERITANCE. [chap.

heritages tliat blend and those that are mutually exclu-
sive, must be here borne in mind. It would be a poor
prerogative to inherit say the fifth part of the peculiarity
of some gifted ancestor, but the chance of 1 to 5, of
inheriting the whole of it, would be deservedly prized.

Separate Contribution of each Ancestor. — In making
the statement that Mid-Parents whose Stature is P±D
have children whose average stature is PzhfD, it is
supposed that no separate account has been taken of
the previous ancestry. Yet though nothing may be
known of them, something is tacitly impKed and has
been tacitly allowed for, and this requires to be elimi-
nated before we can learn the amount of the Parental
bequest, pure and simple. What that something is, we
must now try to discover. When speaking of converse
Eegression, it was shown that a peculiarity in a Man
implied a peculiarity of J- of that amount in his Mid-
Parent. Call the peculiarity of the Mid-Parent D, then
the implied peculiarity of the Mid-Parent of the Mid-
Parent, that is of the Mid- Grand-Parent of the Man,
would on the above supposition be J^D, that of the Mid-
Great- Grand- Parent would be ^D, and so on. Hence
the total bequeathable property would amount to
I>(l+i + i + &c.)=Df.

Do the bequests from each of the successive genera-
tions reach the child without any, or what, diminution
by the way ? I have not sufficient data to yield a direct
reply, and must therefore try limiting suppositions.

First, suppose the bequests by the various generations

VII.] DISCUSSION OF THE DATA OF STATURE. 135

to be equally taxed ; then, as an accumulation of ances-
tral contributions whose sum amounts to Df yields an
effective heritage of only Df, it follows that each piece
of heritable property must have been reduced to f of its
original amount, because f x f = §.

Secondly, suppose the tax not to be uniform, but to
be repeated at each successive transmission, and to be

equal to - of the amount of the property at each
stage. In this case the effective heritage would be
I^ I - + TT^ + 7^2^ ^ — ) = I) , which must, as

before, be equal to Dl- : whence - = —
^ ^ r 11

Thirdly, it might possibly be supposed that the Mid-
Ancestor in a remote generation should on the average
contribute more to the child than the Mid-Parent, but
this is quite contrary to what is observed. The descend-
ants of what was " pedigree wheat," after being left to
themselves for many generations, show little or no trace
of the remarkable size of their Mid- Ancestors in the
generations just before they were left to themselves,
though the offspring of those Mid-Ancestors in the first
generation did so unmistakably.

The results of our only two valid limiting suppositions
are therefore, (l) that the Mid-Parental peculiarities,
pure and simple, influence the offspring to ^ of their
amount ; (2) that they influence it to ^ of their amount.
These values differ but slightly from ^, and their mean
is closely -|, so we may fairly accept that result. Hence

136 NATURAL INHERITANCE. [chap.

tlie influence, pure and simple, of the Mid-Parent may
be taken as ^, and that of tlie Mid- Grand- Parent as ^,
and so on. Consequently the influence of the individual
Parent would be ^, and of the individual Grand-Parent
^, and so on. It would, however, be hazardous on the
present slender basis, to extend this sequence with con-
fidence to more distant generations.

Pedigree Moths. — I am endeavouring at this moment
to obtain data that will enable me to go further, by breed-
ing Pedigree Moths, thanks to the aid of Mr. Frederick
Merrifield. The moths Selenia Illustraria and Illunaria
are chosen for the purpose, partly on account of their being
what is called double brooded ; that is to say, they pass
normally through two generations in a single year, which
is a great saving of time to the experimenter. They are
hardy, prolific and variable, and are found to stand chloro-
form well, previously to being measured and then paired.
Every mfember of each Fraternity is preserved along
three lines of descent — one race of long-winged moths,
one of medium-winged, and one of short- winged moths.
The three parallel sets are reared under identical con-
ditions, so that the medium series supplies a trustworthy
relative base, from which to measure the increasing
divergency of the others. No one can be sure of the
success of any extensive breeding experiment, but this
attempt has been well started and seems to present no
peculiar difficulty. Among other reasons for choosing
moths for the purpose, is that they are born adults, not
changing in stature after they have emerged from the
chrysalis and shaken out their wings. Their families

VII.] DISCUSSION OF THE DATA OF STATURE. 137

are of a convenient size for statistical purposes, say from
50 to 100, neither too few to make satisfactory Schemes,
nor unmanageably large. They can be mounted as
we all know, after their death, with great facility, and
be remeasured at leisure. An intelligent and expe-
rienced person can carry on a large breeding establish-
ment in a small room, supplemented by a small garden.
The methods used and the results up to last spring,
have been described by Mr. Merrifield in papers read
February and December 1887, and printed in the Tran-
sactions of the Entomological Society. I speak of this
now, in hopes of attracting the attention of some who
are competent and willing to carry on collateral experi-
ments with the same breed, or with altogether different
species of moths.

CHAPTER VIII.

DISCUSSION OF THE DATA OF EYE COLOUR.

Preliminary Remarks. — Data. — Persistence of Eye-Colour in tlie Popula-
tion.— Fundamental Eye-Colours. — Principles of Calculation. — Results.

Preliminary Remarhs. — In this chapter I will test
the conclusions respecting stature by an examination
into hereditary Eye-colour. Supposing all female
measures to have been transmuted to their male equi-
valents, it has been shown (l) that the possession of
each unit of peculiarity of stature in a man [that is of
each unit of difference from the average of his race]
when the man's ancestry is unknown, implies the exist-
ence on an average of just one- third of a unit of that
jDCculiarity in his "Mid-Parent," and consequently of
the same amount in each of his parents ; also just one-
third of a unit in his Son ; (2) that each unit of pecu-
liarity in each ancestor taken singly, is reduced in
transmission according to the following average scale ; —
a Parent transmits only |-, and a Grand-Parent only -^^.
Stature and Eye-colour are not only different as
qualities, but they are more contrasted in hereditary

CH. VIII.] DISCUSSION OF THE DATA OF EYE COLOUR. 139

behaviour than perhaps any other common qualities.
Parents of different Statures usually transmit a blended
heritage to their children, but parents of different Eye-
colours usually transmit an alternative heritage. If one
parent is as much taller than the average of his or her
sex as the other parent is shorter, the Statures of their
children will be distributed, as we have already seen, in
nearly the same way as if the parents had both been
of medium height. But if one parent has a light Eye-
colour and the other a dark Eye-colour, some of the
children will, as a rule, be light and the rest dark ; they
will seldom be medium eye-coloured, like the children
of medium eye-coloured parents. The blending in
Stature is due to its being the aggregate of the quasi-
independent inheritances of many separate parts, while
Eye-colour appears to be much less various in its
origin. If notwithstanding this two-fold difference
between the qualities of Stature and Eye-colour, the
shares of hereditary contribution from the various
ancestors are alike in the two cases, as I shall show that
they are, we may with some confidence expect that the
law by which those hereditary contributions are found
to be governed, may be widely, and perhaps universally
applicable.

Data. — My data for hereditary Eye-colour are drawn
from the same collection of "Eecords of Family
Faculties" ("E.F.F.") as those upon which the inquiries
into hereditary Stature were principally based. I have
analysed the general value of these data in respect to

140 NATURAL INHERITANCK [chap.

Stature, and sliown that they were fairly trustworthy.
I think they are somewhat more accurate in respect to
Eye-colour, upon which family portraits have often
furnished direct information, while indirect information
has been in other cases obtained from locks of hair that
were preserved in the family as mementos.

Persistence of Eye-colour in the Population. — The
first subject of our inquiry must be into the existence of
any slow change in the statistics of Eye-colour in the
English j)opulation, or rather in that particular part of
it to which my returns apply, that ought to be taken
into account before drawing hereditary conclusions.
For this purpose I sorted the data, not according to the
year of birth, but according to generations, as that
method best accorded with the particular form in which
all my E.F.F. data are compiled. Those persons who
ranked in the Family Kecords as the '^ children '^ of the
pedigree, were counted as generation I. ; their parents,
uncles and aunts, as generation 11. ; their grandparents,
great uncles, and great aunts, as generation III. ; their
great grandparents, and so forth, as generation IV. No
account was taken of the year of birth of the " children,"
except to learn their age ; consequently there is much
overlapping of dates in successive generations. We
may however safely say, that the persons in generation
I. belong to quite a different period to those in genera-
tion III., and the persons in II. to those in IV. I had
intended to exclude all children under the age of eight
years, but in this particular branch of the inquiry, I

viil] discussion OF THE DATA OF EYE COLOUR. 141

fear tliat some cases of young cliildren have been acci-
dentally included. I would willingly have taken a later
limit than eight years, but could not spare the data
that would in that case have been lost to me.

A great variety of terms are used by the various
compilers of the " Family Kecords " to express Eye-
colours. I began by classifying them under the follow-
ing eight heads ; — 1, light blue ; 2, blue, dark blue ;
3, grey, blue-green ; 4, dark grey, hazel ; 5, light brown ;
6, brown ; 7, dark brown ; 8, black. Then I constructed
Table 15. •

The diagram, page 143, clearly conveys the signifi-
cance of the figures in Table 15. Considering that
the groups into which the observations are divided are
eiffht in number, the observations are far from beino;
sufiiciently numerous to justify us in expecting clean
results ; nevertheless the curves come out surprisingly
well, and in accordance with one another. There can
be little doubt that the change, if any, during four
successive generations is very small, and much smaller
than mere memory is competent to take note o£ I
therefore disregard a current popular belief in the exist-
ence of a gradual darkening of the British population,
and shall treat the eye-colours of those classes of
our race who have contributed the records, as having
been statistically persistent during the period under
discussion.

The concurrence of the four curves for the four
several generations, affords internal evidence of the
trustworthiness of the data. For supposing we had

142 NATURAL INHERITANCE. [chap.

curves that exactly represented the true Eye- colours for
the four generations, they would either be concurrent
or they would not. If these curves were concurrent,
the errors in the R.F.F. data must have been so
curiously distributed as to preserve the concurrence.
If these curves were not concurrent, then the errors
in the E.F.F. data must have been so curiously distri-
buted as to neutralise the non- concurrence. Both of
these suppositions are improbable, and we must con-
clude that the curves really agree, and that the R.F.F.
errors are not large enough to spoil the agreement.
The close similarity of the two curves, derived respec-
tively from the whole of the male and the whole of
the female data, and the more perfect form of the curve
derived from the aggregate of all the cases, are
additional evidences in favour of the goodness of the
data on the whole.

Fundamental Eye-colours. — It is agreed among writers
{cf. A. de Candolle, see footnote overleaf) that the one
important division of eye-colours is into the light and
the dark. The medium tints are not numerous, but
may be derived from any one of four distinct origins.
They may be hereditary with no notable variation, they
may be varieties of light parentage, they may be
varieties of dark parentage, or they may be blends.
Medium tints are classed in my list under the heading
"4. Dark grey, hazel;" these form only 127 per
cent, of all the observed cases. In medium tints, the
outer portion of the iris is often of a dark grey colour,

mi.] DISCUSSION OF THE DATA OF EYE COLOUR. 143

Percentages of the Various Eye-colours in Four Successive Generations.

Number

of

cases

,Q

Sb

.^

a

0

be

g

.0

'd

^

-a

S

aT

^

•¥

1l

%

^

2

^

to

M

O

H

913

1515

1477

5S5

2277

2213

Generation IV,

Total Males

,, Females

4490

Total cases

IG .16.

144 NATURAL INHERITANCE. [cuap.

and the inner of a hazel. The proportion between the
grey and the hazel varies in different cases, and the
eye-colour is then described as dark grey or as hazel,
according to the colour that happens most to arrest
the attention of the observer. For brevity, I will
henceforth call all intermediate tints by the one name
of hazel.

I will now investigate the history of those hazel eyes
that are variations from light or from dark respectively,
or that are blends between them. It is reasonable to
suppose that the residue which were inherited from
hazel-eyed parents, arose in them or in their prede-
cessors either as variations or as blends, and therefore
the result of the investigation will enable us to assort
the small but troublesome group of hazel eyes in an
equitable proportion between light and dark, and thus
to simplify our inquiry.

The family records include 168 families of brothers
and sisters, counting only those who were above eight
years of age, in whom one member at least had hazel
eyes. For distinction I will describe these as " hazel-
eyed families ; " not meaning thereby that all the
children have that peculiarity, but only one or more of
them. The total number of the brothers and sisters
in the 168 hazel-eyed families is 948, of whom 302 or
about one-third have hazel eyes. The eye-colours of
all the 2 x 168, or 336 parents, are given in the records,
but only those of 449 of the grandparents, whose
number would be 672, were it not for a few cases of
cousin marriages. Thus I have information concerning

VIII.] DISCUSSION OF THE DATA OF EYE COLOUR. 145

about only two-tliirds of the grandparents, but this
will suffice for our purpose. The results are given in
Table 16.

It will be observed that the distribution of eye-colour
among the grandparents of the hazel-eyed families is
nearly identical with that among the population at
large. But among the parents there is a notable
difference ; they have a decidedly larger percentage
of light eye-colour and a slightly smaller proportion
of dark, while the hazel element is nearly doubled.
A similar change is superadded in the children. The
total result in passing from generations III. to I., is that
the percentage of the light eyes is diminished from
60 or 61 to 45, therefore by one quarter of its original
amount, and that the percentage of the dark eyes is
diminished from 26 or 27 to 23, that is by about one-
eighth of its original amount, the hazel element in
either case absorbiDg the difference. It follows that
the chance of a light-eyed parent having hazel off-
spring, is about twice as great as that of a dark-eyed
parent. Consequently, since hazel is twice as likely to
be met with in any given light-eyed family as in a
given dark- eyed one, we may look upon two-thirds of
the hazel eyes as being fundamentally light, and one-
third of them as fundamentally dark. I shall allot
them rateably in that proportion between light and
dark, as nearly as may be without using fractions, and
so get rid of them. M. Alphonse de CandoUe^ has

1 Heredite de la Conleur des Yeux dans I'Espece humaine," par
M. Alphonse de Candolle. " Arch. Sc. Phys. et Nat. Geneva," Aug. 1884,
3rd period, vol. xii. p. 97.

146 NATURAL INHERITANCE. [chap.

also shown from liis data, that yeux gris (which I take
to be the equivalent of my hazel) are referable to a
light ancestry rather than to a dark one, but his data
are numerically insufficient to warrant a precise estimate
of the relative frequency of their derivation from each
of these two sources.

In the following discussion I shall deal only with
those fraternities in which the Eye-colours are known
of the two Parents and of the four Grand- Parents.
There are altogether 211 of such groups, containing
an aggregate of 1023 children. They do not, however,
belong to 211 different family stocks, because each
stock which is complete up to the great grand-parents
inclusive (and I have fourteen of these) is capable
of yielding three such groups. Thus, group 1 contains
a, the ^' children ; " h, the parents ; c, the grand-
parents. Group 2 contains a, the father of the
" children " and his brothers and his sisters ; h, the
parents of the father ; c, the grand-parents of the
father. Group 3 contains the corresponding selections
on the mother's side. Other family stocks furnish two
groups. Gufc of these and other data. Tables 19 and
20 have been made. In Table 19 I have grouped
the families together whose two parents and four grand-
parents present the same combination of Eye-colour,
no group, however, being accepted that contains less
than twenty children. The data in this table enable
us to test the average correctness of the law I desire
to verify, because many persons and many families
appear in the same grouj), and individual peculiarities

viil] discussion OF THE DATA OF EYE COLOUR. 147

tend to neutralise each other. In Table 20 I have
separately classified on the same system all the families,
78 in number, that consist of six or more children.
These data enable us to test the trustworthiness of the
law as applied to individual families. It will be
seen from my way of discussing them, that smaller
fraternities than these could not be advantageously
dealt with.

It will be noticed that I have not printed the number
of dark- eyed children in either of these tables. They
are implicitly given, and are instantly to be found by
subtracting the number of light-eyed children from
the total number of children. Nothing would have
been gained by their insertion, while compactness would
have been sacrificed.

The entries in the tables are classified, as I said,
according to the various combinations of light, hazel,
and dark Eye-colours in the Parents and Grand-Parents.
There are six different possible combinations among the
two Parents, and 15 among the four Grand-Parents,
making 6 x 15, or 90 possible combinations altogether.
The number of observations are of course by no means
evenly distributed among the classes. I have no returns
at all under more than half of them, while the entries
of two light-eyed Parents and four light-eyed Grand-
Parents are proportionately very numerous.

The question of marriage selection in respect to
Eye-colour, has been already discussed briefly in p. 86.
It is a less simple statistical question than at a first sight
it may appear to be. so I will not discuss it farther.

L 2

148 NATURAL INHERITANCE. [chap.

Principles of Calculation. — I have next to show
how the expectation of Eye-colour among the children
of a given family is to be reckoned on the basis of
the same law that held in respect to stature, so that
calculations of the probable distribution of Eye-colours
may be made. They are those that fill the three last
columns of Tables 19 and 20, which are headed I.,
IL, and III., and are placed in juxtaposition with
the observed facts entered in the column hea.ded
" Observed." These three columns contain calculations
based on data limited in three difi'erent ways, in order
the more thoroughly to test the applicability of the
law that it is desired to verify. Column I. contains
calculations based on a knowledge of the Eye-colours
of the Parents only ; II. contains those based on a
knowledge of those of the Grand-Parents only ;
III. contains those based on a knowledge of those
both of the Parents and of the Grand-Parents, and
of them only.

I. Eye-colours given of the two Parents —

Let the letter S be used as a symbol to signify the
subject (or person) for whom the expected heritage is to
be calculated. Let F stand for the words " a parent of
S ; " Gi for " a grandparent of S ; " Go for "a great-
grandparent of S," and so on.

We must begin by stating the problem as it would
stand if Stature was under consideration, and then
modify it so as to apply to Eye-colour. Suppose then,
that the amount of the peculiarity of Stature j)os-
sesscd by F is equal to D, and that nothing whatever

VIII.] DISCUSSION OF THE DATA OF EYE COLOUR. 149

is known with certainty of any of tlie ancestors of
S except F. We have seen that though nothing may
actually be known, yet that something definite is implied
about the ancestors of F, namely, that each of his two
parents (who will stand in the order of relationship
of Gi to S) will on the average possess J^D. Similarly
that each of the four grandparents of F (who will stand
in the order of G2 to S) will on the average possess
^D, and so on. Again we have seen that F, on the
average, transmits to S only J of his peculiarity ,- that
Gi transmits only ^^ ; G2 only^^^, and so on. Hence
the aggregate of the heritages that may be expected
to converge through F upon S, is contained in the
following series : —

That is to say, each parent must in this case be
considered as contributino; 0"30 to the heritasre of the
child, or the two parents together as contributing 0*60,
leaving an indeterminate residue of 0*40 due to the
influence of ancestry about whom nothing is either
known or implied, except that they may be taken as
members of the same race as S.

In applying this problem to Eye-colour, we must bear
in mind that the fractional chance that each member
of a family will inherit either a light or a dark Eye-
colour, must be taken to mean that that same fraction

150 NATURAL INHERITANCE. [chap.

of tlie total number of cliilclren in the family will
probably possess it. Also, as a consequence of this
view of the meaning of a fractional chance, it follows
that the residue of 0*40 must be rateably assigned
between light and dark Eye-colour, in the proportion
in which those Eye-colours are found in the race
generally, and this was seen to be (see Table 16) as
61*2 :26'1 ; so I allot 0*28 out of the above residue
of 0'40 to the heritage of light, and 0"12 to the heritage
of dark. When the parent is hazel-eyed I allot f of
his total contribution of 0'30, i.e., 0*20 to light, and
■J-, i.e. O'lO to dark. These chances are entered in the
first pair of columns headed I. in Table 17.

The pair of columns headed I. in Table 18 shows
the way of summing the chances that are given in the
columns that have a similar heading in Table 17. By
the method there shown, I calculated all the entries
that appear in the columns with the heading I. in Tables
19 and 20.

II. Eye-colours given of the four Grand Parents —
Suppose D to be possessed by Gi and that nothing
whatever is known with certainty of any other ancestor
of S. Then it has been shown that the child of Gj
(that is F) will possess ^D ; that each of the two parents
of Gi (who stand in the relation of G2 to S) will also
possess -|-D ; that each of the four grandparents of Gi
(who stand in the relation of G3 to S) will possess -^D,
and so on. Also it has been shown that the shares
of their several peculiarities that will on the average
be transmitted by F, Gj, Go, &c., are \, y\j-, ^i^, &c.,

VIII.] DISCUSSION OF THE DATA OF EYE COLOUR. 151

respectively. Hence tlie aggregate of the probable
heritages from Gi are expressed by the following
series : —

d/1x -+1 xi+lx 2 x3^-+-x 4 xi+&c. ]

il2 V2* 3x2^ 3^x26 Jl Vl2 40

So that each grandparent contributes on the average
0*16 (more exactly 0'1583) of his peculiarity to the
heritage of S, and the four grandparents contribute
between them 0*64, leaving 36 indeterminate, which
when rateably assigned gives 0"25 to light and 0*11
to dark. A hazel-eyed grandparent contributes, accord-
ing to the ratio described in the last paragraph,
0*10 to light and 0*06 to dark. All this is clearly
expressed and employed in the columns IL of Tables 17
and 18.

III. Eye- colours given of the two Parents and four
Grand-Parents —

Suppose F to possess D, then F taken alone., and not
in connection with what his possession of D might imply
concerning the contributions of the previous ancestry,
will contribute an average of 0*25 to the heritage of
S. Suppose Gi also to possess D, then his contribution
together with what his possession of D may imply
concerning the previous ancestry, was calculated in the
last paragraph as D x ^^^ =D x 0'075. For the con-
venience of using round numbers I take this as
DxO"08. So the two parents contribute between

152 NATURAL INHERITANCE. [chap.

them 0'50 of the peculiarity of S, the four grand-
parents together with what they imply of the previous
ancestry contribute 0*32, being an aggregate of 0*82,
leaving a residue of 0"18 to be rateably assigned as
0'12 to light, and 0'6 to dark. A hazel-eyed Parent
is here reckoned as contributing 0'16 to light and 0*9 to
dark; a hazel-eyed Grand-Parent as contributing 0*5
to light and 0*3 to dark. All this is tabulated in
Table 17, and its working exjDlained by an example in
the columns headed III. of Table 1 8.

Results. — A mere glance at Tables 19 and 20 will
show how surprisingly accurate the predictions are, and
therefore how true the basis of the calculations must be.
Their average correctness is shown best by the totals
in Table 19, which give an aggregate of calculated
numbers of light-eyed children under Groups I., II., and
III. as 623, 601, and 614 respectively, when the observed
numbers were 629 ; that is to say, they are correct in
the ratios of 99, 96, and 98 to 100.

Their trustworthiness when applied to individual
families is shown as strongly in Table 20 whose results
are conveniently summarised in Table 21. I have there
classified the amounts of error in the several calculations :
thus if the estimate in any one family was 3 light-
eyed children, and the observed number was 4, I should
count the error as 1 '0. I have worked to one place of
decimals in this table, in order to bring out the different
shades of trustworthiness in the three sets of calcula-
tions, which thus become very apparent. It will be

VIII.] DISCUSSION OF THE DATA OF EYE COLOUR. 153

seen that the calculations in Class III. are by far the
most precise. In more than one-half of those calcula-
tions the error does not exceed 0 "5, whereas in more than
three -quarters of those in I. and II. the error is at least of
that amount. Only one-quarter of Class III., but some-
where about the half of Classes I. and II., are more than
1*1 in error. In comparing I. with 11. , we find I. to
be slightly but I think distinctly the superior estimate.
The relative accuracy of III. as compared with I. and
II., is what we should have expected, supposing the
basis of the calculations to be true, because the addi-
tional knowledge utilised in III., over what is turned
to account in I. and II., must be an advantage.

My returns are insufficiently numerous and too
subject to uncertainty of observation, to make it worth
while to submit them to a moi*e rigorous analysis, but
the broad conclusion to which the present results
irresistibly lead, is that the same peculiar hereditary
relation that was shown to subsist between a man and
each of his ancestors in respect to the quality of
Stature, also subsists in respect to that of Eye-colour.

CHAPTER IX

THE ARTISTIC FACULTY.

Data. — Sexual Distribution. — Marriage Selection. — Regression. — Effect of

Bias in Marriage.

Data. — It is many years since I described the family
history of the great Painters and Musicians in Here-
ditary Genius. The inheritance of much less excep-
tional gifts of Artistic Faculty will be discussed in this
chapter, and from an entirely different class of data.
They are the answers in my R.F.F collection, to the
question of ^' Favourite pursuits and interests ? Artistic
aptitudes ? "

The list of persons who were signalised as being
especially fond of music and drawing, no doubt
includes many who are artistic in a very moderate
degree. Still they form a fairly well defined class,
and one that is easy to discuss because their family
history is complete. In this respect, they are much
more suitable subjects for statistical inquiry than the
great Painters and Musicians, whose biographers usually
say little or nothing of their non-artistic relatives.

CHAP. IX.] THE ARTISTIC FACULTY. 155

The object of the present chapter is not to give a
reply to the simple question, whether or no the Artistic
faculty tends to be inherited. A man must be very
crotchety or very ignorant, who nowadays seriously
doubts the inheritance either of this or of any other
faculty. The question is whether or no its inheritance
follows a similar law to that which has been shown to
govern Stature and Eye- colour, and which has been
worked out with some completeness in the foregoing
chapters. Before answering this question, it will be
convenient to compare the distribution of the Artistic
faculty in the two sexes, and to learn the influence
it may exercise on marriage selection.

I begcin by dividing my data into four classes of
aptitudes ; the first was for music alone ; the second
for drawing alone ; the third for both music and
drawing ; and the fourth includes all those about whose
artistic capacities a discreet silence was observed. After
prefatory trials, I found it so difficult to separate
aptitude for music from aptitude for drawing, that I
determined to throw the three first classes into the
single group of Artistic. This and the group of the Non-
Artistic are the only two divisions now to be considered.
A difficulty presented itself at the outset in respect
to the families that included boys, girls, and young
children, whose artistic tastes and capacities can seldom
be fairly judged, while they are liable to be appraised
too favourably by the compiler of the Family records,
especially if he or she was one of their parents. As the
practice of picking and choosing is very hazardous in

156 NATURAL INHERITANCE. [chap.

statistical inquiries, however fair our intentions may be,
and as it in justice always excites suspicion, I decided,
though with much regret at their loss, to omit the wdiole
of those who were not adult.

Sexual Distribution. — Men and women, as classes,
may differ little in their natural artistic capacity,
but such difference as there is in adult life is some-
what in favour of the women. Table 9b contains
894 cases, 447 of men and 447 of women, divided
into three groups according to the rank they hold in
the pedigrees. These groups agree fairly well among
themselves, and therefore their aggregate results may
be freely accepted as trustworthy. They sho^v that
28 per cent, of the males are Artistic and 72 are
Not Artistic, and that there are 33 per cent. Artistic
females to 67 who are Not Artistic. Part of this
female superiority is doubtless to be ascribed to the
large share that music and drawing occupy in the
education of w^omen, and to the greater leisure that
most girls have, or take, for amusing themselves. If
the artistic gifts of men and women are naturally the
same, as the experience of schools where music and
drawing are taught, apparently shows it to be, the
small difference observed in favour of women in adult
life would be a measure of the smallness of the effect
of education compared to that of natural talent. Dis-
regarding the distinction of sex, the figures in Table
9b show that the number of Artistic to Non-Artistic
persons in the general population is in the proportion

IX.] THE ARTISTIC FACULTY. 157

of 30| to 69^. The data used in Table 22 refer to a
considerably larger number of persons, and do not
include more tban two-thirds of those employed in
Table 9b, and they make the proportion to be 31 to
69. So we shall be quite correct enough if we reckon
that out of ten persons in the families of my E.F.F.
correspondents, three on the average are artistic and
seven are not.

Marriage Selection. — Table 9 b enables us to ascer-
tain whether there is any tendency, or any disinclination
among the Artistic and the Non- Artistic, to marry within
their respective castes. It shows the observed fre-
quency of their marriages in each of the three possible
combinations ; namely, both husband and wife artistic ;
one artistic and one not ; and both not artistic. The
Table also gives the calculated frequency of the three
classes, supposing the pairings to be regulated by the
laws of chance. There is I think trustworthy evidence
of the existence of some slight disinclination to marry
within the same caste, for signs of it appear in each
of the three sets of families with which the Table
deals. The total result is that there are only 36 per
cent, of such marriages observed, whereas if there had
been no disinclination but perfect indifference, the
number would have been raised to 42. The difference
is small and the figures are few, but for the above
reasons it is not likely to be fallacious. I believe the
facts to be, that highly artistic people keep pretty much
to themselves, but that the very much larger body of

158 NATURAL INHERITANCE. [chap.

moderately artistic people do not. A man of liiglily
artistic temperament must look on those who are
deficient in it, as barbarians ; he would continually
crave for a sj^mpathy and response that such persons
are incapable of giving. On the other hand, every
quiet unmusical man must shrink a little from the idea
of wedding himself to a grand piano in constant action,
with its vocal and peculiar social accompaniments ; but
he might anticipate great pleasure in having a wife of
a moderately artistic temperament, who would give
colour and variety to his prosaic life. On the other
hand, a sensitive and imaginative wife would be con-
scious of needing the aid of a husband who had enough
plain common- sense to restrain her too enthusiastic
and frequently foolish projects. If wife is read for
husband, and husband for wife, the same argument
still holds true.

Eegression. — Having disposed of these preliminaries,
we will now examine into the conditions of the inherit-
ance of the Artistic Faculty. The data that bear upon
it are summarised in Table 22, where I have not cared
to separate the sexes, as my data are not immerous
enough to allow of more subdivision than can be
helped. Also, because from such calculations as I have
made, the hereditary influences of the two sexes in
respect to art appear to be pretty equal : as they are
in respect to nearly every other characteristic, exclu-
sive of diseases, that I have examined.

It is perfectly conceivable that the Artistic Faculty

IX.] THE ARTISTIC FACULTY. 159

in any person might be somehow measured, and its
amount determined, just as we may measure Strength,
the power of Discrimination of Tints, or the tenacity of
Memory. Let us then suppose the measurement of the
Artistic Faculty to be feasible and to have been often
performed, and that the measures of a large number
of persons were thrown into a Scheme.

It is reasonable to expect that the Scheme of the
Artistic Faculty would be approximately Normal in
its proportions, like those of the various Qualities and
Faculties whose measures were given in Tables 2 and 3.

It is also reasonable to expect that the same law of
inheritance might hold good in the Artistic Faculty
that was found to hold good both in Stature and in
Eye colour ; in other words, that the value of Filial
Kegression would in this case also be f.

We have now to discover whether these assumptions
are true without any help from direct measurement.
The problem to be solved is a pretty one, and will
illustrate the method by which many problems of a
similar class have to be worked.

Let the graduations of the scale by which the
Artistic Faculty is supposed to be measured, be such
that the unit of the scale shall be equal to the Q of
the Art- Scheme of the general population. Call the
unknown M of the Art-Scheme of the population, P.
Then, as explained in page 52, the measure of any
individual will be of the form P -f (zb D), where D
is the deviation from P. The first fact we have to
deal with is, that only 30 per cent, of the population

IGO NATURAL INHERITANCE. [chap.

are Artistic. Therefore no person whose Grade in the
Art-Scheme does not exceed 70° can be reckoned as
Artistic. Referring to Table 8 we see that the value
of D for the Grade of 70° is + 0*78 ; consequently the
art-measure of an Artistic person, when reckoned in
units of the accepted scale, must exceed P-}-0*78.

The average art-measure of all persons whose Grade
is higher than 70°, may be obtained with sufficient
ajDproximation by taking the average of all the values
given in Table 8, for every Grade, or more simply
for every odd Grade from 71° to 99° inclusive. It
will be found to be l*7l. Therefore an artistic
person has, on the average, an art-measure of
P -h l'7l. We will consider persons of this measure
to be representatives of the whole of the artistic por-
tion of the Population. It is not strictly correct to
do so, but for approximative purposes this rough and
ready method will suffice, instead of the tedious process
of making a separate calculation for each Grade.

The IVI of the Co -Fraternity born of a group of
Mid-Parents whose measure is P -h 171 will be
P -1- (f X 1-71) or (P + 1-4). We will call this value
C. The Q of this or any other Co-Fraternity may be
expected to bear approximately the same ratio to the
Q of the general population, that it did in the case
of Stature, namely, that of 1'5 to 17. Therefore the
Q of the Co-Fraternity who are born of Mid-Parents
whose Art-measure is C, will be 0'88.

The artistic members of this Co-Fraternity will be those
whose measures exceed (P -h 078}. We may write this

IX.] THE ARTISTIC FACULTY. 161

value in the form of {(P + 1-4) -0-36}, or {C — 0-36}.
Table 8 shows that the Deviation of— 0'36 is found
at the Grade of 40°. Consequently 40 per cent, of
this Co-Fraternity will be Non- Artistic and 60 per cent,
will be Artistic. Observation Table 23 shows the
numbers to be 36 and 64, wdiich is a very happy
agreement.

Next as regards the Non-Artistic Parents. The Non-
Artistic portion of the Population occupy the 70 first
Grades in the Art-Scheme, and may be divided into
two groups ; one consisting of 40 Grades, and standing
between the Grades of 70° and 30°, or between the
Grade of 50° and 20 Grades on either side of it, the
average Art-measure of whom is P ; the other group
standing below 30°, whose average measure maybe taken
to be P — 1*71, for the same reason that the group
above 70° was taken as P + 1'71. Consequently the
average measure of the entire Non-Artistic class is
-J^{(40 X P) -h 30 (P - 1-71)}
=3 P - f g X 1-71 = P - 073.
Supposing Mid-Parents of this measure, to represent the
entire Non- Artistic group, their offspring will be a Co-
Fraternity having for their IVI the value of P — {f x 0*73}
or P — 0*49, which we will call C, and for their Q the
value of 0'88 as before.

Such among them as exceed {P — 0'78}, which we
may write in the form of {(P — 0*49) + (1'27)}, or
{C + 1*27}, are Artistic, and they are those who,
according to Table 8, rank higher than the Grade 83°.
In other words, 83 per cent, of the children of Non-

M

162 NATURAL INHERITANCE. [chap.

Artistic parents will be Non-Artistic, and tlie re-
mainder of 17 per cent, will be Artistic. Observation
gives the values of 79 and 21, wbicb is a very fair
coincidence.

When one parent is Artistic and the other Not, their
joint hereditary influence would be the average of the
above two cases; that is to say, -^ (40 4- 83), or 61-^
per cent, of their children would be Non -Artistic, and
^ (60 ■+ 17), or 381 would be Artistic. The observed
numbers are 61 and 39, which agree excellently well.

We may therefore conclude that the same law of
Eegression, and all that depends upon it, which governs
the inheritance both of Stature and Eye-colour, applies
equally to the Artistic Faculty.

Effect of Bias in Marriage. — The slight apparent
disinclination of the Artistic and the Non- Artistic to
marry in their own caste, is hardly worth regarding,
but it is right to clearly understand the extreme effect
that might be occasioned by Bias in Marriage. Suppose
the attraction of like to like to become paramount, so
that each individual in a Scheme married his or her
nearest available neighbour, then the Scheme of Mid-
Parents would be practically identical wi th the Scheme
drawn from the individual members of the population.
In the case of Stature their Q would be 1'7 inch, instead
of 1'7 divided by \/2. The regression and subsequcut
dispersion remaining unchanged, the Q of the offspring
would consequently be increased.

On the other hand, suppose the attraction of contrast

IX.] THE ARTISTIC FACULTY. 163

to become suddenly paramount, so that Grade 99°
paired in an instant witli Grade 1°; next 98° with 2°;
and so on in order, until the languid desires of 49° and
51° were satisfied last of all. Then every one of
the Mid-Parents would be of precisely the same stature
P. Consequently their Q would be zero ; and that of
the system of the Mid-Co-Fraternities would be zero
also ; hence the Q of the next generation would con-
tract to the Q of a Co-Fraternity, that is to 1'5 inch.

Whatever might be the character or strength of the
bias in marriage selection, so long as it remains constant
the Q of the population would tend to become con-
stant also, and the statistical resemblance between
successive generations of the future Population would
be ensured. The stability of the balance between the
opposed tendencies of Eegression and of Co-Fraternal
expansion is due to the Eegression increasing with the
Deviation. Its efi'ect is like that of a spring acting
against a weight ; the spring stretches until its gradually
increasing resilient force balances the steady pull of the
weight, then the two forces of spring and weight are
in stable equilibrium. For, if the weight be lifted by the
hand, it will obviously fall down again as soon as the
hand is withdrawn ; or again, if it be depressed by the
hand, the resilience of the spring will become increased,
and the weight will rise up again when it is left free to
do so.

M 2

CHAPTEE X.

13ISEASE.

Preliminary Problem. — Data. — Trustwortliiiiess of R.F.F. Data. — Mixture
of Inheritance?. — Consumption : General Remai-ks ; Parent to Child ;
Distribution of Praternities ; Severely Tainted Fraternities ; Con-
snmptivity. — Data for Hereditary Diseases.

The vital statistics of a population are tliose of a
vast army marching rank behind rank, across the
treacherous table-lancl of life. Some of its members
drop out of sight at every step, and a new rank is ever
rising up to take the place vacated by the rank that
preceded it, and which has already moved on. The popu-
lation retains its peculiarities although the elements of
which it is composed are never stationary, neither are
the same individuals present at any two successive
epochs. In these respects, a population may be com-
pared to a cloud that seems to rejDOse in calm upon a
mountain plateau, while a gale of wind is blowing
over it. The outline of the cloud remains unchanged,
although its elements are in violent movement and in
a condition of perpetual destruction and renewal. Tlie

X.] DISEASE. 1G5

well understood cause of sucli clouds is the deflection
of a wind laden with invisible vapour, by means of
the sloping flanks of the mountain, up to a level at
which the atmosphere is much colder and rarer than
below. Part of the invisible vapour with wdiich the
wdnd was charged, becomes thereby condensed into the
minute particles of water of which clouds are formed.
After a while the process is reversed. The particles
of cloud having been carried by the wind across the
plateau, are swept down the other side of it again to a
lower level, and during their descent they return into
invisible vapour. Both in the cloud and in the
population, there is on the one hand a continual supply
and inrush of new individuals from the unseen ; they
remain a while as visible objects, and then disappear.
The cloud and the population are composed of elements
that resemble each other in the brevity of their exist-
ence, while the general features of the cloud and of the
population are alike in that they abide.

Preliminary Problem. — The proportion of the
population that dies at each age, is well known, and the
diseases of which they die are also w^ell known, but the
statistics of hereditary disease are as yet for the most
part contradictory and untrustworthy.

It is most desirable as a preliminary to more minute
inquiries, that the causes of death of a large number of
persons should be traced during two successive genera-
tions in somewhat the same broad way that Stature
and several other peculiarities were traced in the pre-

166 NATURAL INHERITANCE. [chap.

ceding chapters. There are a certain number of recog-
nized groups of disease, which we may call A, B, C, &c.,
and the proportion of persons who die of these diseases
in each of the two generations is the same. The pre-
liminary question to be determined is whether and to
what extent those who die of A in the second genera-
tion, are more or less often descended from those who
died of A in the first generation, than would have been
the case if disease were neither hereditarily transmitted
nor clung to the same families for any other reason.
Similarly as regards B, C, D, and the rest.

This inquiry would be more difficult than those
hitherto attempted, because longevity and fertility are
both affected by the state of health, and the circum-
stances of home life and occupation have a great effect
in causing and in checking disease. Also because the
father and mother are found in some notable cases to
contribute disease in very different degrees to their
male and female descendants.

I had hoped even to the last moment, that my
collection of Family Eecords would have contributed
in some small degree towards answering this question,
but after many attempts I find them too fragmentary
for the purpose. It was a necessary condition of success
to have the completed life-histories of many Fraternities
who were born some seventy or more years ago, that
is, during the earlier part of this century, as well as
those of their parents and all their uncles and aunts.
My Records contain excellent material of a later date,
that will be vahiable in future years ; but they must

X.] DISEASE. 167

bide tlieir time ; they are insufficient for the period in
question. By attempting to work with incompleted life
histories the risk of serious error is incurred.

Data, — The Schedule in Appendix G, which is illus-
trated in more detail by Tables A and B that follow it,
shows the amount of information that I had hoped to
obtain from those' who were in a -position to furnish
complete returns. It relates to the "Subject" of the
pedigree and to each of his 1 4 direct ancestors, up to the
great-grandparents inclusive, making in all 15 persons.
Also, to the Fraternities of which each of these 15 per-
sons was a member. Eeckoning the total average
number of persons in each fraternity at 5, which is
under the mark for my R.F.F collection, questions
were thus asked concerning an average of 75 different
persons in each family. The total number of the
Eecords that I am able to use, is about 160; so the
aggregate of the returns of disease ought to have been
about twelve thousand, and should have included the
causes of death of perhaps 6,000 of them. As a matter of
fact, I have only about one-third of the latter number,

Trustivorthiness of R.F.F. data. — The first object was
to ascertain the trustworthiness of the medical informa-
tion sent to me. There is usually much disinclination
among families to allude to the serious diseases that
they fear to inherit, and it was necessary to learn whether
this tendency towards suppression notably vitiated the
returns. The test applied was both simple and just.

168 NATURAL INHERITANCE. [chap.

If consumption, cancer, drink and suicide, appear among
tlie recorded cases of death less frequently than they do
in ordinary tables of mortality, then a bias towards
suppression could be proved and measured, and would
have to be reckoned wnth ; otherwise the returns might be
accepted as being on the whole honest and outspoken.
T find the latter to be the case. Sixteen per cent, of
the causes of death (or 1 in 6^) are ascribed to consump-
tion, 5 per cent, to cancer, and nearly 2 per cent.
to drink and to suicide respectively. Insanity was not
specially asked about, as I did not think it wise to put
too many disagreeable questions, however it is often
mentioned. I dare say that it, or at least eccentricity,
is not unfrequently passed over. Careful accuracy in
framing the replies appears to have been the rule rather
than the exception. In the preface to the blank forms
of the Records of Family Faculties .and elsewhere, I had
explained my objects so fully and they were so reason-
able in themselves, that my correspondents have
evidently entered with interest into what was asked for,
and shown themselves willing to trust me freely with
their family histories. They seem generally to have
given all that was known to them, after making much
search and many inquiries, and after due references to
registers of deaths. The insufiiciency of their returns
proceeds I feel sure, much less from a desire to suppress
unpleasant truths than from pure ignorance, and the
latter is in no small part due to the scientific ineptitude
of the mass of the members of the medical profession
two and more generations ago, when even the stetho-

X.] DISEASE. 109

scope was unknown. They were then incompetent to
name diseases correctly.

Mixture of Inheritances. — The first tiling that struck
me after methodically classifying the diseases of each
family, in the form shown in the Schedule, w^as their
great intermixture. The Tables A and B in Appendix Gl-
are offered as ordinary specimens of what is everywhere
to be found. They are actual cases, except that I have
given fancy names and initials, and for further conceal-
ment, have partially transposed the sexes. Imagine an
intermarriage between any two in the lower division of
these tables, and then consider the variety of inheritable
disease to wdiicli their children would be liable ! The
problem is rendered yet more complicated by the
metamorphoses of disease. The disease A in the parent
does not necessarily appear, even when inherited, as A in
the children. We know very little indeed about the
effect of a mixture of inheritable diseases, how far they
are mutually exclusive and how far they blend ; or how
far when they blend, they change into a third form.
Owing to the habit of free inter-marriage i)o person can
be exempt from the inheritance of a vast variety of
diseases or of special tendencies to them. Deaths by
mere old age and the accompanying failure of vital
powers without any w^ell defined malady, are very
common in my collection, but I do not find as a rule,
that the children of persons who die of old age have any
marked immunity from specific diseases.

There is a curious double appearance in the Eecords,

170 NATURAL INHERITANCE. [chap.

tlie one of an obvions liereditary tendency to disease
and the other of the reverse. There are far too many
striking instances of coincidence between the diseases of
the parents and of the children to admit of reasonable
doubt of their being often inherited. On the other hand,
when I hide with my hand the lower part of a page such
as those in Tables A and B, and endeavour to make
a forecast of what I shall find under my hand after
studying the upper portion, I am sometimes greatly mis-
taken. Very unpromising marriages have occasionally
led to good results, especially where the parental disease
is one that usually breaks out late in life, as in the case
of cancer. The children may then enjoy a fair length
of days and die in the end of some other disease ;
although if that disease had been staved off it is quite
possible that the cancer would ultimately have appeared.
I have two remarkable instances of this. In one of
them, three grandparents out of four died of cancer. In
each of the fraternities of which the father and mother
were members, one and one person only, died of it.
As to the children, although four of them have lived to
past seventy years, not one has shown any sign of
cancer. The other case differs in details, but is equally
remarkable. However diseased the parents may be, it
is of course possible that the children may inherit the
healthier constitutions of their remoter ancestry. Pro-
mising looking marriages are occasionally found to lead
to a sickly progeny, but my materials are too scanty to
permit of a thorough investigation of these cases.

The general conclusion thus far is, that owing to

X.] DISEASE. 171

the hereditary tendencies in each person to disease
being usually very various, it is by no means always
that useful forecasts can be made concerning the health
of the future issue of any couple.

Consumption.

General Remarks. — The frequency of consumption
in England being so great that one in at least every six
or seven persons dies of it, and the fact that it usually
appears early in life, and is therefore the less likely to
be forestalled by any other disease, render it an appro-
priate subject for statistics. The fact that it may be
acquired, although there has been no decided hereditary
tendency towards it, introduces no serious difficulty,
being more or less balanced by the opposite fact that it
may be withstood by sanitary precautions although a
strong tendency exists. Neither does it seem worth
while to be hypercritical and to dwell overmuch on the
different opinions held by experts as to what constitutes
consumption. The ordinary symptoms are patent
enough, and are generally recognized ; so we may be
content at first with lax definitions. At the same
time, no one can be more strongly impressed than
myself with the view that in proportion as we desire
to improve our statistical work, so we must be in-
creasingly careful to divide our material into truly
homogeneous groups, in order that all the cases con-
tained in the same group shall be alike in every
important particular, difi"ering only in petty details.
This is far more important than adding to the number

172 NATURAL INHERITANCE. [chap.

of cases. My material admits of no such delicacy of
division ; nevertlieless it leads to some results worth
mentioning.

In sorting my cases, I included under the liead of
Consumption all tlie causes of death described by one or
the other following epithets, attention being also paid
to the context, and to the phraseology used elsewhere
by the same writer : — Consumption ; Phthisis ; Tuber-
cular disease ; Tuberculosis ; Decline ; Pulmonary, or
lung disease ; Lost lung ; Abscess on lung ; Haemorrhage
of lungs (fatal) ; Lungs affected (here especially the
context was considered). All of these were reckoned
as actual Consumption.

In addition to these there were numerous phrases of
doubtful import that excited more or less reasonable
suspicion. It may be that the disease had not suffi-
ciently declared itself to justify more definite language,
or else that the phrase employed was a euphemism to
veil a harsh truth. Paying still more attention to the
context than before, I classed these doubtful cases
under three heads: — (1) Highly suspicious ; (2) Sus23i-
cious ; (3) Somewhat suspicious. They were so rated
that four cases of the first should be reckoned equivalent
to three cases of actual consumption, four cases of the
second to two cases, and four of the third to one case.

The following is a list of some of the phrases so dealt
with. The occasional appearance of the same phrase
under different headings is due to differences in the
context : —

1. Highly suspicious: — Consumptive tendency, Con-

X.] DISEASE 173

sumption feared, and died of bad cliill. Chest colds
with pleurisy and congestion of lungs. Died of an
attack on the chest. Always delicate. Delicate lungs.
Haemorrhage of lungs. Loss of part of lung. Severe
pulmonary attacks and chest affections.

2. Suspicious : — Chest complaints. Delicate chest.
Colds, cough and bronchitis. Delicate, and died of
asthma. Scrofulous tendency.

3. Somewhat suspicious : — Asthma when young. Pul-
monary congestion. Not strong ; anaemic. Delicate.
Colds, coughs. Debility ; general weakness. [The con-
text was especially considered in this group.]

Parent to Child. — I have only four cases in which both
parents were consumptive ; these will be omitted in the fol-
lowing remarks ; but whether included or not, the results
would be unaltered, for they run parallel to the rest.

There are QQ marriages in which one parent was
consumptive ; they produced between them 413 chil-
dren, of whom 70 were actually consumptive, and others
who were suspiciously so in various degrees. When
reckoned according to the above method of computation,
these amounted to 37 cases in addition, forming a total
of 107. In other words, 26 per cent, of the children
were consumptive. Where neither parent was consump-
tive, the proportion in a small batch of well marked
cases that I tried, was as high as 18 or 19 per cent, but
this is clearly too much, as that of the general population
is only 16 per cent. Again, by taking each fraternity
separately and dividing the quantity of consumption in
it by the number of its members, I obtained the averao;e

174

NATURAL INHERITANCE.

[chap.

consumptive taint of each fraternity. For instance, if
in a fraternity of 10 members there was one actually
consumptive member and four "somewhat suspiciously"
so, it would count as a fraternity of ten members, of
whom two were actually consumptive, and the average
taint of the fraternity would be reckoned at one-fifth
part of the wdiole or as 20 per cent.

Treating each fraternity separately in this way, and
then averaging the whole of them, the mean taint of
the children of one consumptive parent was made out
to be 28 per cent.

Distribution of Fraternities. — Next I arranged the
fraternities in such way as would show whether, if we
reckoned each fraternity as a unit, their respective
amounts of consumptive taint were distributed ^'nor-
mally " or not. The results are contained ia line A of
the following table : —

Percentage of Cases having various Percentages of Taint.

Percentages of Taint.

0

and

under

9

10

and

under

19

20

and

under

29

30

and

under

39

40

and

above

Total.

A. 66 cases, one
parent con-
sumptive.

27

20

9

15

29

100

B. 84 cases, one
brother con-
sumptive.

49

14

10

13

14

100

X.] DISEASE. 175

They struck me as so remarkable, in the way shortly
to be explained, that I proceeded to verify them by as
different a set of data as my Records could afford. I
took every fraternity in which at least one member
was consumptive, and treated them in a way that would
answer the following question. " One member of a
fraternity, whose number is unknown, is consumptive ;
what is the chance that a named but otherwise un-
known brother of that man will be consumptive also ? "
The fraternity that was taken above as an example,
would be now reckoned as one of nine members, of
whom one was actually consumptive. There were 84
fraternities available for the present purpose, and the
results are given in the line B of the table. The data
in A and B somewhat overlap, but for the most part
they differ.

They concur in telling the same tale, namely, that it
is totally impossible to torture the figures so as to make
them yield the single-humped " Curve of Frequency "
(Fig. 3 p. 38). They make a distinctly double-humped
curve, whose outline is no more like the normal curve
than the back of a Bactrian camel is to that of an
Arabian camel. Consumptive taints reckoned in this
way are certainly not " normally " distributed. They
depend mainly on one or other of two groups of causes,
one of which tends to cause complete immunity and
the other to cause severe disease, and these two groups
do not blend freely together. Consumption tends to
be transmitted strongly or not at all, and in this respect
it resembles the baleful influence ascribed to cousin

17G NATURAL INHERITANCE. [ciiap.

marriages, which appears to be very small when
statistically discussed, but of whose occasional severity
most persons have observed examples.

I interpret these results as showing that consumption
is largely acquired, and that the hereditary influence of
an acquired attack is small when there is no accom-
panyiag "malformation." This last phrase is intended
to cover not only a narrow chest and the like, but what-
ever other abnormal features may supply the physical
basis upon which consumptive tendencies depend, and
which I presume to be as hereditary as any other
malformations.

Severely -tainted Fraternities. — Pursuing the matter
further, I selected those fraternities in which consump-
tion was especially frequent, and in which the causes of
the deaths both of the Father and of the Mother were
given. They were 14 in number, and contained be-
tween them a total of 102 children, of whom rather
more than half died before the age of 40. Though
records of infant deaths were asked for, I doubt if
they have been fully supplied.. As 102 differs little
from 100, the following figures will serve as per-
centages : 42 died of actual consumption and 11 others
of lung disease variously described. Only one case
was described as death from heart disease, but weakness
of the heart during life was spoken of in a few cases.
The remaining causes of death were mostly undescribed,
and those that were named present no peculiarity worth
notice. I then took out the causes of death of the

x.|

DISEASE.

177

Fathers and Mothers and their ages at death, and
severally classified them as in the Table below. It
must be understood that there is nothing in the Table
to show how the persons were paired. The Fathers are
treated as a group by themselves, and the Mothers as a
separate group, also by themselves.

Causes of Death of the Parents of those Fraternities in which
Consumption Greatly Prevailed.

Father ^S® ^*
^^^'^^^' death.

Mother. ^^l^^
death.

Order of
ages at death.

F. M.

Asthma 70

Bronchitis 89

Inf. kidneys and bronchitis . 73
Abscess of liver through lung(alive)

Heart 68

Heart 74

Apoplexy 62

Apoplexy 75

Apoplexy. . 78

Decay 74

Cancer 52

Senile gangrene 76

(2 bros, d. of cancer).
Mortification of toe .... 59
Accident 51

(3 bros. and 2 ss. d. of cons.)

Consumption 40

Consumption 43

Consumption 47

Consumption 55

Consumption 65

Consumption 66

Water on chest ■. . . .60
Weak chest .... (alive)
(1 br. and 2 ss. d. of cons. )
Haemorrhage of lungs . 44
Ossification of heart . . 50

Nose bleeding 83

Cancer 42

Atrophy 73

Age 74

51
52
59
62
68
70
73
74
74
75
76
78
89

40
42
43
44
47
50
58
60
65
66
73
74
83

Very little account is given of the fraternities to which the fathers and
mothers belong, and nothing of interest beyond what is included in the above.

The contrast is here most striking between the
tendencies of the Father and Mother to transmit a
serious consumptive taint to their children. The cases
were selected without the slightest bias in favour of
showing this result ; in fact, such is the incapacity to
see statistical facts clearly until they are pointed out,
that 1 had no idea of the extraordinary tendency on

178 NATURAL INHERITANCE. [chap.

tlie part of tlie mother to transmit consumption, as
sliown in this Table, until I had selected the cases and
nearly finished sorting them. Out of the fourteen
families, the mother was described as actually dying
of consumption in six cases, of lung complaints in two
others, and of having highly consumptive tendencies
in another, making a total of nine cases out of the
fourteen. On the other hand the Fathers show hardly
any consumptive taints. One was described as of a
very consumptive fraternity, though he himself died of
an accident ; and another who was still alive had suffered
from an abscess of the liver that broke through the
lungs. Beyond these there is nothing to indicate
consumption on the Fathers' side.

Another way of looking at the matter is to compare
the ag^es at death of the Mothers and of the Fathers
respectively, as has been done at the side of the Table,
when we see a notable difference between them, the
Mid-age of the Mothers being 58, as against 73 of
the Fathers.

The only other group of diseases in my collection,
that affords a fair number of instances in which frater-
nities are greatly afiected, are those of the Heart.
The instances are only nine in number, but I give an
analysis of them, not for any value of their own, but
in order to bring the peculiarities of the consumptive
fraternities more strongly into relief by means of com-
parison. In one of these there was no actual death
from heart disease, though three had weak hearts and
two others had rheumatic gout and fever. These nine

X.]

DISEASE.

179

families contained between them sixty-nine children,
being at the rate of 7*7 to a family. The number of
deaths from heart disease was 24 ; from ruptured
blood vessels, 2 ; from consumption and lung disease,
8 ; from dropsy in various forms, 3 ; from apoplexy,
paralysis, and epilepsy, 5 ; from suicide, 2 ; from

Causes of Death of the Parents of those Fraternities in which
Heart Disease Prevailed.

Causes of death.

Ages at death.

Order of
ages at death.

Father.

Mother.

F.

M.

Heart

Apoplexy and paralysis .

Consumption

Asthma

Gout

Senile Gangrene ....
Tumour in liver ....

Cancer

Living

Unknown

59, 70
74, 78
53
70
55

75
old.

61, 63, 74

62, 70, 72

si

77

85
2 bros. and 1 sis.
d. of heart disease
and 1 of paralysis
cet. 40.

53

55
59
70
70
74
75
78
old.

61
62
63
70

72.
74
77
81
85

cancer, 1. There is no obvious difference between the
diseases of their Fathers and Mothers as shown in the
Table, other than the smallness of the number of cases
would account for. Their mid-ages at death were
closely the same, 70 and 72, and the ages in the two
groups run alike.

I must leave it to medical men to verify the amount
of truth that may be contained in what I have deduced
from these results concerning the distinctly superior

N 2

180 NATURAL INHERITANCE. [chap.

power of the mother over that of the father to produce
a highly consumptive family. Any physician in large
practice among consumptive cases could test the ques-
tion easily by reference to his note-books. A " highly
consumptive " fraternity may conveniently be defined
as one in which at least half of its members have
actually died of consumption, or else are so stricken
that their ultimate deaths from that disease may be
reckoned upon. Also to avoid statistical accidents, the
fraternities selected for the inquiry should be large,
consisting say of six children and upwards. Of course
the numerical proportions given by the above 14 frater-
nities are very rude indications indeed of the results to
which a thorough inquiry might be expected to lead.

Accepting the general truth of the observation
that consumptive mothers produce highly consumptive
families much more commonly than consumptive fathers,
it is easy to offer what seems to be an adequate ex-
planation. Consumption is partly acquired by some
form of contagion or infection, and is partly an here-
ditary malformation. So far as it is due to the latter
in the wide sense already given to the word " mal-
formation," it may perhaps be transmissible equally by
either parent. But so far as it is contagious or
infectious, we must recollect that the child is pecu-
liarly exposed during all the time of its existence
before birth, to contagion from its mother. Daring
infancy, it lies perhaps for hours daily in its mother's
arms, and afterwards lives much by her side, closely
caressed, and breathing the tainted air of her sheltered

X.] DISEASE. 181

rooms. The ex23lanatioii of the fact that we have
been discussing appears therefore to be summed u^ in
the single word — ^Infection.

Consumptivity . — Before abandoning the topic of
hereditary consumption, it may be well to discuss it
from the same point of view that was taken when
discussing the artistic temperament. Consumption
being so common in this country that fully one person
out of every six or seven die of it, and all forms of
hereditary disease being intermixed through marriage,
it follows that the whole population must be n]ore or
less tainted with consumption. That a condition which
we may call '' consumptivity," for want of a better
word, may exist without showing any outward sign,
is proved by the fact that as sanitary conditions worsen
by ever so little, more persons are affected by the
disease. It seems a fair view to take, that when the
amount of consumptivity reaches a certain level, the
symptoms of consumption declare themselves ; that
when it approaches but falls a little short of that level,
there are threatening symptoms ; that when it falls
far below the level, there is a fallacious appearance of
perfect freedom from consumptivity. We may reason-
ably proceed on the hypothesis that consumptivity
might somehow be measured, and that if its measure-
ment was made in each of any large group of persons,
the measures would be distributed " normally."

So far we are on fairly safe ground, but now un-
certainties begin upon which my data fail to throw

182 NATURAL INHERITANCE. [chap.

sufficient light. Longevity, marriage, and fertility
must all be affected by the amount of consumptivity,
whereas in the case of the faculties hitherto discussed
they are not affected to any sensible extent. It how-
ever happens that these influences tend to neutralize
one another. It is true that consumptive persons die
early, and many of them before a marriageable age.
On the other hand, they certainly marry earlier as a
rule than others, one cause of which lies in their
frequent great attractiveness ; and again, when they
marry, they produce children more quickly than others.
Consequently those who die even long before middle
age, often contrive to leave large families. The greater
rapidity with which the generations follow each other,
is also a consideration of some importance. There
is therefore a fair doubt whether a group of young
persons destined to die of consumption, contribute
considerably less to the future population than an
equally large group who are destined to die of other
diseases, I will at all events assume that consumptivity
does not affect the numbers of the adult children,
simply as a working hypothesis, and will afterwards
compare its results with observed facts.

I should add that the question whether the sexes
transmit consumption equally, lies outside the present
w^ork, at least for practical purposes ; for whether they
transmit it equally or not would not affect the results
materially. Our list of data is therefore limited to
these: — that 16 per cent, of the population die of
consumption, that consumptivity is normally distri-

X.] DISEASE. 183

buted, and that tlie law of hereditary regression from
a deviation of three units on the part of either
parent to an average of one unit in the child, may
be supposed to apply here, just as it did to Stature
and to the other subjects of the preceding chapters.

Let the scale by which consumptivity is measured be
such that the Q of the general population = 1. Let
its IVI = N, when measured on the same scale ; the
value of N is and will remain unknown. Let N + C
be the number of units of consumptivity that just
amount to actual consumption. Our data tell us that
16 per cent, of the population have an amount of con-
sumptivity that exceeds N + C. On referring to
Table 8, w^e find the value of C that corresponds to the
Grade of (100°— 16°), or of 84°, to be 1-47. There-
fore whenever the consumptivity of a person exceeds
N + 1*47, he has actual consumption.

Adding together the tabular values in Table 8 at all
the odd grades above 84°, we shall find their average
value to be 2*23. We may therefore assume (see p. 160)
that a group of persons each of whom has a consumpt-
ivity of N + 2*23 will approximately represent all the
grades above 84°. The Co-Fraternity descended . from
such a group will have an IVI whose value according
to the law of Eegression ought to be [N -f- ^ (2*23)]
or [N + 0-74 units.]

Those members of the Co-Fraternity are consumptive
whose consumptivity exceeds N -j- 1*47 ; these are the
same as those whose deviation from [N-l-0'74] which
is the IVI of the Co-Fraternity, exceeds -h 073 unit.

184 NATURAL INHERITANCE. [cHAr.

Let tlie Q of the Co-Fraternity be called n. The Grade
at which this amount of deviation occurs should be
found in Table 8 opposite to the value of 073 divided
by n.

Next as regards the value to be assigned to n, we
may be assured that the Q of a Co-Fraternity cannot
exceed that of the general population. Therefore n
cannot exceed 1. In the case of Stature the relation
between the Q of the Co-Fraternity and that of the
Population was found to be as 1 5 to 1 7. If the same
proportion held good here, its value would be 0"9.
This is I think too high an estimate for the following
reasons. The variability of the Co-Fraternity depends
on two groups of causes. First, on fraternal variability ;
which itself is due in part to mixed ancestry, and in
part to variety of nurture in the same Fraternity, both
before as well as after birth. Secondly, it depends upon
the variety of ancestry and nurture in different Frater-
nities. As to the first of the two groups of causes,
they seem to affect consumptive fraternities in the same
way as others, but not so with respect to the second
group. The household arrangements of vigorous, of
moderately vigorous, and of invalided parents are
not alike. I have already spoken of infection. There
is also a tradition in families that are not vio^orous, of
the necessity of avoiding risks and of never entering
professions that involve physical hardship. There is
no such tradition in families who are vigorous. Thus
there must be much greater variability in the environ-
ments of a group of persons taken from the population

X.] DISEASE. 185

at large, than there is in a group of consumptive
families. It would be quite fair to estimate the value
of n at least as low as 0'8.

We have thus three values of n to try; viz. 1, 0*9,
and 0*8, of which the first is scarcely possible and the
last is much the more suitable of the other two. The
corresponding values of 0'73 divided by 7i, are + 0.73,
+ O'Sl, and + 0'91. Eeferring to Table 8 we find the
Grades corresponding to those deviations to be 69, 71,
and 73. We should therefore expect 69, 71, or 73
per cent, of the Co-Fraternit}^ to be non-consumptive,
according to the value of n we please to adopt, and
the complement to those percentages, viz. 31, 29, or 27,
to be consumptive. Observation (p. 173), gave the value
of 26 by one method of calculation, and of 28 by
another.

Too much stress must not be laid on this coincidence,
because many important points had to be slurred over,
as already explained. Still, the prima facie result is
successful, and enables us to say that so far as this
evidence goes, the statistical method we have employed
in treating consumptivity seems correct, and that the
law of heredity found to govern all the difierent faculties
as yet examined, appears to govern that of consump-
tivity also, although the constants of the formula difi'er
slightly.

Data for Hereditary Diseases. — The knowledge of
the officers of Insurance Companies as to the average
value of unsound lives is by the confession of many of

186 NATURAL INHERITANCE. [chap. x.

them far from being as exact as is desirable. [See, for
example, tlie discussion on a memoir by G. Humphreys,
Actuary to the Eagle Insurance Company, read before
the Institute of Actuaries. — Insur. Mag. xviii. p. 178.]

Considering the enormous money value concerned, it
would seem well worth the while of the higher class
of those offices to combine in order to obtain a collec-
tion of completed cases for at least two generations, or
better still, for three ; such as those in Examples A and
B, Appendix G, but much fuller in detail. Being com-
pleted and anonymous, there could be little objection
on the score of invaded privacy. They would have no
perceptible effect on the future insurances of descend-
ants of the families, even if these were identified, and
they would lay the basis of a very much better
knowledge of hereditary disease than we now possess,
serving as a step for fresh departures. A main point
is that the cases should not be picked and chosen to
support any theor}", but taken as they come to hand.
There must be a vast amount of good material in
existence at the command of the medical officers of
Insurance Companies. If it were combined and made
freely accessible, it would give material for many
years' work to competent statisticians, and would be
certain, judging from all experience of a like kind,
to lead to unexpected results.

CHAPTER XL

LATENT ELEMENTS.

Latent Elements not very numerous. — Pure Breed. — Simplification of

Hereditary Inquiry.

Latent Elements not very numerous. — It is not
possible tliat more than one half of the varieties
and number of each of the parental elements, latent
or personal, can on the average subsist in the off-
spring. For if every variety contributed its repre-
sentative, each child would on the average contain
actually or potentially twice the variety and twice the
number of the elements (whatever they may be) that
were possessed at the same stage of its life by either
of its parents, four times that of any one of its
grandparents, 1024 times as many as any one of
its ancestors in the 10th degree, and so on, which is
absurd. Therefore as regards any variety of the entire
inheritance, whether it be dormant or personal, the
chance of its drojDping out must on the whole be equal
to that of its being retained, and only one half of the
varieties can on the average be passed on by inherit-

188 NATURAL INHERITANCE. [chap.

ance. Now we have seen that the personal heritage
from either Parent is one quarter, therefore as the total
heritage is one half, it follows that the Latent Elements
must follow the same law of inheritance as the Personal
ones. In other words, either Parent must contribute
on the average only one quarter of the Latent
Elements, the remainder of them dropping out and
their breed becoming absolutely extinguished.

There seems to be much confusion in current ideas
about the extent to which ancestral qualities are
transmitted, supposing that what occurs occasionally
must occur invariably. If a maternal grandparent be
found to contribute some particular quality in one
case, and a paternal grandparent in another, it seems
to be argued that both contribute elements in every
case. This is not a fair inference, as will be seen by
the following illustration. A pack of playing cards
consists, as we know, of 13 cards of each sort — hearts,
diamonds, spades, and clubs. Let these be shuffled
together and a batch of 13 cards dealt out from them,
forming the deal, No. 1. There is not a single card
in the entire pack that may not appear in these 13,
but assuredly they do not all appear. Again, let the
13 cards derived from the above pack, which we will
suppose to have green backs, be shuffled with another
13 similarly obtained from a pack with blue backs,
and that a deal. No. 2, of 13 cards be made from the
combined batches. The result will be of the same kind
as before. Any card of either of the two original
packs may be found in the deal, No. 2, but certainly

XL] LATENT ELEMENTS. 189

not all of tliem. So I conceive it to be with hereditary
transmission. No given pair can possibly transmit the
whole of their ancestral qualities ; on the other hand,
there is probably no description of ancestor whose
qualities have not been in some cases transmitted to
a descendant.

The fact that certain ancestral forms persist in breaking
out, such as the zebra-looking stripes on the donkey,
is no argument against this view. The reversion may
fairly be ascribed to precisely the same cause that makes
it almost impossible to wholly destroy the breed of
certain weeds in a garden, inasmuch as they are prolific
and very hardy, and wage successful battle with their
vegetable competitors whenever they are not heavily
outmatched in numbers.

If the Personal and Latent Elements are transmitted
on the average in equal numbers, it is difficult to
suppose that there can be much difference in their
variety.

Pure Breed. — In a perfectly pure breed, maintained
during an indefinitely long period by careful selection,
the tendency to regress towards the M of the general
population, would disappear, so far as that tendency
may be due to the inheritance of mediocre ancestral
qualities, and not to causes connected with the relative
stability of different types. The Q of Fraternal Devia-
tions from their respective true Mid-Fraternities which
we called 6, would also diminish, because it is partly
dependent on the children in the same family taking

190 NATURAL INHERITANCE. [chap

variously after different and unlike progenitors. But
tlie difference between 5 in a mixed breed such as we
have been considering, and the value whicli we may
call /3, wliich it would have in a pure breed, would be
very small. Suppose the Prob: Error of the implied
Stature of each separate Grand-Parent to be even as
great as the Q of the general Population, which is 17
inch (it would be less, but we need not stop to discuss
its precise value), then the Prob : Error of the implied
Mid-Grand-Parental stature would be \/ J x 1'7 inch, or
say 0*8 inch. The share of this, which would on the
average be transmitted to the child, would be only ^ as
much, or 0'2. From all the higher Ancestry, put
together, the contribution would be much less even than
this small value, and we may disregard it. It results
that ¥ is a trifle greater than ^8^ 4-0*04. But 6 = 1'0;
therefore 13 is only a trifle less than 0*98.

Simplification of Hereditary Inquiry. — These
considerations make it probable that inquiries into
human heredity may be much simplified. They assure
us that the possibilities of inheritance are not likely to
differ much more than the varieties actually observed
among the members of a large Fraternity. If then we
have full life-histories of the Parents and of numerous
Uncles and Aunts on both sides, we ought to have a
very fair basis for hereditary inquiry. Information of
this limited kind is incomparably more easy to obtain
than that which I have hitherto striven for, namely,
family histories during four successive generations.

XI.] LATENT ELEMENTS. 191

When tlie " cliildren " in the pedigree are from 40 to
55 years of age, their own life-histories are sufficiently
advanced to be useful, though they are incomplete,
and it is still easy for them to compile good histories
of their Parents, Uncles, and Aunts. Friends who
knew them all would still be aliYC, and numerous
documents such as near relations or personal friends
preserve, but which are mostly destroyed at their
decease, would still exist. If I were undertaking
a fresh inquiry in order to verify and to extend my
previous work, it would be on this basis. I should not
care to deal with any family that did not number at
least six adult children, and the same number of uncles
and aunts on both the paternal and maternal sides.
Whatever could be learnt about the grandparents
and their brothers and sisters, would of course be
acceptable, as throwing further light. I should how-
ever expect that the peculiarities distributed among
any large Fraternity of Uncles and Aunts would fairly
indicate the variety of the Latent Elements in the
Parent. The complete heritage of the child, on the
average of many cases, might then be assigned as
follows : One quarter to the personal characteristics of
the Father ; one quarter to the average of the personal
characteristics of the Fraternity taken as a whole, of
whom the Father was one of the members; and similarly
as regards the Mother's side.

CHAPTEE XIL

SUMMARY

The investigation now concluded is based on tlie fact
tliat the characteristics of any population that is in
harmony with its environment, may remain statistically
identical durino; successive orenerations. This is true
for every characteristic whether it be affected to a great
degree by a natural selection, or only so slightly as to
be practically independent of it. It was easy to see
in a vague way, that an equation admits of being based
on this fact ; that the equation might serve to suggest
a theory of descent, and that no theory of descent that
failed to satisfy it could possibly be true.

A large part of the book is occupied with preparations
for putting this equation into a working form. Obstacles
in the way of doing so, which I need not recapitulate,
appeared on every side ; they had to be confronted in
turns, and then to be either evaded or overcome. The
final result was that the higher methods of statistics,
which consist in applications of the law of Frequency
of Error, were found eminently suitable for expressing

CHAP. XII.] SUMMARY. 193

the processes of heredity. By their aid, the desired
equation was thrown into an exceedingly simple form
of approximative accuracy, and it became easy to
compare both it and its consequences with the varied
results of observation, and thence to deduce numerical
results.

A brief account of the chief hereditary processes
occupies the first part of the book. It was inserted
principally in order to show that a reasonable a priori
probability existed, of the law of Frequency of Error
being found to apply to them. It was not necessary for
that purpose to embarrass ourselves with any details
of theories of heredity beyond the fact, that descent
either was particulate or acted as if it were so. I need
hardly say that the idea, though not the phrase of
particulate inheritance, is borrowed from Darwin's pro-
visional theory of Pangenesis, but there is no need in
the present inquiry to borrow more from it. Neither
is it requisite to take Weissmann's views into account,
unless I am mistaken as to their scope. It is freely
conceded that particulate inheritance is not the only
factor to be reckoned with in a complete theory of
heredity, but that the stability of the organism has also
to be regarded. This may perhaps become a factor of
great importance in forecasting the issue of highly bred
animals, but it was not found to exercise any sensible
influence on those calculations with which this book is
chiefly concerned. Its existence has therefore been only
noted, and not otherwise taken into account.

The data on which the results mainly depend had to be

0

194 NATURAL INHERITANCE. [chap.

collected specially, as no suitable material for the purpose
was, so far as I know, in existence. This was done by
means of an offer of prizes some years since, that placed
in my hands a collection of about 160 useful Family
Records. These furnished an adequate though only
just an adequate supply of the required data. In order
to show the degree of dependence that might be placed
on them they were subjected to various analyses, and
the result proved to be even more satisfactory than
might have been fairly hoped for. Moreover the errors
in the Records probably affect different generations in
the same way, and would thus be eliminated from the
comparative results.

As soon as the character of the problem of Filial descent
had become well understood, it was seen that a general
equation of the same form as that by which it was
expressed, also expressed the connection between Kins-
men in every degree. The unexpected law of universal
Regression became a theoretical necessity, and on
appealing to fact its existence was found to be con-
spicuous. If the word "peculiarity" be used to signify
the difference between the amount of any faculty pos-
sessed by a man, and the average of that possessed
by the population at large, then the law of Regression
may be described as follows. Each peculiarity in a man
is shared by his kinsmen, but on the average in a less
deg:ree. It is reduced to a definite fraction of its
amount, quite independently of what its amount might
be. The fraction differs in different orders of kinship,
becoming smaller as they are more remote. When the

XII.] SUMMARY. 195

kinsliip is so distant that its effects are not worth, taking
into account, the peculiarity of the man, however re-
markable it may have been, is reduced to zero in his
kinsmen. This apparent paradox is fundamentally due
to the greater frequency of mediocre deviations than of
extreme ones, occurring between limits separated by
equal widths.

Two causes affect family resemblance ; the one is
Heredity, the other is Circumstance. That which is
transmitted is only a sample taken partly through the
operation of "accidents," out of a store of otherwise un-
used material, and circumstance must always play a
large part in the selection of the sample. Circumstance
comprises all the additional accidents, and all the pecu-
liarities of nurture both before and after birth, and every
influence that may conduce to make the characteristics
of one brother differ from those of another. The
circumstances of nurture are more varied in Co -Fra-
ternities than in Fraternities, and the Grandparents
and previous ancestry of members of Co-Fraternities
differ; consequently Co-Fraternals differ among them-
selves more widely than Fraternals.

The average contributions of each separate ancestor
to the heritage of the child were determined apparently
within narrow limits, for a couple of generations at
least. The results proved to be very simple; they
assign an average of one quarter from each parent,
and one sixteenth from each grandparent. According
to this geometrical scale continued indefinitely back-
wards, the total heritage of the child would be

o 2

196 NATURAL INHERITANCE. [chap

accounted for, but the factor of stability of type has
to be reckoned witli, and this has not yet been
adequately discussed.

The ratio of filial Eegression is found to be so bound
up with co-fraternal variability, that when either is
given the other can be calculated. There are no
means of deducing the measure of fraternal variability
solely from that of co-fraternal. They differ by an element
of which the value is thus far unknown. Consequently
the measure of fraternal variability has to be calculated
separately, and this cannot be done directly, owing to
the small size of human families. Four different and
indirect methods of attacking the problem suggested
themselves, but the calculations were of too delicate a
kind to justify reliance on the E.F.F. data. Separate
and more accurate measures, suitable for the purpose,
had therefore to be collected. The four problems were
then solved by their means, and although different
groups of these measures had to be used with the
different problems, the results were found to agree
together.

The problem of expressing the relative nearness of
different degrees of kinship, down to the point where
kinship is so distant as not to be worth taking into
account, was easily solved. It is merely a question of
the amount of the Eegression that is appropriate to the
different degrees of kinship. This admits of being
directly observed when a sufficiency of data are acces-
sible, or else" of being calculated from the values found
in this inquiry. A table of these Eegressions was given.

XII.] SUMMARY. 197

Finally, considerations were oflfered to show that
latent elements probably follow the same law as personal
ones, and that though a child may inherit qualities from
any one of his ancestors (in one case from this one, and
in another case from another), it does not follow that the
store of hidden property so to speak, that exists in any
parent, is made up of contributions from all or even
very many of his ancestry.

Two other topics may be mentioned. Eeason
was given in p. 16 why experimenters upon the
transmission of Acquired Faculty should not be dis-
couraged on meeting with no affirmative evidence
of its existence in the first generation, because it
is among the grandchildren rather than among the
children that it should be looked for. Again, it is
hardly to be expected that an acquired faculty, if
transmissible at all, would be transmitted without dilu-
tion. It could at the best be no more than a variation
liable to Eegression, which would probably so much
diminish its original amount on passing to the grand-
children as to render it barely recognizable. The
difficulty of devising experiments on the transmission
of acquired faculties is much increased by these
considerations.

The other subject to be alluded to is the funda-
mental distinction that may exist between two
couples whose personal faculties are naturally alike.
If one of the couples consist of two gifted mem-
bers of a poor stock, and the other of two ordinary
members of a gifted stock, the difference between

198 NATURAL INHERITANCE. [chap. xii.

them will betray itself in their offspring. The children
of the former will tend to regress ; those of the latter
will not. The value of a good stock to the well-
being of future generations is therefore obvious, and
it is well to recall attention to an early sign by
which we may be assured that a new and gifted
variety possesses the necessary stability to easily
originate a new stock. It is its refusal to blend
freely with other forms. Some among the members
of the same fraternity might possess the character-
istics in question with much completeness, and the
remainder hardly or not at all. If this alternative
tendency was also witnessed among cousins, there
could be little doubt that the new variety was of a
stable character, and therefore capable of being easily
developed by interbreeding into a pure and durable
race.

TABLES.

Table 1.

Strength of Pull.

519 Males aged 23-26.

From mea sures made at the International Health Exhibition in 1884.

Strength of Pull.

No. of cases
observed.

Percentages.

No. of cases
observed.

Sums from
beginning.

Under 50 lbs.

10

2

2

„ 60 ,,

42

8

10

„ 70 „

140

27

37

,, 80 „

168

33

70

„ 90 „

113

21

91

„ 100 „

22

4

95

Above 100 ,,

24

5

100

Total

519

100

200

NATURAL INHERITANCE.

_o

-^ CO

CN 0

00 0

CO OS

'^

la

C<1 Oi

0 «o

CO ^

'^ l?q

•

-* CM

CM ir^

(X) 0

-^ (io

!>. -^

Oi 00

Oil 0

0 t^

CO CO

CO CO

j:^ ^

CO CO

t^ CO

r-l I— 1

CM 1-1

7-1

CM r-l

o

o

0

OT '^

x^^ CO

CO t^

CO CO

o

• •

X^i CM

J>. t—

Oi I— 1

0 l^

•

CM iH

Oi

j-i i>

t- iO

CO CO

CO '^H

ir- t^

C30 iO

0 CO

CM CO

CO CO

^
rt

X:^ 1:0

CO CO

J>. CO

rH l-H

CM r-l

7-1

CM rH

<1

o

0 CO

T-l 05

CO ^

OS iH

o

•

•

•

CO CO

00 ^

CM t^

XO CM

• •

0 OS

o

o

I— 1
o

oo

0 iO

CO CO

CM >0
t^ CO

10 CO
r-\ tH

-* CO
CM i-l

00 '"^

Oi CO

0 xo
CM iH

CO CM

-g

o

(>? 0

t^ CO

^ IC

0 »o

"73

o

o

• •

• •

• •

0 CM

«0 7-4

0 '^

7-1 00

CO !>.

o

J>.

05 -*

CO ■<*
CO CO

7— 1 -*

t^ CO

10 CO

I— I I— 1

CO 10

CM i-l

00 -^

Oi XO

0 -<*
CM iH

CM CM

fii

o

03

s

iM

0

iO 05

CO <M

CO 1>-

iH 0

aT

O

• •

J>. Oi

CO -*

t^ CM

00 XO

• •

CO CO

CO

00 CO
«0 CO

CO -^
CO CO

0 CO

t^ CO

'^ CM

7-1 I— 1

CM ^
<M 7-1

t^ -^

00 XO

OS -*
tH tH

CM CM

^"

O

t/3

r^

0

05 CO

0 95

05 0

7H -■*

Eh iT

(D

O

•

• •

CO <M

Oi CO

^ 0

xn> CM

" •

XO '^

0,00

*^oo

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1^^ CO

CO CD

CO CO
CO CO

05 CO
CO CO

^ CM
rH rH

7—1 CO
CM T-t

i:^ ^

00 XQ

CO CO

tH tH

CM CM

(D I— 1

+3

■■■"

HB^^^^

CD

a

0

CO Jr^

^ CO

0 -*

CO 00

o

•

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05 CO

7—1 7—1

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CM 05

• •

CO CM

S o

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t^ CM

CO CO

IH) CO
CO CO

Oi CM

CO CO

CO 7-1
7-1 7-<

7-1 CO

CM T-l

t^ CO

00 -^

t-- (M

iH iH

CM CM

o • r3

Pi

IB

!:§

0

10 r-l

CO CO

cq t^

CM iH

Co .Th

:S

o

•

10 ^

Oi '^

00 CO

Oi t^

(M OS

m-^

+3

CO

CO CM

kO CO

QO r-l

CO rH

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CO CO

i>. ^

CO cq

CM iH

S >^

rf

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CO CO

I— 1 rH

1—1 1-4

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(U

g'^

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05 Oi

cq t^

CM CO

■3
>

0

o

CM

7-1 0

t-- U5

'::i4 -rjl

CO CO

0 CO

^ §

10 r-l
CO CO

'^ CM
CO CO

t^ 0

CO CO

CO 7—1
7-1 1-1

00 7—1
r-l T-l

CO CO

t^ ^

XO iH
7H r-<

CM iH

»p Oi

<M CO

T* 'P

7H tH

M -p

O

10 10

t^ CM

0 CM

7-1 Oi

t^ (M

4t< 05

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CO Oi

CM 0

t^ 0

CO CO

t^ CO

'^ 0

7H iH

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tH

CO 0

CO CO

CO 10

I— 1 r-l

1—1 7—1

tH rH

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F3 5

C<5 OS

ip CO

0 CO

CM CM

Q

T-H (M

T-l (M

CO 0

t^.CO

00 0

a"*^

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CO T-l

iO CXD

(M 0

CO Oi

iO CO

CD CO

CO Oi

tH t-<

DO.S

2

3 1-

CD VO

CO CO

CD >0

1—1 1—1

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pi

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l-H 0

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0 CO

CM ir^

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CO rH

CO CO

5? o

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7—1 t^

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1-1 1^

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tH t^

OS CO

6 2

n +-

O

00 i>-

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CM CM

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CO '^

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tw O

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,

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^— v--

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a;)

W

0

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CD

m

0 a>

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ft §

03

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+f

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CD

^

r^

r^

rt

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r^

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a

0

0

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pi

pi

pi

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0

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f

B

fl

rt

i=l

0

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h— 1

HH

l-H

1— H

Ph

p^

l-H

ft

1-4

T-i

T-H

CO

CO

c©

«o

CO

CO

<b"

VO

0

\a

CM

CM

CM

CM

<M

CM

fq-

fefl

1

1

1

1

1

1

1

1

1

o

-*i

CO

CO

CO

CO

CO

CO

CO

CO

CO

02

CM

c^

CM

CM

CM

(M

CM

CM

CM

H

,-w^^-^

—^.-^^

^.^-^-^

,-^>--^

^ .'

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s

c

>

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>>

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(U +3

^

CO © ■

f=l

f

&c •

^•5

•

•rH

03 ^

■^ 5R

5R '^ S •

o
m

o

H

i

<

c
5

3

s

0

?

2

PJ

■^ (D

C 0

<S ^
*^

-^ 2

•rH ii-t

CO 0
d

S p

2

f-
eJ

0

ft
w.

0 0

0

^ P!
o-i 0

0 w

f-< 5. 2

W.

0

l-H

«i-l
0

00

•l-H

rt -1-^ -^

i^ 0 0 s

TABLES.

201

^

^ o

^^

> ce

.So-
o

_© X:^

IS ^
O o

CO

CM

§ O!

-(-' ni
2 '^

PQ ;^ (D

CO

H

(M PI

O

•rH r^

gj CO

CO ^

O

o

m
o

M

<

l-l

>•
p

05

O

CO'vtiCOlOCOCOOS-^OO^OSOO -^CO CC(M CMVO

iJqC<lC^Cq<M<MCM<MC<l(NCNrH CMC<I ^(M C^i-H

ooi— lOs-t^asoooocMcooito coci t^i>. laco

a505t^ot;^C5(MC50cooo5-^ Oicrs t^°o i>-co

J— ItHi— IC<Ji— li— ICNi— l(MC<IrHiH i-(i— I iHi— I i— IrH

(NC<:)10<MO00OO«01O«0C0 05CO OOO lOlO

J^CMi— (G<)rHC<IO-DCOrHCOOas COCO »7^^7^ CMOS

rHi-Hi— It— li— (I— li— li— It— li— li-H rHi— I i— li-H i— (

OOCOlOCMOOOOOt^OCO Jr^O Ot-H ioi>.

t^OOJ>.00 1-^OOJ>-C5?0<p0010 i>.00 COt>. l>.iO

lOt^rHOCOt^OOOOi— lOt^ 050 CNCO ITiOO

COCOMCOCOCO-^CDCqcO'^CN CO-:f< I^^CO (MICO

O " * ' ' •'"'

o

CO

o

CM

oooooooooooo oo oo

>Ot^CO«DCO(NOOGvI?OOl-^ 050 ^00
COCO«OCOM1CO^-«*ICOCO-<*(N CO-<:t< COCO

O OO
lO CO

7-l^COCO(N05000COOCO 1>.?0 0-*
OOt^:>.t>.OOCOOOl^OOt^GOiO t^^O GOOO

(NCOlOC<IOCOOO,OOOCOO ?DO (MIO
(N(Mi— ICqcOCMCMj— ICNCMCOOO i-tCN 05C0

lO (M
CM lO

I— I i-H 1— I T— I

cooos»ocoi>.ooa3i^<;o^ -hco ooco
Oil— ioooioooooo<;ooooc30CD ooi>. «oi— i

CO t—

Oi cq

00 05

05 I— I

J>. OO

CO CO

05 O
CO -*

o o

CO
CO

CM CM

00 oo

^£

C0rHCMV0i:0l0OO(M0i05(M CM>7<I «Dt-I OCO

I^t^lOKlCOCOCMCX)COCOCOOi COi— I Ot^ o«o

C^CMCMCMC^CMCmAhcMCMCmAh CMCM <M(M C0(M

o ^

THOCOVOr-HOOCDCMt^CiO OiO COi— I
(X)t>-01>.QOJ?>-XOCMCM<MO(M XOCM lOCM

00 CO
Oi CO
CO ^

xn

%^^^^%^%^%^%^ %^ %r^ %^

iT: OJ S CS

t5«

PI

pi

o

=^ PI

PI
pi
o

p)

05 'Ti

i_i PL, Oi— I PM

Pi E>^

(A O

!>

<M(MiOCMi>.t^OOOOO(M
Jr^OCSlOOOOOOOOOlOCM

XO O

O CM
O CM

1— li— IOOCMr-tOi-(Ttl05J>.10 J>-1>. (Mi— I

•S r5 ^

CD £ O

PQ ^ S

OJ O

O M

CO ^'^

r/5

ni

1

V)

CI

c3

P!

p)

03

^ §.

1-1

'-5

g=?

j/2 o o c

o

PI
as

o

OO
CO

C3»

202

NATURAL mHERITANCE.

Tables 4 to 8 inclusive give data for drawing Normal Curves
of Frequency and Distribution. They also show the way in
which the latter is derived from the values of the Probability
Integral.

The equation for the Probablity Curve^ is y = k e in which

A is "th-e Measure of Precision." By taking ^ and h each as
unity, the values in Table 4 are computed.

Table 4.

Data for a Normal Curve of Frequency.

y

= e

X

y

X

y

X

y

X

y

0

1-00

±

10

0-37

± 2-0

0-0183

± 3-0

0-0001

±

0-2

0-96

±

1-2

0

23

± 2-2

0-0079

±

0-4

0-85

±

1-4

0

14

± 2-4

0-0032

± infi-

0-0000

±

0-6

0-70

±

1-6

0

78

±2-6

0-0012

nity

±

0-8

0-53

±

1-8

0-40

± 2-8

0-0004

Table 5.

2 r* -f2

Values of the Probability Integral, — = I e

cU, for Argument t.

t{=hx)

•0

•1

•2

-3

•4

•5

-6

•7

•8

-9

.1

2-0
infinite

0-00

0-843

-9953

1-0000

0-11

0-880
•9970

0-22
0 910
-9981

0-33

0-934

■9989

0-43

0-952

•9993

0-52

0-966

-9996

0-60

0-976

•9998

0-68
0-984
9999

0-74

0-989

•9999

0-80

0-923

•9999

When t = '4769 the corresponding tabular entry would be '50;
therefore, '4769 is the value of the " Probable Error."

1 See Merriman O71 the Method of Least Squares (Macmillan, 1885), pp. 26, 186,
where fuller Tables than 4, 5, and 6 \Aill be found

TABLES.

20:

Table 6.

Yalues of the Probability Integral for Argument q^^j^', that is, when the unit
of measurement = the Probable error.

Multiples

of the

•0

•1

•2

•3

•4

•5

•6

•7

•8

•9

Probable

Error.

0

0-00

0-65

0-11

0-16

0-21

0-26

0-31

0-36

0-41

0-46

1-0

•50

•54

'58

•62

•66

•69

••72

•75

•78

•80

2-0

•82

•84

•86

.88

•89

•91

•92

•93

•94

•95

3-0

•957

.964

•969

•974

•978

•982

•985

•987

•990

•992

4-0

•9930

.9943

•9954

•9963

•9970

•9976

•9981

•9985

•9988

•9990

5-0
infinite

•9993
1^000

•9994

•9996

•9997

•9997

•9998

•9998

•9999

•9999

•9999

Tables 5 and 6 show the proportion of cases in any Normal
system, in which the amount of Error lies within various extreme
values, the total number of cases being reckoned as 1 'O. Here no re-
gard is paid to the sign of the Error, whether it be plus or minus, but
its amount is alone considered. The unit of the scale by which the
Errors are measured, differs in the two Tables. In Table 5 it is
the " Modulus," and the result is that the Errors in one half of the
cases, that is in 0 50 of them lie within the extreme value (found by
interpolation) of 0*4769, while the other half exceed that value.
In Table 6 the unit of the scale is 0'4769. It is derived from Table
5 by dividing all the tabular entries by that amount. Consequently
one half of the cases have Errors that do not exceed 1*0 in terms of
the new unit, and that unit is the Probable Error of the System.
It will be seen in Table 6 that the entry of "50 stands opposite to
the argument of I'O.

If it be desired to transform Tables 5 and 6 into others that shall
show the proportion of cases in which the plus Errors and the minus
Errors respectively lie within various extreme limits, their entries
would have to be halved.

Let us suppose this to have been done to Table 6, and that a
new Table, which it is not necessary to print, has been thereby pro-
duced and which we will call 6a. Next multiply all the entries in the
new Table by 100 in order to make them refer to a total number
of 100 cases, and call this second Table 6b. Lastly make a converse
Table to 66 ; one in which the arguments of 6b become the entries,
and the entries of 6b become the arguments. From this the Table 7

202

NATURAL INHERITANCE.

is made. For example, in Table 6, opposite to the argument TOO, the
entry of '50 is found ; that entry becomes "25 in 6a, and 25 in 66.
In Table 7 the argument is 25, and the corresponding entry is 1-00.
The meaning of this is, that in 25 per cent, of the cases the greatest
of the Errors just attains to ± 1-0. Similarly Table 7 shows that
the greatest of the Errors in 30 per cent, of the cases, just attains
to ± 1"25 ; in 40 per cent, to 1*90, and so on. These various per-
centages correspond to the centesimal Grades in a Curve of Distri-
bution, when the Grade 0° is placed at the middle of the axis, which
is the point where it is cut by the Curve, and where the other
Grades are reckoned outwards on either hand, up to + 50° on the
one side, and to — 50° on the other.

To recapitulate : — In order to obtain Table 7 from the primary
Table 5, we have to halve each of the entries in the body of Table 5,
then to multiply each of the arguments by 100, and divide it by
°4769. Then we expand the Table by interpolations, so as to
include among its entries every whole number from 1 to 99 inclusive.
Selecting these and disregarding the rest, we turn them into the
arguments of Table 7, and we turn their corresponding arguments
into the entries in Table 7.

Table 7.

Ordina-tes to Normal Curve of Distribution

on a scale whose unit = the Probable Error ; and in which the 100 Grades run
from 0° to + 50° on the one side, and to - 50° on the other.

Grades.

0

1

2

3

4

5

6

7

8

9

0

0-00

0-04

0-07

0-11

0-15

0.19

0-22

0-26

0-30

0-34

10

0-38

0-41

0-45

0-49

0-53

0-57

0-61

0-65

0-69

0-74

20

0-78

0-82

0-86

0-97

0-95

1-00

1*05

1-10

1-15

1-20

30

3-25

1-30

1-36

1-42

1-47

1-54

1-60

1-67

1-74

1-82

40

1-90

1-99

2-08

2-19

2-31

2-44

2-60

2-79

3-05

3-45

But in the Schemes, the 100 Grades do not run from— 50° through
0° to + 50°, but from 0° to 100°. It is therefore convenient to
modify Table 7 in a manner that will admit of its being used
directly for drawing Schemes without troublesome additions or
subtractions. This is done in Table 8, where the values from
50° onwards, and those from 50° backwards are identical with
those in Table 7 from 0° to ± 50°, but the first half of those
in Table 8 are positive and the latter half are negative.

TABLES.

205

00

o
Ph

(O

o

o
)^

o
o

H
H

I— I
o

O "

c3

05
05

o

CO

CM

00

I— 1

O

CO

1:-

o

CM

00

C5

rH
1

r— 1
I

O
1

o

1

O
1

o

+•

o

+

rH

+

I— 1

+

CO

+

CO

o

CO
CO

CO

00

o

o

CO

C5
CO

rH

o

CO

1

1— H

1

o

I

o

1

o

1

o

1

o

+

rH

+

1-^

+

CO

+

OS
I— 1

1—1

05

as

1—1

CO

CO

o
1— 1

CO

05

1:^

CM

1

rH
1

o

1

o
1

o

1

o

+

o

+

I— 1

+

I— <
+

CM

+

1—1
CO

05

CO

1—1

cq

CM

1—1

CO

o

o

CO

o

CO

CO

I

I— 1
1

o
1

o

1

o

1

o

+

o

+

I— 1

+

rH
+

CM

+

o
o

05

I— <

C5
1—1

o
o

lO

1

I— i
1

1—1

1

o

1

o

o

+

o

+

I— 1

+

1 — 1

+

cq

+

O

o

CO

XO

o

I— 1
CO

C<1

Id

1 — 1

CO

t-

^

1 — 1

CO

^

1

I— 1

1

1—i

1

o

1

o

1

o

+

o

+

o

+

7— <

CM

+

CO

ir-

1

1:^

CO

T— 1

I

o
I

o

1

CO

cq

o

1

1—1

rH

o

+

05

6

+

I— 1

o

+

r-H
+

Ci
rH

CM

+

o

-*
t-

1—1

CO

o
CO

O

CO
GO

CO
CO

00

o

(M

CO

1

I— 1

I

r— 1

1

o

1

o

1

o

+

o

+

o

+

I-H

+

CM
+

00

o

1:-

CO

o

rH

00

o

CO

05
C5

T-H

CO

I

I— 1

1

rH
1

o
1

o

1

o

+

o

+

o

+

I— 1

+

rH
+

o

05

CM

00
1:-

CO

CO

o
o

GO

CO

CO

o

C5

o

1

1—1

1

rH
1

O
1

o

1

o

o

+

o

+

1 — 1
+

rH
+

o

o

T— 1

o

o

CO

o

o

o

CO

o

o

00

o

o

o

tH

>^

+

+->

1=1

•1-1

yd

4J

o

+

»o

x~-.

OJ

r^

^

o

o
o

^

tH

^

1

a

a

,W r^

lO

nC

CM

+->

-(-3

o

o

o

iH

(N

(1)

GO

nri

rt

u

1

O

tn

aj

^

(D . IT
tH

O

O)
W -(J

O O

CO

_o ."S ^

IS i-i ^

^ d O "

•S I Oi

^ ^ ^

oa O 0)

fl o

o

206

NATURAL INHERITANCE.

Table 9.

Marriage Selection in respect to Stature.

The 205 male parents and the 205 female parents are each divided into three
groups — T, M, and S, and t, m, and s, respectively — that is. Tall, Medium, and
Stiort (medium male measurements being taken as 67 inches, and upwards to 70
inches). The number of marriages in each possible combination between them
were then counted, with the result that men and women of contrasted heights,
Short and Tall, or Tall and Short, married about as frequently as men and women
of similar heights, both Tall or both Short ; there were 32 cases of the one to
27 of the other.

s., t.

12 cases.

M., t.

20 cases.

T., t.
18 cases.

S., m.
25 cases.

M., m.

51 cases.

T., m.

28 cases.

S., s.
9 cases.

M., s.
28 cases.

T., s.
14 cases.

Short and tall, 12 + 14 = 3 2 cases.

Short and short, 9 \ _ ^,7

Tall and tall, 18 f - ^' ^^a^®^-

We may therefore regard the married folk as couples picked out of the general
population at haphazard when applying the law of probabilities to heredity of
stature.

Table 9a.

Marriage Selection in respect to Eye- Colour
in 78 Parental Couples.

Eye Colour of

No. of

cases

observed.

Per Cents.

'Eije Colour
of Husband
and Wife.

Husband

Wife.

Obs.

Chance.

Observed.

Chance.

Light
Hazel
Dark

Light
Hazel
Dark

29
2
6

37
3

8

37
2

7

}"

46

Alike

Light
Hazel

Hazel
Dark

Hazel
Light

Dark
Hazel

} -
1 ^

23
5

15

7

V 28

22

/ Half-con-
\ trasted

Light
Dark

Dark

Light

i "

24

32

24

32

Contrasted

The chance combinations in pairs are calculated for a population containing
61*2 per cent, of Light Eye-colour, 12-7 of Hazel, and 26-1 of Dark.

TABLES.

207

Table 9 b.

Marriages of the Artistic and the Not Artistic.

Rank in Pedigrees.

No. of
per-
sons.

Percentages.

Pairs of artistic and not artistic
persons.

Marriages
observed.

Chance
combinations.

art. ,

not.

art.

not.

both
art.

1 art.
Inot.

both
not.

both
art.

1 art.
Inot.

both
not.

Parents

326

280

288

32

27
24

68
73

76

39
30

28

61

70

72

14

12

9

31
31
41

50
57
50

12

8

7

46
41
39

42
51
54

Paternal grandparents..
Maternal grandparents..

Totals and means...

894

28

72

33

67

12

36

52

9

42

49

Tastes of Husband and Wife — alil^'ft

12 -f 52 =64
36

9 + 49 = 58
42

(

3ontrastp.d

Table 10.

Effect upon Adult Children of Differences in Height of their

Parents.

Difference in inches

between the Heights

of the Parents.

Proportion per 50 of cases in which

the Heights^ of the Children

deviated to various amounts from

the Mid-filial Stature of their

respective families.

Number of

Children whose

Heights were

observed.

(Total 525. )

Less than
2 inches.

^CO

Cj (X)

Under 1 inch

21
23
16
24

18

35
37
34
35
30

43
46
41
41

40

46
49
45
47
47

48
50
49
49
49

105
122
112

108

78

1 and under 2

2 „ 3

3 „ 5 ,

5 and above

^ Every female height has been transmuted to its male equivalent by multi-
plying it byl"08, and only those families have been included in which the
number of adult children amounted to six, at least.

j^OTE. — When these figures are protracted into curves, it will be seen — (1)
that they run much alike ; (2) that their peculiarities are not in sequence ; and
(3) that the curve corresponding to the first line occupies a medium position. It
is therefore certain that differences in the heigh ts of the Parents have on the
whole an inconsiderable effect on the heights of their Offspring.

208

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TABLES.

211

Table 14 (Special Data).

Deviations of individual Brothees from their Mid-Fraternal

Statures.

Number of brothers in eacli family

4

5

6

7

Number of Families

39

23

8

6

Amount of Deviation.

Number
of cases.

Number
of cases.

Number
of cases.

Number
of cases.

Under 1 inch

88

49

15

4

62

30

17

3

3

20

18

5

3

2

21

14

6

1

1 and under 2

2 and under 3

3 and under 4

4 and above

P 2

212

NATURAL INHERITANCE.

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o

TABLES.

213

Table 16.

The Descent of Hazel-eyed Families.

Total
cases.

Observed.

Percentages,

Light.

Hazel, Dark,

Light,

Hazel.

Dark.

General population

III. Grandparents

11 Parents

4490
449
336
948

2746
267
165
430

569
61

85
302

1175
121

86
216

61-2
60
49
45

12-7
13

25
32

26^
27
26
23

I. Children

Table 17.

Calculated Contributions of Eye-colour.

Contribution to the
heritage from each.

Data limited to the eye-colours of the

2 parents.

4 grandparents.

2 parents and
4 grandparents.

L

IL

in.

Light.

Dark.

Light.

Dark.

Light.

Dark.

Light-eyed parent

0-30
0-20

0-28

0-10
0-30

0'12

0-16
0-10

0-25

■ 0-66
0-16

0-11

0-25
0-16

0-08
0-05

0-12

0'09
0-25

0 -OS
0-08

0-06

Hazel-eyed parent

Dark-eyed parent

Light-eyed grandparent..
Hazel-eyed grandparent .
Dark-eyed grandparent...

Residue, rateably as-
signed

214

NATURAL INHERITANCE.

Table 18.

Example of One Calculation in each of the Theee Cases.

Ancestry and their
eye-colours.

I.

o

O

Light-eyed parents.
Hazel-eyed parents.
Dark-eyed parents .

Light-eyed grand-
parents

Hazel-eyed grand-
parents

Dark-eyed grand
parents

Contribute
to

Lisrht.

Dark.

0-60

Residue, rateably as-
signed

Total contributions

0-28

0-88

0-12

0-12

1-00

6 '^

II.

Contribute
to

Light.

0-16
0-20

0-25

0-61

Dark.

012
0-16

0-11

0-39

1-00

o

O cS

d

III.

Contribute
to

Light.

016

0-08
010

012

0-46

Dark.

0-09
0-25

0-06
0-08

0-06

0-54

1-00

TABLES.

215

Table 19.

Obseeved and Calculated Eye-coloues in 16 Geoups of Families.

Those families are grouped together in whom the distribution of Light, Hazel,
and Dark Eye-colour among the Parents and Grandparents is alike. Each group
contains at least Twenty Brothers or Sisters.

Eye-colours of the

Total

Number of the light eye-
coloured children.

Parents.

Grandparents.

child-

Calculated.

ren.

Ob-
served.

Light.

Hazel.

Dark.

Light.

Hazel,

Dark.

I.

II.

III.

2

4

183

174

161

163

172

2

3

i

53

46

47

44

48

2

3

...

"i

92

88

81

67

79

2

2

i

1

27

26

24

18

22

...

2

2

2

22

11

6

12

6

3

i

62

52

48

51

51

3

"i

42

30

33

31

32

1

2

2

...

31

28

24

24

20

2

"i

49

35

38

28

34

2

"i

1

31

25

24

21

23

3

1

76

45

44

55

46

2

. . •

2

66

30

38

38

35

2

1

27

15

16

18

16

1

...

3

20

9

12

8

9

1

i

2

22

8

13

11

11

"i

1

1

2

24

9

14

12

10

629

623

601

614

216

NATURAL INHERITANCE,

Table 20,

Observed and Calculated Eye-Coloues in 78 separate Families, each

OF NOT less than SiX BROTHERS OR SiSTERS.

Eye-colours of the

Number of the light eye-

Total

coloured children.

Parents.

Grandparents.

child-
ren.

Ob-
served.

Calculated.

Light.

Hazel.

Dark.

Light.

Hazel,

Dark.

L

n.

III.

2

4

6

6

5-3

5-3

5-6

2

4

6

6

5-3

5-3

5-6

2

4

6

6

5-3

5-3

5-6

2

4

6

5

5-3

5-3

5-6

2

4

7

7

6-2

6-2

Q-Q

2

4

7

7

6-2

6-2

6-6

2

4

7

7

6-2

6-2

6-6

2

4

7

7

6-2

6-2

Q-Q

2

4

7

7

6-2

6-2

Q-Q

2

4

8

8

7-0

7-1

7-5

2

4

8

8

7-0

7-1

7-5

2

4

8

8

7-0

7-1

7-5

2

4

8

8

7-0

7-1

7-5

2

4

8

7

7-0

7-1

7-5

2

4

8

7

7-0

7-1

7-5

2

4

12

12

10-6

10-7

11-3

2

3

"'i

7

7

6-2

5-8

6-4

2

3

1

10

4

8-8

8-3

9-1

2

3

1

12

12

10-6

10-0

10-9

2

3

1

' 1

6

6-2

5-1

6-0

2

3

1

8

8

7-0

5-8

6-9

2

3

1

9

9

7-9

6-6

7-7

2

S

1

9

9

7-9

Q-Q

7-7

2

3

1

9

7

7-9

^■Q

7-7

2

3

1

10

10

8-8

7-3

8-6

2

2

2

7

7

6-2

5-4

6-2

2

2

2

10

9

8-8

7-7

8-8

2

2

1

"i

6

6

5-3

4-0

5-0

2

2

1

1

10

10

8-8

6-7

8-3

2

2

1

1

7

4

6-2

4-7

4 6

2

2

2

8

5

5-4

4-6

4-8

2

3

1

6

2

1-7

4-4

2-2

2

2

2

9

1

2-5

5-1

2-5

2

1

3

6

1

2-7

2-5

1-2

2

1

3

11

3

3-1

4-5

2-2

2

1

2

6

1-7

3-0

1-5

2

1

2

7

4

2-0

3-6

1-8

. ■ •

3

6

6

4-7

5 0

4-9

3

7

6

5-5

5-7

5-7

3

8

6

6-2

6-6

%-Q

3

9

7

7-0

7-5

7-4

3

11

10

8-6

9-1

9-2

TABLES.

Table 20 — continued.

217

Eye-colours of the

Total

Number of the light eye-
coloured children.

Parents.

Grandparents.

child-

Childreii

I.

ren.

Ob-
served.

Light.

Hazel,

De

irk. Light.

Hf

izel. Dark.

I.

II.

III.

1

1

3

1

9

6

7-0

6

6

6-9

1

1

3

1

11

7

8-6

8

0

8-5

1

1

2

2

7

6

5-5

5-

4

4-4

1

1

2

2

9

9

7-0

" 6

9

5-7

1

1

2

2

11

1

8-6

8

5

6-9

1

1

2

2

6

6

4-7

3

4

4-1

1

2

2

6

4

4-7

3

4

4-1

1

2

2

8

5

6-2

4

6

5-5

1

2

2

9

7

7-0

5

1

6-2

1

2

1 1

6

6

4-7

4

0

4-4

1

2

1 1

10

9

7-8

6

7

7-4

1

1

3

9

4

7-0

5

5

6-8

1

1

1 2

8

5

6-2

4

1

5-3

1 4

7

3

4-1

6

2

4-8

1 3

i

6

4

3-5

4

4

3-7

1 3

1

7

3

41

5

1

4-3

1 3

1

8

6

4-6

5

8

4-9

1 3

1

8

5

4-6

. 5

8

4-9

1 3

1

8

4

4-6

5

8

4-9

1 3

1

9

6

5 2

6

6

5-5 .

1 3

1

9

5

5-2

6

6

5-5

1 2

2

6

5

3-5

3

•4

3-2

1 2

2

6

3

3-5

3

•4

3-2

1 2

2

8

4

4-6

4

•6

4-2

1 2

2

10

2

5-8

5

•7

5-3

1 2

2

14

9

8-1

8

•0

7-4

1 2

1 1

7

5

4-1

4

•7

4-1

1 1

2 1

7

3

4-1

4

3

3-9

1 1

1 2

7

4

4-1

3

6

3 5

1 1

3

8

4

4-6

3

•3

3-6

I

1 1

3

8

3

4-6

3

3

3-6

1 3

6

3

3-5

2

1

2-6

1

1 2

2

6

3

4-8

3

•4

2-6

1

1 2

1 1

9

4

7-0

6

•0

4-4

1

1 1

3

13

8

10-1

5

•3

4-7

...

1

4

7

2

5-5

4-6

3-4

218

NATURAL INHERITANCE.

Table 21.

Error in Calculatioxs.

Numbers of Errors of various Amounts in the 3 Calculations, Table 20, of the
Number of Light Eye-coloured Children in the 78 Families.

Data employed referring to

Amount of Errors.

Total

Cases.

0-0

to

0-5.

0-6
to
1-1

1-2

to

1-7

1-8

to

2-3

2-4
and
above.

I. The 2 parents only

II. The 4 grandparents only

III. The 2 parents and 4 grand-
p arents

19
16

41

30

28

17

18
10

8

5
10

4

6

14

8

78
78

78

Table 22.
Inheritance of the Artistic Faculty.

Parents.

Children.

Observed.

Per cents.

Number

of
Fraterni-
ties.

Total
children.

Of whom

are
artistic.

Observed.

Calculated.

art.

not
art.

art.

not
art.

Both artistic

30
101
150

148
520
839

95
201
173

64
39
21

36
61
79

60
39
17

40
61
83

One artistic; one not..
Neither artistic ...

Totals

281

1507

469

100

100

100

100

The "parents " and the " children " in this Table usually rank respectively as
Grandparents and Parents in the E.F.F. pedigrees.

APPENDIX.

The following memoirs by the author, bearing on Heredity, have
been variously utilised in this volume :

Experiments in Pangenesis. Proc. Royal Soc, No. 127, 1871, p. 393,

Blood Relationship. Froc. Royal Soc, No. 136, 1872, p. 394.

A Theory of Heredity. Journ. Anthropol. Inst., 1875, p. 329.

Statistics by Inter comparison. Phil. Mag., Jan. 1875.

*0n the Probability of the Extinction of Families. Journ. Anthropol.

Inst., 1875.
Typical laws of Heredity. Journ. Royal Inst., Feb. 1877.
^Geometric Mean in Vital and Social Statistics. Proc. Royal Soc,

No. 198, 1879. See subsequent memoir by Dr. Macalister.
Address to Anthrop. Section British Association at Aberdeen.

Journ. Brit. Assoc, 1885.
Regression towards Mediocrity in Hereditary Stature, Journ.

Anthropol. Inst, 1885.
Presidential Addresses to Anthropol. Inst., 1885, 6 and 7.
Family Likeness in Stature. Proc Royal Soc, No. 242, 1886.
Family Likeness in Eye-colour. Proc Royal Soc, No. 245, 1886.
*Good and Bad Temper in Eoglish Families. Fortnightly Review,

July, 1887.
Pedigree Moth Breeding.* Trans. Entomolog. Soc, 1887. See

also subsequent memoir by Mr. Merrifield, and another read

by him, Dec. 1887.

Those marked with an asterisk (*) are reprinted with slight revision in the
Appendices F, D, and E.

220 NATURAL INHERITANCE.

WORKS ON HEREDITY BY THE AUTHOR.

(Published by Messrs. Macmillan &, Co.)

Hereditary Genius. 1869.
EDglish Men of Science. 1874.
Inquiries into Human Faculty. 1883.

Record of Family Faculties.! 1884. 2s. Qd.

Life History Album. '^ (edited byF. Galton). 1884. 3s. 6d. and 45. 6d.

^ The Eecord of Family Facnl-tieis consists ,of Tabular Forms and Directions
for entering Data, with an Explanatory Preface. It is a large thin quarto book
of seventy pages, bound in limp cloth. The first part of it contains a preface,
with explanation of the object of the work and of the way in which it is to be
used. The rest consists of blank forms, with printed questions and blank spaces to
be :^l!ed withj\Titing. The Record is designed to facilitate the orderly collection of
such data as are important to a family from an hereditably point of view. It allots
equal space to everj^ direct ancestor in the nearer degrees, and is supposed to be filled
up in most cases by a parent, say the father of a growing family. If he takes
pains to make inquiries of elderly relatives and friends, and to seek in registers,
he will be able to ascertain most of the required particulars concerning not only
his own parents, but also concerning his four grandparents ; and he can ascertain
like particulars concerning those of his wife. Therefore his children will be pro-
vided with a large store of information about their two parents, four grandparents,
and eight great-grandparents, which form the whole of their fourteen nearest
ancestors. A separate schedule is allotted to each of them. Space is afterwards
provided for the more important data concerning many at least, of the brothers
and sisters of each direct ancestor. The schedules are followed by Summary
Tables, in which the distribution of any characteristic throughout the family at
large may be compendiously exhibited.

^ The Life History Album was prepared by a Sub-Committee of the Collective
Investigation Committee of the British Medical Association. It is designed to
serve as a continuous register of the principal biological facts in the life of its
owner. The book begins with a few pages of explanatory remarks, followed by
tables and charts. The first table is to contain a brief medical historj^ of each
member of the near ancestry of the owaier. This is followed by printed forms
on which the main facts of the owner's growth and development from birth
onwards may be registered, and by charts on winch measurements may be laid
down at appropriate intervals and compared with the curves of normal growth.
Most of the required data are such as any intelligent person is capable of record-
ing ; those that refer to illnesses should be brief and technical, and ought to be
filled up by the medical attendant. Explanations are given of the most 'con-
venient tests of muscular force, of keenness of eyesight and hearing, and of the
colour sense. The 4.s. 6d. edition contains a card of variously coloured wools to
test the sense of colour.

*)f."^ These two works pursue similar objects of personal and scientific utility,
along different paths. The Album is designed to lay the foundation of a practice

APPENDIX B. 221

of maintaining tmslworthy life-Mstories that shall be of medical service in after-
life to the person who keeps them. The Record shows how the life histories of
members of the same family may be collated and used to forecast the development
in mind and body of the younger generation of that family. Both works are
intended to promote the registration of a large amount of information that has
hitherto been allowed to run to waste in oblivion, instead of accumulating and
forming stores of recorded experience for future personal use, and from which
future inquirers into heredity may hope to draw copious supplies.

B.

PROBLEMS BY J. D. HAMILTON DICKSONj FELLOW AND TUTOR OF

ST. Peter's college, Cambridge.

{Reprinted from Proc. Royal S'oc, No. 242, 1886, p. 63.)

Prohlem 1. — A point P is capable o£ moving along a straight line
P'OP, making an angle tan~i| ^ith the a2:is of y, which is drawn
through O the mean position of P ; the probable error of the pro-
jection of P on Oy is 1*22 inch : another point jt?, whose mean posi-
tion at any time is P, is capable of moving from P parallel to the
axis of X (rectangular co-ordinates) with a probable error of
1'50 inch. To discuss the "surface of frequency" of p.

1. Expressing the " surface of frequency " by an equation in
X, y, z, tbe exponent, with its sign changed, of the exponential
which appears in the value of z in the equation of the surface is,
save as to a factor,

y^ ^ (3^'-2y)2 , . . ^ ^ /2)

(1-22)2 9(1-50)2

hence all sections of the " surface of frequency " by planes parallel
to the plane of xy are ellipses, whose equations may be written in
the form,

2. Tangents to these ellipses parallel to the axis of 7/ are found,

222

NATURAL INHERITANCE.

by differentiatiDg (2) and putting the coefficient of dy equal to zero,
to meet the ellipses on the line,

(1-22)^

^ 3a?-22/_^
"9(1-50)2 '

6

that is

y_^ 9(i-5oy

X

1

+

17-6

(3)

(1-22)2 9(1-50)^

X. Let this be the line OM.

or, approximately, on the line y -
(See Fig. 11, p. 101.)

From the nature of conjugate diameters, and because P is the
mean position of p, it is evident that tangents to these ellipses
parallel to the axis of x meet them on the line x = §?/, viz., on OP.

3. Sections of the '' surface of frequency " parallel to the plane
of xz^ are, from the nature of the question, evidently curves of fre-
quency with a probable error 1 -50, and the locus of their vertices
lies in the plane z OP.

Sections of the same surface parallel to the plane of yz are got
from the exponential factor (1) by making £c constant. The result is
simplified by taking the origui on the line OM. Thus putting x^=. x^
and y = yi + y', where by (3)

(1-22)2 9(1-50)2

0

the exponential takes the form
1.4)

{

+ ■

■y'' +

f .vi^ A^^i-W

+

(1-22)2 ■ 9(1-50)2) "^ ' ((1-22)2 9(l-50;2
whence, if e be the probable error of this section,

i 1.4

72

}

(4)

+

(5)

(1-22)2 9(1-50)2

or Ton referring to (3)1 e = 1-50 /

that is, the probable error of sections parallel to the plane of yz is
nearly —y=- times that of those parallel to the plane of xz, and the
locus of their vertices lies in the plane ^iOM.

APPENDIX B. 223

It is important to notice that all sections parallel to the same
co-ordinate plane have the same probable error.

4. The ellipses (2) when referred to their principal axes become,
after some arithmetical simplification,

/2 '2

+ -^ — = constant, (6)

20-68 5-92 ' ^ '

the major axis being inclined to the axis of x at an angle whose
tangent is 0"5014. [In the approximate case the ellipses are

— + -^^— = const., and the maior axis is inclined to the axis of x at

7 2 -■

an angle tan~"ii.]

5. The question may be solved in general terms by putting
YON = ^, XOM = ^, and replacing the probable errors 1*22 and
1*50 by a and h respectively; then the ellipses (2) are,

^ ^ (x - y tan Of ^ ^ .^.

equation (3) becomes

2/^,4- n^-V tan 0 /-.

V , , o?- tan B C ' ' ' ' ' \ )

or - = tan <p = — -—

X 0^ + a'^ tan^^

and (5) becomes — _,=—- + -— — (9)

whence % =— „ (10)

tan 0 h^ ^ ^

If G be 'the probable error of the projection of ^^'s whole motion
on the plane of xz, then

c^ = a^ tan^ 6 + Ij^,

which is independent of the distance of ^'s line of motion from the

axis of X. Hence also

tan 4> _ci^ /-1 1 \

t^^^~~¥ ^ ^

Prohlem 2. — An index q moves under some restraint up and down
a bar AQB, its mean position for any given position of the bar

224 NATURAL INHERITANCE.

being Q ; the bar, always carrying tbe index with it, moves under
some restraint up and down a fixed frame YMY', the mean position
of Q being M : the movements of the index relatively to the bar
and of the bar relatively to the frame being quite independent. For
any given observed position of q, required the most probable position
of Q fwhich cannot be observed) ; it being known that the probable
error of q relatively to Q in all positions is h, and that of Q rela-
tively to M is G. The ordinary law of error is to be assumed.

If in any one observation, MQ = x, Q,q = y^ then the law of error
requires

^ + r (12)

to be a minimum, subject to the condition

X + y = a, 2^ constant.
Hence we have at once, to determine the most probable values of

and the most probable position of Q, measured from M, when ^'s ob-
served distance from M is a, is

h^ + c2 ""'

It also follows at once that the probable error i? of Q (which may
be obtained by substituting a—xiovy in (12)) is given by

11,1 ^«

V^ G^ 0^ V62_j_c2 ^ ^

which it is important to notice, is the same for all values of a.

APPENDIX C.

223

C.

EXPERIMENTS ON SWEET PEAS BEARING ON THE LAW OF REGRESSION.

The reason why Sweet Peas were chosen, and the methods of
selectiug and planting them are described in Chapter YI., p. 79. The
following Table justifies their selection by the convenient and accu-
rate method of weighing, as equivalent to that of measuring them.
It will be seen that within the limits of observed variation a
difference of 0*172 grain in weight corresponds closely to an average
difference of O'Ol inch in diameter.

Table 1.

Comparison of Weights of Sweet Peas with their Diameters.

Distinguishing
letter of

"Weight of one
seed in grains.

Length of row of
100 seeds in

Diameter of one

seed in hundredths

of inch.

seed.

Common difference
= 0'172 grain.

inches.

Common difference
= 0 01 inch.

K

1-750

21-0

21

L

1-578

20-2

20

M

1-406

19-2

19

N

r234

17-9

18

0

1-062

17-0

17

P

•890

16-1

16

Q

•718

15-2

15

The results of the experiment are given in Table 2 ; its first and
last columns are those that especially interest us ; the remaining
columns showiog how these two were obtained.

It will be seen that for each increase of one unit on the part of
the parent seed, there is a mean increase of only one-third of a unit
in the filial seed ; and again that the mean filial seed resembles the
parental when the latter is about 15*5 hundredths of an inch in
diameter. Taking 15-5 as the point towards which Filial Hegression
points, whatever may be the parental deviation from that point, the
mean Filial Deviation will be in the same direction, but only one-
third as much.

Q

226 NATURAL INHERITANCE.

Table 2.

Parent Seeds and their Produce.

Tlie proportionate number of sweet peas of diififerent sizes, produced by parent
seeds also of different sizes, are given below. The measurements are those ot
their mean diameters, in hundredths of an inch.

Diameter
of Parent

Diameters of Filial Seeds.

Total.

Mean Diameter
of Filial Seeds.

Seed.

Under
15.

15-

16-

17-

18-

19-

20-

Above
21-

Observed

Smoothed

21

22

8

10

18

21

13'

6

2

100

17-5

17-3

20

23

10

12

17

20

13

3

2

100

17-3

17-0

19

35

16

12

13

11

10

2

1

100

16-0

16 6

IS

34

12

13

17

16

6

2

0

100

16-3

16-3

17

37

16

13

16

13

4

1

0

100

15-6

16-0

16

34

15

18

16

13

3

1

0

100

16-0

15-7

15

46

14

9

11

14

4

2

0

100

15-3

15-4

This point is so low in the scale, that I possess less evidence than I
desired to prove the bettering of the produce of very small seeds.
The seeds smaller than Q were such a miserable set that I could
hardly deal with them. Moreover, they were very infertile. It did,
however, happen that in a few of the sets some of the Q seeds
turned out very well.

If I desired to lay much stress on these experiments, I could make
my case considerably stronger by going minutely into other details,
including confirmatory measurements of the foliage and length of
pod, but I do not care to do so.

D.

GOOD AND BAD TEMPER IN ENGLISH FAMILIES.

One of the questions put to the compilers of the Family Records
spoken of in page 72, referred to the "Character and Tempera-
ment " of the persons described. These were distributed through

^ Eeprinted after slight revision from FortnigMly R&view, July, 1887.

APPENDIX D. 227

three and sometimes four generations, and consisted of those who
lay in the main line of descent, together with their brothers
and sisters.

Among the replies, I find that much information has been
incidentally included concerning what is familiarly called the
"temper" of no less than 1,981 persons. As this is an adequate
number to allow for many inductions, and as temper is a strongly
marked characteristic in all animals ; and again, as it is of social
interest from the large part it plays in influencing domestic hap-
piness for good or ill, it seemed a proper subject for investigation.

The best explanation of what I myself mean by the word
" temper" will be inferred from a list of the various epithets used
by the compilers of the Kecords, which I have interpreted as
expressing one or other of its qualities or degrees. The epithets
are as follows, arranged alphabetically in the two main divisions
of good and bad temper : —

Good temjjer. — Amiable, buoyant, calm, cool, equable, forbearing,
gentle, good, mild, placid, self-controlled, submissive, sunny, timid,
yielding. (15 epithets in all.)

Bad tem^oer. — Acrimonious, aggressive, arbitrary, bickering,
capricious, captious, choleric, contentious, crotchety, decisive, de-
spotic, domineering, easily offended, fiery, fits of anger, gloomy,
grumpy, harsh, hasty, headstrong, huffy, impatient, imperative, im-
petuous, insane temper, irritable, morose, nagging, obstinate, odd-
tempered, passionate, peevish, peppery, proud, pugnacious, quarrel-
some, quick-tempered, scolding, short, sharp, sulky, sullen, surly,
uncertain, vicious, vindictive. (46 epithets in all.)

I also grouped the epithets as well as I could, into the following
five classes : 1, mild ; 2, docile ; 3, fretful ; 4, violent ; 5, masterful.

Though the number of epithets denoting the various kinds of
bad temper is three times as large as that used for the good, yet
the number of persons described under the one general head is about
the same as that described under the other. The first set of data
that I tried, gave the proportion of the good to the bad-tempered as
48 to 52 ; the second set as 47 to 53. There is little difference
between the two sexes in the frequency of good and bad temper, but
that little is in favour of the women, since about 45 men are re-

2 Q

228 NATURAL INHERITANCE.

corded as good-tempered for every 55 wlio are bad, and conversely
55 women as good-tempered for 45 who are bad.

I will not dwell on the immense amount of unhappiness, ranging
from family discomfort down to absolute misery, or on the breaches
of friendship that must have been occasioned by the cross-grained,
sour, and savage dispositions of tho^e who are justly labelled by
some of the severer epithets ; or on the comfort, peace, and good-
will diffused through domestic circles by those who are rightly
described by many of the epithets in the first group. We can
hardly, too, help speculating uneasily upon the terms that our own
relatives would select as most appropriate to our particular selves.
But these considerations, interesting as they are in themselves, lie
altogether outside the special purpose of this inquiry.

In order to ascertain the facts of which the above statistics are a
brief summary, I began by selecting the larger families out of my
lists, namely, those that consisted of not less than four brothers or
sisters, and by noting the persons they included who were described
as good or bad-tempered ; also the remainder about whose temper
nothing was said either one way or the other, and whom perforce I
must call neutral. I am at the same time well aware that, in some
few cases a tacit refusal to describe the ^temper should be inter-
preted as reticence in respect to what it was thought undesirable
even to touch upon.

I found that out of a total of 1,361 children, 321 were described
as good-tempered, 705 were not described at all, and 342 were
described as bad-tempered. These numbers are nearly in the pro-
portion of 1, 2, and 1, that is to say, the good are equal in number
to the bad-tempered, and the neutral are just as numerous as the
good and bad-tempered combined.

The equality in the total records of good and bad tempers is an
emphatic testimony to the correct judgments of the compilers in the
choice of their epithets, for whenever a group has to be divided into
three classes, of which the second is called neutral, or medium, or
any other equivalent term, its nomenclature demands that it should
occupy a strictly middlemost position, an equal number of con-
trasted cases flanking it on either hand. If more cases were
recorded of good temper than of bad, the compilers would have laid
down the boundaries of the neutral zone unsymmetrically, too far

APPENDIX D. 229

from the good end of the scale of temper, and too near the bad end.
If the number of cases of bad temper exceeded that of the good, the
error would have been in the opposite direction. But it appears, on
the whole, that the compilers of the records have erred neither to
the right hand nor to the left. So far, therefore, their judgments
are shown to be correct.

ISText as regards the proportion between the number of those who
rank as neutrals to that of the good or of the bad. It was recorded
as 2 to 1 ; is that the proper poportion 1 Whenever the nomencla-
ture is obliged to be somewhat arbitrary, a doubtful term should be
interpreted in the sense that may have the widest suitability. Now
a large class of cases exist in which the interpretation of the word
neutral is fixed. It is that in which the three grades of magnitude
are conceived to result from the various possible combinations of
two elements, one of which is positive and the other negative, such
as good and bad, and which are supposed to occur on each occasion
at haphazard, but in the long run with equal frequency. The
number of possible combinations of the two elements is only four,
and each of these must also in the long run occur with equal
frequency. They are: 1, both positive; 2, the first positive, the
second negative ; 3, the first negative, the second positive ; 4, both
negative. In the second and third of these combinations the
negative counterbalances the positive, and the result is neutral.
Therefore the proportions in which the several events of good,
neutral, and bad would occur is as 1, 2, and 1. These proportions
further commend themselves on the ground that the whole body of
cases is thereby divided into two main groups, equal in number, one
of which includes all neutral or medium cases, and the other all
that are exceptional. Probably it was this latter view that was
taken, it ma,y be half unconsciously, by the compilers of the Eecords.
Anyhow, their entries conform excellently to the proportions speci-
fied, and I give them credit for their practical appreciation of what
seems theoretically to be the fittest standard. I speak, of course,
of the Records taken as a whole ; in small groups of cases the
proportion of the neutral to the rest is not so regular.

The results shown in Table I. are obtained from all my returns.
It is instructive in many ways, and not least in showing to a
statistical eye how much and how little value may reasonably be

230

NATURAL INHERITANCE.

attached to my materials. It was primarily intended to discover
whether any strong bias existed among the compilers to spare the
characters of their nearest relatives. In not a few cases they have
written to me, saying that their records had been drawn up with
perfect frankness, and earnestly reminding me of the importance of
not allowing their remarks to come to the knowledge of the persons
described. It is almost needless to repeat what I have published
miore than once already, that I treat the Records quite confidentially.
I have left written instructions that in case of my death they should
all be destroyed unread, except where I have left a note to say that
the compiler wished them returned. In some instances I know that
the Records were compiled by a sort of family council, one of its
members acting as secretary ; but I doubt much whether it often
happened that the Records were known to many of the members of
the family in their complete form. Bearing these and other con-
siderations in mind, I thought the best test for bias would be
to divide the entries into two contrasted groups, one including
those who figured in the pedigrees as either father, mother, son, or
daughter— that is to say, the compiler and those who were very
nearly related to him — and the other including the uncles and
aunts on both sides.

Table 1.

Distribution of Temper in Families (per cents.)

Relationships.

3

r-H

o

o

ft

1

CD
CO

1 — 1

o

m

O

CO

o t

O CQ

a. Fathers and Sons

&. Mothers and Daughters

c. Uncles

d. Aunts

a + b. Direct line

35
39
32
39

74
71

12
18
13
14
30
27

32
31
25
29
63
54

12
8

18
9

20

27

9

4

12

9

13

21

100
100
100
100
200
200

188
179
272
238
367
510

c + d. Collaterals

Good.

Bad Temper.

200
200

367
510

a + b. Dhect line

10^

Qfi

c + d. Collaterals

9

8

102

APPENDIX D.

231

On compariDg the entries, especially tlie summaries in the lower
lines of the Table, it does not seem that the characters of near
relatives are treated much more tenderly than those of the more
remote. There is little indication of the compilers having been
biased by affection, respect, or fear. More cases of a record being
left blank when a bad temper ought to have been recorded, would
probably occur in the direct line, but I do not see how this could be
tested. An omission may be due to pure ignorance ; indeed I find
it not uncommon for compilers to know very little of some of their
uncles or aunts. The Records seem to be serious and careful com-
positions, hardly ever used as vehicles for personal animosity, but
written in much the same fair frame of mind that most people force
themselves into when they write their wills.

Table 2.
Combinations of Temper in Marriage (per cents.).

Tempers
of Husbands.

A. — Observed Pairs.

B. — Haphazard Pairs.

Tempers of Wives.

Tempers of Wives.

Good.

Bad Tempers.

Good.

Bad Tempers,

1

2

3

4

5

2

2
1
1

1

13
5

11

6
4

2

3

4

5

Good 1

„ 2

6
4

10

2

9
5

6

2

5

2

10
4

3
1

2
1

2
1
1

Bad 3

„ 4

„ 5

14

7
3

4
3

9
3

2

3

2

5
2
2

8
5
3

2
1
1

Good

22

24

25

21

Bad

3

1

23

3

0

24

The sexes are separated in the Table, to show the distribution of
the five classes of temper among them severally. There is a large
proportion of the violent and masterful among the men, of the
fretful, the mild, and the docile among the women. On adding
the entries it will be found that the proportion of those who fall

232 NATURAL INHERITANCE.

within the several classes are 36 per cent, of mild-tempered, 15 per
cent, of docile, 29 per cent, of fretful, 12 per cent of violent, 8 per
cent, of masterful.

The importance assigned in marriage-selection to good and bad
temper is an interesting question, not only from its bearing on
domestic happiness, but also from the influence it may have in
promoting or retarding the natural good temper of our race, assum-
ing, as we may do for the moment, that temper is hereditary. I
caDnot deal with the~ question directly, but will give some curious facts
in Table II. that throw indirect light upon it. There a comparison
is made of (A) the actual frequency of marriage between persons,
each of the various classes of temper, with (B) the calculated fre-
quency according to the laws of chance, on the supposition that
there had been no marriage-selection at all, but that the pairings,
so far as temper is concerned, had been purely at haphazard. There
are only 111 marriages in my lists in which the tempers of both
parents are recorded. On the other hand, the number of possible
combinations in couples of persons who belong to the five classes of
temper is very large, so I make the two groups comparable by
reducing both to percentages.

It will be seen that with two apparent exceptions in the upper
left-hand corners of either Table (of 6 against 13, and of 10 against
5), there are no indications of predilection for, or avoidance of
marriage between persons of any of the five classes, but that the
figures taken from observation run as closely with those derived
through calculation, as could be expected from the small number of
observations. The apparent exceptions are that the percentage of
mild-tempered men who marry mild-tempered women is only 6, as
against 13 calculated by the laws of chance, and that those who
marry docile wives are 1 0, as against a calculated 5. There is little
difference between mildness and docility, so we may throw these
entries together without much error, and then we have 6 and 10,
or 16, as against 13 and 5, or 18, which is a close approximation.
We may compare the frequency of marriages between persons
of like temper in each of the five classes by reading the Table
diagonally. They are as (6), 2, 9, 2, 1, in the observed cases,
against (13), 2, 8, 1, 1, in the calculated ones; here the irregularity
of the 6 and 13, which are put in brackets for distinction sake, is

APPENDIX D. 233

conspicuous. Elsewhere there is not the slightest indication of a
dislike in persons of similar tempers, whether mild, docile, fretful,
violent, or masterful, to marry one another. The large initial
figures 6 and 13 catch the eye, and at a first glance impress them-
selves unduly on the imagination, and might lead to erroneous
speculations about mild tempered persons, perhaps that they find one
another rather insipid ; but the reasons I have given, show conclu-
sively that the recorded rarity of the marriages between mild-tempered
persons is only apparent. Lastly, if we disregard the five smaller
classes and attend only to the main divisions of good and bad
temper, there does not appear to be much bias for, or against, the
marriage of good or bad-tempered persons in their own or into the
opposite division.

The admixture of different tempers among the brothers and
sisters of the same family is a notable fact, due to various causes
which act in different directions. It is best to consider them before
we proceed to collect evidence and attempt its interpretation. It
becomes clear enough, and may be now taken for granted, that the
tempers of progenitors do not readily blend in the offspring, but
that some of the children take mainly after one of them, some after
another, but with a few threads, as it w^ere, of various ancestral
tempers woven in, which occasionally manifest themselves. If no
other influences intervened, the tempers of the children in the same
family would on this account be almost as varied as those of their
ancestors ; and these, as we have just seen, married at haphazard,
so far as their tempers were concerned ; therefore the numbers of
good and bad children in families would be regulated by the same
laws of chance that apply to a gambling table. But there are other
influences to be considered. There is a well-known tendency to
family likeness among brothers and sisters, which is due, not to
the blending of ancestral peculiarities, but to the prepotence of one
of the progenitors, who stamped more than his or her fair share of
qualities u.pon the descendants. It may be due also to a familiar
occurrence that deserves but has not yet received a distinctive name,
namely, where all the children are alike and yet their common
likeness cannot be traced to their progenitors. A new variety has
come into existence through a process that affects the whole Frater-
nity and may result in an unusually stable variety (see Chapter III.).
The most strongly marked family type that I have personally met

234 NATURAL INHERITANCE.

with, first arose simultaneously in the three brothers of a family
who transmitted their peculiarities with unusual tenacity to numer-
ous descendants through at least four generations. Other influences
act in antagonism to the foregoing ; they are the events of domestic
life, which instead of assimilating tempers tend to accentuate slight
differences in them. Thus if some members of a family are a little
submissive by nature, others who are naturally domineering are
tempted to become more so. Then the acquired habit of dictation
in these reacts upon the others and makes them still more sub-
missive. In the collection I made of the histories of twins who
were closely alike, it was most commonly said that one of the twins
was guided by the other. I suppose that after their many childish
struggles for supremacy, each finally discovered his own relative
strength of character, and thenceforth the stronger developed into
the leader, while the weaker contentedly subsided into the position
of being led. Again, it is sometimes observed that one member of
an otherwise easygoing family, discovers that he or she may exer-
cise considerable power by adopting the habit of being persistently
disagreeable whenever he or she does not get the first and best of
everything. Some wives contrive to tyrannise over husbands who
are mild and sensitive, who hate family scenes and dread the dis-
grace attending them, by holding themselves in readiness to fly
into a passion whenever their wishes are withstood. They thus
acquire a habit of " breaking out," to use a term familiar to the
warders of female prisons and lunatic asylums ; and though their
relatives and connections would describe their tempers by severe
epithets, yet if they had married masterful husbands their characters
might have developed more favourably.

To recapitulate briefly, one set of influences tends to mix good
and bad tempers in a family at haphazard ; another set tends to
assimilate them, so that they shall all be good or all be bad ; a
third set tends to divide each family into contrasted portions.
We have now to ascertain the facts and learn the results of these
opposing influences.

In dealing with the distribution of temper in Fraternities,^ we

^ A Fraternity consists of the brothers of a family, and of the sisters after the
qualities of the latter have been transmuted to their Male Equivalents ; but as
no change in the Female values seems really needed, so none has been made in
respect to Temper.

APPENDIX D.

235

can only make use of those in which at least two cases of temper
are recorded ; they are 146 in number. I have removed all the
cases of neutral temper, treating them as if they were non-existent,
and dealing only with the remainder that are good or bad. We
have next to eliminate the haphazard element. Beginning with
Fraternities of two persons- only, either of whom is just as likely to
be good as bad tempered, there are, as we have already seen, four
possible combinations, resulting in the proportions of 1 case of both
good, 2 cases one good and one bad, and one case of both bad. I
have 42 such Fraternities, and the observed facts are that in 10
of them both are good tempered, in 20 one is good and one bad,
and in 12 both are bad tempered. Here only a trifling and un-
trustworthy difference is found between the observed and the
haphazard distribution, the other conditions having neutralised
each other. But when we proceed to larger Fraternities the test
becomes shrewder, and the trifling difference already observed
becomes more marked, and is at length unmistakable. Thus the
successive lines of Table III. show a continually increasing diverg-
ence between the observed and the haphazard distribution of
temper, as the Fraternities increase in size. A compendious com-

TABLE 3.

DlSTEIBTJTION OF TeMPEE IN FeATERNITIES.

A. — Observed.

B. — Haphazard.

Number

in each

Fraternity.

Numl>er
of Fra-
ternities.

All
good-
tem-
pers.

Intermediate
cases.

All

bad-

tem-

" pers.

All
good-
tem-
pers.

Intermediate
cases.

All
bad-
tem-
pers.

2
3
4
5
6

42
55
29
6
14

10

11

5

1

1

20

15 21

6 9 8

0 2 10

0 13 3 2

12
8
1
2
4

10

7
2
0
0

21

20 21

8 12 8

12 2 1

2 4 5 4 2

11

7
2
0
0

4 to 6

49

7

7

2

2

236 NATUR.VL INHERITANCE.

parison is made in the bottom line of the Table by adding together
the instances in which the Fraternities are from 4 to 6 in number,
and in taking only those in which all the members of the Fraternity
were alike in temper, whether good or bad. There are 7 + 7, or 14,
observed cases of this against 2 + 2, or 4, haphazard cases, found in
a total of 49 Fraternities. Hence it follows that the domestic influ-
ences that tend to differentiate temper wholly fail to overcome the
influences, hereditary and other, that tend to make it uniform in
the same Fraternity.

As regards direct evidences of heredity of temper, we must frame
our inquiries under a just sense of the sort of materials we have to
depend upon. They are but coarse portraits scored with white or
black, and sorted into two heaps, irrespective of the gradations of
tint in the originals. The processes I have used in discussing the
heredity of stature, eye-colour, and artistic faculty, cannot be
employed in dealing with the heredity of temper. I must now
renounce those refined operations and set to work with ruder tools
on my rough material.

The first inquiry will be. Do good-tempered parents have, on the
whole, good-tempered children, and do bad-tempered parents have
bad-tempered ones? I have 43 cases where both parents are
recorded as good-tempered, and 25 where they were both bad-
tempered. Out of the children of the former, 30 per cent, were
good-tempered and 10 per cent, bad; out of the latter, 4 per cent,
were good and 52 per cent, bad-tempered. This is emphatic testi-
mony to the heredity of temper, I have worked out the other less
contrasted combinations of parental temper, but the results are
hardly worth giving. There is also- much variability in the
proportions of the neutral cases.

I then attempted, with still more success, to answer the converse
question. Do good-tempered Fraternities have, on the whole, good-
tempered ancestors, and bad tempered Fraternities bad-tempered
ones 1 After some consideration of the materials, I defined — rightly
or wrongly — a good-tempered Fraternity as one in which at le itt
two members were good-tempered and none were bad, and a bad-
tempered Fraternity as one in which at least two members were
bad-tempered, whether or no any cases of good temper were said to
be associated with them. Then, as regards the ancestors, I thought

APPENDIX D. 237

by far the most trustworthy group was that which consisted of
the two parents and of the uncles and aunts on both sides. I
have thus 46 good-tempered Fraternities with an aggregate of 333
parents, uncles, and aunts ; and 71 bad-tempered, with 638 parents,
uncles, and aunts. In the former group, 26 per cent, were good
tempered and 18 bad ; in the latter group, 18 were good-tempered
and 29 were bad, the remainder being neutral. These results are
almost the exact counterparts of one another, so I seem to have
made good hits in framing the definitions. More briefly, wo mav
say that when the Fraternity is good-tempered as above defined,
the number of good-tempered parents, uncles, and aunts, exceeds
that of the bad-tempered in the proportion of 3 to 2 ; and that
when the Fraternity is bad-tempered, the proportions are exactly
reversed.

I have attempted in other ways to work out the statistics of
hereditary tempers, but none proved to be of sufficient value for
publication. I can trace no prepotency of one sex over the other
in transmitting their tempers to their children. I find clear
indications of strains of bad temper clinging to families for three
generations, but I cannot succeed in putting them into a numerical
form.

It must not be thought that I have wished to deal with temper
as if it were an unchangeable characteristic, or to assign more
trustworthiness to my material than it deserves. Both these
views have been discussed ; they are again alluded to to show
that they are not dismissed from my mind, and partly to give the
opportunity of adding a very few further remarks.

Persons highly respected for social and public qualities may be
well-known to their relatives as having sharp tempers under strong
but insecure control, so that they " flare up " now and then. I
have heard the remark that those who are over- suave in ordinary
demeanour have often vile tempers. If this be the case — and I
have some evidence of its truth — I suppose they are painfully
conscious of their infirmity, and through habitual endeavours to
subdue it, have insensibly acquired an exaggerated suavity at the
times when their temper is unprovoked. Illness, too, has much
influence in affecting the temper. Thus I sometimes come across
entries to the effect of, " not naturally ill-tempered, but peevish

238 NATURAL INHERITANCE.

through illness." Overwork and worry will make even mild-tempered
men exceedingly touchy and cross.

The accurate discernment and designation of character is almost
beyond the reach of any one, but, on the other hand, a rough estimate
and a fair description of its prominent features is easily obtainable ;
and it seems to me that the testimony of a member of a family
who has seen and observed a person in his unguarded moments
and under very varied circumstances for many years, is a verdict
deserving of much confidence. I shall have fulfilled my object in
writing this paper if it leaves a clear impression of the great range
and variety of temper among persons of both sexes in the upper
and middle classes of English society ; of its disregard in Marriage
Selection; of the great admixture of its good and bad varieties
in the same family ; and of its being, nevertheless, as hereditary
as any other quality. Also, that although it exerts an immense
influence for good or ill on domestic happiness, it seems that good
temper has not been especially looked for, nor ill temper especially
shunned, as it ought to be in marriage- selection.

E.

THE GEOMETRIC MEAN, IN VITAL AND SOCIAL STATISTICS.^

My purpose is to show that an assumption which lies at the basis
of the well-known law of " Frequency of Error" is incorrect when
applied to many groups of vital and social phenomena, although that
law has been applied to them by statisticians with partial success.
Next, I will point out the correct hypothesis upon which a Law of
Error suitable to these cases ought to be calculated ; and subsequently
I will communicate a memoir by Mr. (now Dr.) Donald Macalister,
who, at my suggestion, has mathematically investigated the subject.

The assumption to which I refer is, that errors in excess or in
deficiency of the truth are equally probable ; or conversely, that if two
fallible measurements have been made of the same object, their

^ Epprinted, with slight revision, from the Proceedings of the Eoyal Society,
No. 198, 1879. ^

APPENDIX E. 239

arithmetical mean is more likely to be the true measurement than
any other quantity that can be named.

This assumption cannot be justified in vital phenomena. For ex-
ample, suppose we endeavour to match a tint ; Weber's law, in its
approximative and simplest form, of Sensation varying as the
logarithm of the Stimulus, tells us that a series of tints, in which
the quantities of white scattered on a black ground are as 1, 2, 4,
8, 16, 32, &c., will appear to the eye to be separated by equal in-
tervals of tint. Therefore, in matching a grey that contains 8 por-
tions of white, we are just as likely to err by selecting one that has
16 portions as one that has 4 portions. In the first case there
Would be an error in excess, of 8 units of absolute tint ; in the
second there would be an error in deficiency, of 4. Therefore, an
error of the same magnitude in excess or in deficiency is not equally
probable in the judgment of tints by the eye. Conversely, if two
persons, who are equally good judges, describe their impressions of
a certain tint, and one says that it contains 4 portions of white and
the other that it contains 16 poitions, the most reasonable conclu-
sion is that it really contains 8 portions. The arithmetic mean of
the two estimates is 10, which is not the most probable value ; it
is the geometric mean 8, (4 : 8 : : 8 : 16), which is the most probable.

Precisely the same condition characterises every determination by
each of the senses; for exa^mple, in judgiug of the weight of bodies or
of their temperatures, of the loudness and of the pitches of tones,
and of estimates of lengths and distances as wholes. Thus, three
rods of the lengths a, b, c, when taken successiv^ely in the hand,
appear to dilf er by equal intervals when a : h : : b : c, and not when
a—b^b - G. In all physiological phenomena, where there is on the
one hand a stimulus and on the other a response to that stimulus
Weber's or some other geometric law may be assumed to prevail
in other words, the true mean is geometric rather than arithmetic.

The geometric mean appears to be equally applicable to the ma-
jority of the influences, which, combined with those of purely vital
phenomena, give rise to the events with which sociology deals. It is
difficult to find terms sufficiently general to apply to the varied topics
of sociology, but there are two categories which are of common oc-
currence in which the geometric mean is certainly appropriate. The
one is increase, as exemplified by the growth of population, where an

240 NATURAL INHERITANCE.

already large nation tends to receive larger accessions than a small
oDe under similar circumstances, or when a capital employed in a
business increases in proportion to its size. The other category is
the influences of circumstances or of " milieux " as they are often
called, such as a period of plenty in which a larger held or a larger
business yields a greater excess over its mean yield than a smaller
one. Most of the causes of those differences with which sociology are
concerned, and which are not purely vital phenomena, such as those
previously discussed, may be classified under one or other of these
two categories, or under such as are in principle almost the same.
In short, sociological phenomena, like vital phenomena are, as a
general rule, subject to the condition of the geometric mean.

The ordinary law of Frequency of Error, based on the arithmetic
mean, corresponds, no doubt, sufficiently well with the observed facts
of vital and social phenomena, to be very serviceable to statisticians,
but it is far from satisfying their wants, and it may lead to absurdity
when applied to wide deviations. It asserts that deviations in excess
must be balanced by deviations of equal magnitude in deficiency ;
therefore, if the former be greater than the mean itself, the latter
must be less than zero, that is, must be negative. This is an impossi-
bility in many cases, to which the law is nevertheless applied by sta-
tisticians with no small success, so long as they are content to confine
its application within a narrow range of deviation. Thus, in respect
of Stature, the law is very correct in respect to ordinary measure-
ments, although it asserts that the existence of giants, whose height
is more than double the mean height of their race, implies the possi-
bility of the existence of dwarfs, whose stature is less than nothing
at all.

It is therefore an object not only of theoretical interest but of
practical use, to thoroughly investigate a Law of Error, based on the
geometric mean, even though some of the expected results may
perhaps be apparent at first sight. With this view I placed the fore-
going remarks in Mr. Donald Macalister's hands, who contributed
a memoir that will be found in the Froc. Royal Soc, No. 198, 1879,
following my own. It should be referred to by such mathematicians
as may read this book.

APPENDIX F. 241

F.

PROBABLE EXTINCTION OF FAMILIES.^

The decay of the families of men who occupied conspicuous posi-
tions in past times has been a subject of frequent remark, and has
given rise to various conjectures. It is not only the families of men
of genius or those of- the aristocracy who tend to perish, but it is
those of all with whom history deals, in any way, even such men
as the burgesses of towns, concerning whom Mr. Doubleday has
inquired and written. The instances are very numerous in which
surnames that were once common have since become scarce or have
wholly disappeared. The tendency is universal, and, in explanation
of it, the conclusion has been hastily drawn that a rise in physical
comfort and intellectual capacity is necessarily accompanied by
diminution in "fertility" — using that phrase in its widest sense
and reckoning abstinence from marriage as one cause of sterility.
If that conclusion be true, our population is chiefly maintained
through the " proletariat," and thus a large element of degradation
is inseparably connected with those other elements which tend to
ameliorate the race. On the other hand, M. Alphonse de Candolle
has directed attention to the fact that, by the ordinary law of
chances," a large proportion of families are continually dying out,
and it evidently follows that, until we know what that proportion is,
we cannot estimate whether any observed diminution of sur-
names among the families whose history we can trace, is or is not a
sign of their diminished "fertility." I give extracts from M. De
Candolle' s work in a foot-note,^ and may add that, although I have
not hitherto published anything on the matter, I took considerable
pains some years ago to obtain numerical results in respect to this

1 Reprinted, with slight revision, from the Journ. Anthropol. Inst. 1888.

2 " An milieu des renseignements precis et des opinions tres-sensees de
MM. Benoiston de Chateaunenf, Galton, et autres statisticiens, je n'ai pas ren-
contre la reflexion bien importaiite qu'ils auraient du faire de I'extinction inevitable
des nonis de famille. Evidemment tons les noms doivent s'eteindre .... Un
matliematicien pourrait calculer comment la reduction des noms ou titres aurait
lieu, d'apres la probabilite des naissances toutes feminines ou toutes masculines
ou melangees et la probabilite d'absence de naissances dans un couple quelconque,"
&c. — Alphoxse de Candolle, Histoire des Sciences et des Savants, 1873.

R

242 NATURAL INHERITANCE.

very problem. I made certain very simple and not very inaccurate
suppositions concerning average fertility, and I worked to the
nearest integer, starting with 10,000 persons, but the computation
became intolerably tedious after a few steps, and I had to abandon
it. The Rev. H. W. Watson kindly, at my request, took the pro-
blem in hand, and his results form the subject of the following
paper. They do not give what can properly be called a general
solution, but they do give certain general results. They show (1)
how to compute, though with great labour, any special case ; (2) a
remarkably easy way of computing those special cases in which the
law of fertility approximates to a certain specified form; and (3)
how all surnames tend to disappear.

The form in which I originally stated the problem is as follows.
I purposely limited it in the hope that its solution might be more
practicable if unnecessary generalities were excluded : —

A large nation, of whom we will only concern ourselves with the
adult males, N in number, and who each bear separate surnames,
colonise a district. Their law of population is such that, in each
generation, a^ per cent, of the adult males have no male children
who reach adult life ; a^ have one such male child ; a^ have two ;
and so on up to a^y who have five. Find (1) what proportion of the
surnames will have become extinct after r generations ; and (2) how
many instances there will be of the same surname being held by m
persons.

Discussion of the iwobhm hy the Rev. H. W. Watson, D.Sc, F.R.S.,
formerly Fellow of Trinity College, Gamhridge.

Suppose that at any instant all the adult males of a large
nation have different surnames, it is required to find how many of
these surnames will have disappeared in a given number of genera-
tions upon any hypothesis, to be determined by statistical investiga-
tions, of the law of male population.

Let, therefore, a^ be the percentage of males in any generation
who have no sons reaching adult life, let a^ be the percentage that
have one such son, «2 the percentage that have two, and so on up to
a^, the percentage that have q such sons, q being so large that it is
not worth while to consider the chance of any man having more
than q adult sons — our first hypothesis will be that the numbers

APPENDIX F. 243

a^, a-^, ^2' 6^^-? remain the same in each succeeding generation.
We shall also, in what follows, neglect the overlapping of genera-
tions— that is to say, we shall treat the problem as if all the sons born
to any man in any generation came into being at one birth, and as
if every man's sons were born and died at the same time. Of course
it cannot be asserted that these assumptions are correct. Yery
probably accurate statistics would discover variations in the values
of CTq, a-^, etc., as the nation progressed or retrograded ; but it is not
at all likely that this variation is so rapid as seriously to vitiate any
general conclusions arrived at on the assumption of the values
remaining the same through many successive generations. It is
obvious also that the generations must overlap, and the neglect to
take account of this fact is equivalent to saying, that at any given
time we leave out of consideration those male descendants, of any
original ancestor who are more than a certain average number of
generations removed from him, and compensate for this by giving
credit for such male descendants, not yet come into being, as are not
more than that same average number of generations removed from
the original ancestors.

Let then -^, —J-, —-4-, etc., up to -—^ be denoted by the sym-
100 100 100 ^100 ^ ^

bols i^Q, t^, t^j etc., up to ^g, in other words, let ^q, t-^, etc., be the
chances in the first and each succeeding generation of any individual
man, in any generation, having no son, one son, two sons, and so on,
who reach adult life. Let N be the original number of distinct sur-
names, and let ^m^ be the fraction of IST which indicates the number
of such surnames with s representatives in the rth generation.

Now, if any surname have p representatives in any generation, it
follows from the ordinary theory of chances that the chance of that
same surname having s representatives in the next succeeding gene-
ration is the coefficient of x^ in the expansion of the multinomial

(^0 -1- t-^x 4- t^x^ -i- , etc. 4- t^x'^y

Let then the expression t^ + t-^x -f t^x'^ -f etc. -f t^x*^ be repre-
sented by the symbol T.

Then since, by the assumption already made, the number of sur-
names with no representative in the r-lth generation is ^.^m^ N, the

K 2

244 NATURAL INHERITANCE.

number with one representative ^_;^m^.N, the number with two
r.im.2. N and so on, it follows, from what we last stated, that the
number of surnames with s representatives in the rth generation
must be the coefficient of x' in the expression

I ^.imo + ,_imiT + ,.im2T2+ etc. +,_iW,,_iT^'-i |n

If, therefore, the coefficient of N in this expression be denoted by
y^ (x) it follows that r-i^n-^^, r-i^h ^^^ ^^ ^^' ^^® ^^^ coefficients of x,
x^ and so on, in the expression y]._j^ {x).

If, therefore, a series of functions be found such that

f^{x):=^tQ + t-^x+ etc. +tqX'^ and/]. {x)=/,._-^ (f^o + ^i^ ®*^- +^^^*)

then the proportional number of groups of surnames with s represen-
tatives in the rth generation will be the coefficient of x^inf^ {x)
and the actual number of such surnames will be found by multiplying
this coefficient by N. The number of surnames nonrepresented or be-
come extinct in the rth generation will be found by multiplying
the term independent of x in./^ (x) by the number N.

The determination, therefore, of the rapidity of extinction of sur-
names, when the statistical data, t^, t-^, etc., are given, is reduced to
the mechanical, but generally laborious process of successive substi-
tution of Iq + t-^x 4- t.^x^ + etc., for x in successively determined values
of y,. (x), and no further progress can be made with the problem until
these statistical data are fixed ; the following illustrations of the ap-
plication of our formula are, however, not without interest.

(1) The very simplest case by which the formula can be illustrated
is when q = 2 and t^, tj, t^ are each equal to J.

Here f, (x) = l±|±^/,(x) = I j 1 + ^ {l+x + x'^)+ \ l+x + x^)^J

and so on.

Making the successive substitutions, we obtain

_j. , . 1 ( 13 5a3 Qx^ 2x X \

f-, {x)=.— { 1 \-— -\ 1-— 1-

''"^ ^ 3(99999/

■^''^ ^ 2187 2187 2187 2187 2187 2187 2187 2187*^ 2l87

fpi)= -63183+ •08306a; + -10635x2+ •07804a;3+ ■0Qi89x^+ -05443^5+ .oi437a;6
+ -01692:^7+ •01144a;8+ -00367x9+ -00104x10+ '00015x11+ -00005x^2
+ -00001x13 + -00000x1* + -00000x15 + -OOOOOx^^

APPENDIX F. 245

and the constant term in./^ (x) or ^ttIq is therefore
«.oiQQ . '08306 , -10635 , '07804 , '06489 , '05443 , '01437 , '01692 , '01144

0 oioo + + + + + + + +

3 9 27 81 243 729 2187 6561

•00367 '00104-00015
19683 59049 177147

The value of which to five places of decimals is '67528.

The constant terms, therefore, in y^, /^ up to /^ when reduced to
decimals, are in this case '33333, '48148, '57110., '64113, and -65628
respectively. That is to say, out of a million surnames at starting,
there have disappeared in the course of one, two, etc., up to five
generations, 333333, 481480, 571100, 641130, and 675280 re-
spectively.

The disappearances are much more rapid in the earlier than in the
later generations. Three hundred thousand disappear in the first
generation, one hundred and fifty thousand more in the second, and
so on, while in passing from the fourth to the fifth, not more than
thirty thousand surnames disappear.

All this time the male population remains constant. For it is
evident that the male population of any generation is to be found by
multiplying that of the preceding generation, by ^^ + 2^2? ^^^ ^^^^
quantity is in the present case equal to one.

If axes Ox and Ot/ be drawn, and equal distances along Ox repre-
sent generations from starting, while two distances are marked
along every ordinate, the one representing the total male population
in any generation, and the other the number of remaining surnames
in that generation, of the two curves passing through the extremities
of these ordinates, the j^opulation curve w^ll, in this case, be a straight
line parallel to Ox, while the surname curve will intersect the popu-
lation curve on the axis of y, will proceed always convex to the axis
of X, and will have the positive part of that axis for an asymptote.

The case just discussed illustrates the use to be made of the general
formula, as well as the labour of successive substitutions, when the
expressions/^ (x) does not follow some assigned law. The calcula-
tion may be infinitely simplified when such a law can be found ;
especially if that law be the expansion of a binomial, and only the
extinctions are required.

For example, suppose that the terms of the expression tQ + t-^x +
etc. + tgCCg are proportional to the terms of the expanded binomial

246 NATURAL INHERITANCE.

(a-\-hxY i.e. suppose tliat fr. — „ t\=^Q ;— and so on.

Here/, (^)=^ — -,, and .m. = . —

'^^ ^ ^ {a + by ^ ^ {a + bf

J- / \ 1 / , i{a + bxy\q

f^ (^) ^ 1 7T 1 « + 0^-7 TV- \

2^/^o "^ " ^ "^ ^

{a + bY\ ' M

Generally .m, = ^-1^^ { « + 5.,mo } ^ = ^^^ { ^ + ..,m, } ^

If, therefore, we wish to find the number of extinctions in any
generation, we have only to take the number in the preceding

generation, add it to the constant fraction _ , raise the sum to the

b

power of q, and multiply by

{a-\-bY

"With the aid of a table of logarithms, all this may be effected for
a great number of generations in a very few minutes. It is by no
means unlikely that when the true statistical data ifg, t^^, etc., t^ are
ascertained, values of a, b, and q may be found, which shall render
the terms of the expansion (a + bxy approximately proportionate to
the terms of/ (x). If this can be done, we may ajjproximate to
the determination of the rapidity of extinction with very great ease,
for any number of generations, however great.

For example, it does not seem very unlikely that the value of q

might be 5, while t^, t^...t^ might be '237, '396, 264, -088, '014, -001,

or nearly, J, J, -^\, -^j, ^-i^, and jJ^o-

(3 + xY 3^

Should that be the case, we have, /j (x) = -^ ^ ^rriQ = _

and generally ^m^ = 75 ] 3 + ^.-^ttiq >

45

Thus we easily get for the number of extinctions in the first ten
generations respectively.

•237, -346, -410, -450, -477, -496, -510, -520, -527, -533.

We observe the same law noticed above in the case of —

3

viz., that while 237 names out of a thousand disappear in the first

APPENDIX F. 247

step, and an additional 109 names in the second step, there are only
27 disappearances in the fifth step, and only six disappearances in the
tenth step.

If the curves of surnames and of population were drawn from this
case, the former would resemble the corresponding curve in the case
last mentioned, while the latter would be a curve whose distance
from the axis of x increased indefinitely, inasmuch as the expression

^1 + 2^2 +^^3 + 4^4 + ^^5

is greater than one.

"Whenever /-^ (x) can be represented by a binomial, as above sug-
gested, we get the equation

whence it follows that as r increases indefinitely the value of ^m^ ap-
proaches indefinitely to the value ?/ where

^=(^){''+^4

that is where y=l.

All the surnames, therefore, tend to extinction in an indefinite
time, and this result might have been anticipated generally, for a sur-
name once lost can never be recovered, and there is an additional
chance of loss in every successive generation. This result must not
be confounded with that of the extinction of the male population ; for
in every binomial case where q is greater than 2, we have t-^ + 21^ + etc.
-\-qt^>l, and, therefore an indefinite increase of male population.

The true interpretation is that each of the quantities, ^m^,

Ml

2'

etc., tends to become zero, as t is indefinitely increased, but that it
does not follow that the product of each by the infinitely large num-
ber N is also zero.

As, therefore, time proceeds indefinitely, the number of surnames
extinguished becomes a number of the same order of magnitude as the
total number at first starting in N, while the number of surnames
represented by one, two, three, etc., lepresentatives is some infinitely
smaller but finite number. "When the finite numbers are multiplied
by the corresponding number of representatives, sometimes infinite in
number, and the products added together, the sum will generally ex-
ceed the original number N. In point of fact, just as in the cases
calculated above to five generations, we had a continual, and indeed

248 NATURAL INHERITANCE.

at first, a rapid extinction of surnames, combined in the one case
with a stationary, and in the other case an increasing population, so
is it when the number of generations is increased indefinitely. We
have a continual extinction of surnames going on, combined with
constancy, or increase of population, as the case may be, until at
length the number of surnames remaining is absolutely insensible, as
compared with the number at starting ; but the total number of
representatives of those remaining surnames is infinitely greater than
the original number.

We are not in a position to assert from actual calculation that a
corresponding result is true for every form oif^ (x), but the reason-
able inference is that such is the case, seeing that it holds whenever

/j (x) may be compared with ^ y whatever a, h, or q may be.

G.

ORDERLY ARRANGEMENT OF HEREDITARY DATA.

There are many methods both of drawing pedigrees and of
describing kinship, but for my own purposes I still prefer those that
I designed myself. The chief requirements that have to be fulfilled
are compactness, an orderly and natural arrangement, and clearly
intelligible symbols.

Nomenclature.— A. symbol ought to be suggestive, consequently
the initial letter of a word is commonly used for the purpose. But
this practice would lead to singular complications in symbolizing
the various ranks of kinship, and it must be applied sparingly. The
letter F is equally likely to suggest any one of the three very diffe-
rent words of Father, Female, and Fraternal. The letter M suggests
both Mother and Male ; S would do equally for Son and for Sister.
Whether they are English, French, or German words, much the
same complexity prevails. The system employed in Hereditary
Genius had the merit of brevity, but was apt to cause mistake ; it
was awkward in manuscript and difficult to the printer, and I have
now abandoned it in favour of the method employed in the Records

APPENDIX G.

249

of Family Faculties, This will now be briefly described again.
Each kinsman can be described in two ways, either by letters or by
a number. In ordinary cases both the letter and number are
intended to be used simultaneously, thus FF.8. means the Father's
Father of the person described, though either FF or 8, standing by
themselves, would have the same meaning. The double nomen-
clature has great practical advantages. It is a check against mis-
take and makes reference and orderly arrangement easy.

As regards the letters, F stands for Father and M for Mother,
whenever no letter succeeds them ; otherwise they stand for Father's
and for Mother's respectively. Thus F is Father ; FM is Father's
Mother ; FMF is Father's Mother's Father.

As regards the principle upon which the numbers are assigned,
arithmeticians will understand me when I say that it is in accord-
ance with the binary system of notation, which runs parallel to the
binary distribution of the successive ranks of ancestry, as two
parents, four grandparents, eight great-grandparents, and so on.
The '' subject " of the pedigree is of generation O ; that of his
parents, of generation 1'; that of his grandparents, of generation 2, &c.
This is clearly shown in the following table : —

Kinship.

Order
of

Genera-
tion.

Numerical Yalues

in Binary Notation.

in Decimal Nota-
tion.

Child

0

1

1

Parents

1

10

11

2 .

3

Gr. Par.

2

100

101

110

111

4

5

6

7

G. Gr. Par. ......

3 <

1000
1001

1010
1011

1100
1100

1110

1111

8
9

10
11

12
13

14
15

All the male ancestry are thus described by even numbers and the
female ancestry by odd ones. They run as follows : —

250 NATURAL INHERITANCE.

E,2. M, 3.

FF, 4. FM, 5. MF, 6. MM, 7.

FFF, 8. FMF, 10. MFF, 12. MMF, 14.

FFM, 9. FMM, 11. MFM, 13. MMM, 15.

It will be observed that the double of the number of any ancestor
is that of his or her Father ; and that the double of the number
2olus 1 is that of his or her Mother ; thus FM 5 has for her father
FMF 10, and for her mother FMM 11.

When the word Brother or Sister has to be abbreviated it is safer
not to be too stingy in assigning letters, but to write hr, sr, and in
the plural hrs, srs ; also for the long phrase of '' brothers and sisters,"
to write hrss.

All these symbols are brief enough to save a great deal of space,
and they are perfectly explicit. When such a phrase has to be
expressed as " the Fraternity of whom FF is one " I write in my
own notes simply FF', but there has been no occasion to adopt this
symbol in the present book.

I have not satisfied myself as to any system for expressing
descendants. Theoretically, the above binary system admits of
extension by the use of negative indices, but the practical applica-
tion of the idea seems cumbrous.

We and the French sadly want a word that the Germans possess
to stand for Brothers and Sisters. Fraternity refers properly to the
brothers only, but its use has been legitimately extended here to
mean the brothers and the sisters, after the qualities of the latter
have been reduced to their male equivalents. The Greek word
adelpliic would do for an adjective.

Pedigrees. — The method employed in the Record of Family Faculties
for entering all the facts concerning each kinsman in a methodical
manner was fully described in that book, and could not easily be
epitomised here ; but a description of the method in which the
manuscript extracts from the records have been made for my own
use will be of service to others when epitomising their own family
characteristics. It will be sufficient to describe the quarto books
that contain the medical extracts. Each page is ten and a half inches
high and eight and a half wide, and the two pages, 252, 253, that are

APPENDIX G.

251

P

H
o

^1

fH

(B

(D

ri:1

rCj

03 03

-)J

-(J

?-( O

1^

&1 !=^

03 +J

03 g

^"'3

1 1 a^H

C/2 JO

l9 S

O^

CO f^

^ .2

02 i^

%%

fe-r)

In '^

03

M

-^ 9

o

13 rt

o

i'

o
o
W

%

%

, 's

.

03 4S

03

Pm

rC3 CS
-1^ pH

■5

t3

O ^

^ 03

3

u

r-l
<D

r^

o

<

1-5

■5 .

03 -tf

PI
03

2 -^

1^ 1^

HR -M

-J5 c3

11^

(73
02 ?H

^"^

[^H M

rv. fH

03 03

^'"^

a:,^

:S^

o

o3

02 m

JLm

P^

a>

(13

i-Sh

r^

03 a5

-M •

-M

,

53 '^

03 if

o 53

O «*-!

_aj ciU

^ CO

l=H .1-1

03 3

M --^

■ ^-^

-1-^ "—I

"h 'Ti

"ph 't:!

03 rrr*,

M

03 Pi

o
o

C^
^

c3

°3

U 03

03
O

l-H

03 +?

Ph

03
03

>-5

CO !>2

03

^ ^

03

P-l

03 (T)

CO -fH
03 M

w^

.«=^

In'^

"Vh "TIJ

5^

03

g 03*

,

2 i=l

^ 03
P^ p^

C«

C3

CO M

P^

E=4

252

NATURAL INHERITANCE.

Example A.

Father's name James Gladding.

Mother's maiden name .... Maey Claeemont.

Initials.
J. G.

R. G-
W. G.
F. L.
C. G.

M. G.

A. C.
W. C.

E. C.

F. R.
R.N.
L. C.

Kin.

Principal illnesses and cause of death.

Age at
death.

Father

Bad rheum, fever ; agonising headaches ; diar-
rhoea ; bronchitis ; pleurisy . . Heart disease

54

56
83
73

63

46
62
19
85
50
21

bro.
bro.
sis.
sis.

Rheum, gout Apoplexy

Good health except gout ; paralysis later Apoplexy
Rheum, fever and rheum, gout . . . Apoplexy
Delicate (inoculated) Small pox

Mother

Tendency to lung disease ; biliousness ; fre-
quent heart attacks . Heart disease and dropsy

bro.
bro.
bro.

sis.
sis.
sis.

Good health . Accident

Led a wild life Premature old age

Always delicate Consumption

Small-pox three times .... General failure

Bilious ; weak health Cancer

Fever

M. G.
K. G.
G. L.

F. S.
R. F.
L. G.

bro.
bro.

sis.

sis.
sis.

sis.

Inflam. lungs ; rheum, fever . . Heart disease
Debility ; heart disease ; colds . Consumption
Bai headaches ; coughs ; weak spine ; hysteria ;

apoplexy Paralysis

Bad colds ; inflam. lungs ; hysteria

Infantile paralysis ; colds ; nervous depression .
Inflam. brain, also lungs ; neuralgia ; nervous

fever

17
40

50
living
living

living

(Space left for remarks.)

APPENDIX G.

253

Example B.

Fatlier's name Julius Fitzeoy.

Mother's maiden name . . . Amelia Mereyweathee.

Initials.

R. F.

L. F.i
A. G. F.
W. F.

P. M.
A. M.

N. M.
R. B.
C. M.
F. L.

Kin.

Father

bro.
hro.
bro.

Mother

bro.
bro.
bro,

sis. •

sis.

sis.

Principal illnesses and cause of death.

Gouty Habit . . Weak Heart and Congest. Liver

Gout and Decay
. . . . Accideiit
. . . . Typhoid

Gall stones

Internal Malady (?) Cancer

Still living.

Paralysis
Paralysis

1 died an infant.

. . Consumption
PJieum. in Head
Softening of Brain

Age at
death.

73

48
16

55

86
85

33

88
76

G.

F.

H.

F.

S.

T. F.

H.

G.

H.

B.R.

N.

F.

E.

L. F.

bro.

bro.

bro.

sis.
sis.
sis.
sis.

Gout : tendency to mesenteric disease ; eruptive

disorders . . , Blood poisoning after a cut

Liver deranged ; bad headaches ; once supposed

consumptive Gradual Paralysis

Eruptive disorder ; mesentery disease ; inflam-
mation of liver . . Inflamrtiation of Lungs
Eruptive disorder ; liver . . . Infiam. of Lungs
Delicate ; tend, to mesent. disease , Consumption

Colds ; liver disorder Consumpition

Mesenteric disease ; grandular swellings . Atrophy
2 died infants.

46

45

42
47
29
30
16

(Space left for remarks.)

254 NATURAL INHERITANCE.

found wherever the book is opened, relate to the same family. The
open book is ruled so as to resemble the accompanying schedule,
which is drawn on a reduced scale on page 251. The printing within
the compartments of the schedule does not appear in the MS. books,
it is inserted here merely to show to whom each compartment refers.
It will be seen that the paternal ancestry are described in the left
page, the maternal in the right. The method of arrangement is
quite orderly, but not altogether uniform. To avoid an unpleasing
arrangement like a tree with branches, and which is very wasteful
of space, each grandparent and his own two parents are arranged in
a set of three compartments one above the other. There are, of
course, four grandparents and therefore four such sets in the
schedule. Reference to the examples A andB pages 252 and 253 will
show how these compartments are filled up. The rest of the Schedule
explains itself. The children of the pedigree are written below
the compartment assigned to the mother and her brothers and
sisters ; the spare spaces are of much occasional service, to receive
the overfi.ow from some of the already filled compartments as well
as for notes. It is astonishing how much can be got into such a
schedule by writing on ruled paper with the lines one-sixth of an
inch apart, which is not too close for use. Of course the writing
must be small, but it may be bold, and the figures should be written
very distinctly.

For a less ambitious attempt, including the grandparents and
their fraternity, but not going further back, the left-hand page
would sufiice, placing " Children " where " Father " now stands,
"Father's Father" for "Father," and so on throughout.

INDEX.

INDEX.

Accidents, 19, 55, 65

Acquired peculiarities, inheritance of,
14

Album for Life History, 220

Ancestral contributions, 134

Adelphic, 250

Aiitliropometric Committee of the
British Assoc, 95 ; anthrop. labo-
ratory data, 43, 46, 79

Apparatus, see Models

Acquired faculties, transmission of, 16,
197

Artistic Faculty, 154

Averages tell little, 36 ; comparison of
with medians, 41

Awards for E.F.F., 75

Bartholomew's Hospital, 47

Bias, Statistical effect of, in marriage
selection, 162 ; in suppressing cause
of death, 168

Blends, or refusals to blend, 12 ; in
issue of unlike parents, 89 ; in hazel
eyes, 145 ; in diseases, 169 ; in new
varieties, 198 ; in temper, 233 ; have
no effect on statistical results, 17

Cabs, 26, 30, 31

Candolle, A de, 142, 145, 241 n

Cards, illustration by, 188

Chance, 19

Chaos, order in, 66

Child, its relation to mother, 15 ; to
either parent, 19; of drunken mother,
15 ; of consumptive mother, 177

Cloud compared to a population, 164

Co-Fraternities, 94

Consumption, 171 ; consumptivity, 181

Contributions from separate ancestors,
134

Cookery, typical dishes, 24

Cousins, their nearness in kinship, 133 ;
marriages between, 175

Crelle's tables, 7

Crowds, characteristic forms, 23

Curve of Frequency, 40, 49 ; of Dis-
tribution, 40, 54

Darwin, 4, 19

Data, 71

De Candolle, 142, 145, 241 n

Deviations, schemes of, 51, 60 ; cause
of, 55. See Error.

Dickson, J. D. H., 69, 102, 115, Ap-
pendix B., 221

Disease, 164; skipping a generation,
12

Distribution, schemes of, 37 ; normal
curve of, 54

Error, curve of Frequency, 49 ; law of,

55 ; probable, 57
Evolution not by minute steps only, 32
Eye coloue., 138

Families, extinction of, Ajipendix F.,

241
Family Records, see Records
Father, see Parent
Files in a squadron, 111
Filial relation, 19 ; regression, 95
Fraternities, meaning of word, 94, 234 ;
to be treated as units, 35 ; issued
from unlike parents, 90 ; variability
in, 124, 129 ; regression in, 108

S

258

INDEX.

Frequency, Scheme of, 49 ; model, 63
surface of, 102

Museums to illustrate evolution, 33
Music, 155, 158

Geometric Mean, 118, Appendix E, 238
Gouffe, cookery book, 24
Governments, 22
Grades, 37, 40 ; of modulus, mean

error, &c., 57
Grove battery, 31

Natural, its meaning, 4 ; natural selec-
tion, 32, 119
Nephews, 133
Nile expedition, 23
Nomenclature of kinship, 248

NOEMAL YARI ABILITY, 51

Hazel eyes, 144

Hospital, St. Bartholomew's, 47

Humphreys, G., 186

Incomes of the Euglish, 35
Infertility of mixed types, 31
Insurance companies, 185
Inventions, 25
Island and islets, 10

Kenilworth Castle, 21
Kinship, formula of, 114 ; table of
nearness in different degrees, 132

Laboratory, anthropometric, 43, 46, 79
Landscape, characteristic features, 23
Latent Elements, 187 ; characters,
11

M, its signification, 41

Macalister, D., 238

McKendrick, Professor, 20

Malformation, 176

Marriage selection, in temper, 85, 232 ;
in eye-colour, 86, 147 ; in stature,
87 ; in artistic faculty, 157

Means, 41 ; mean error, 57

Mechanical inventions, 25

Median, 41

Medical students, 47

Merrifield, F., 136

Mid, 41 ; Mid-parent, 87 ; mid-popula-
tion, 92 ; mid-fraternity, 124 ; mid-
error, 58

Models, to illustrate Stability, 27 ;
Curve of Frequency, 63 ; Forecast of
stature of children, 107 ; Surface of
Frequency, 115

Modulus, its grade, 57

Moths, pedigree, 136

Mother's relation to her child, 1 5 ; in
consumption, 177. See Parent

Mulatto blends, 13

O'Brien, 84
Omnibuses, 26, 32
Order in apparent chaos, Q'd
OEaANic Stability, 4

Paget, Sir J., 47

Palmer, 48

Pangenesis, 19, 193

Parents, unlike in stature, issue of, 88 ;
indirect relation to children, 19 ;
parental relation, 110, 132

Particulate inheritance, 7

Peas, experiments with, 79, 225

Peculiarities, natural and acquired, 4 ;
inheritance of, 138 ; definition, 138,
194

Pedigree moths, 136

Pedigrees, arrangement of, see Appen-
dix G., 248, 250

Percentiles, 46

Personal elements, 187 ; in incipient
structure, 9

Petty influences, 16

Population to be treated as units, 35 ;
their mid-stature, 92 ; their Q, 93 :
successive generations of, 115 ; com-
pared to a cloud, 164

Priestley, Dr. W, O., 15

Probability integral, 54 ; tables, 202 to
205

Probable error, 53, 57

Problems in the law of error, 66

Processes in Heredity, 4

Pure Breed, 189

Q, its meaning, 53, 59

R. F.F., see Records of Family Faculties
Rank of Faculty, 36, 46 ; in a squadron,

110
Records of Family Faculties, data, 72 ;
arrangement of, 250 ; prefaced re-
marks, 168 ; object of book, 220 ;
trustworthiness of, 130, 167, 231

INDEX.

259

Regression, filial, 95, 98, 131 ; mid-
parental, 99, 101 ; parental, 100 ;
fraternal, 109 ; generally, 103, 110,
114 ; is a measure of nearness of
kinship, 132 ; in artistic faculty, 158;
in consuniptivity, 181 ; an element
of stability in characteristics of a
people, 163

Schemes of Distribution and Fre-
quency, 35

Scientific societies, their government,
22

Selection in marriage, 85, 157, 147 ;
eff"ect of bias in, 162 ; Natural Selec-
tion, 32, 119

Ships of war, 123

Simplification of inquiries into heredity,
191

Solomon, 24

Special data, 78

Sports, stability of, 30, 198

Squadron, 110

Stable forms, 20, 123, 198 ; subordi-
nate, 25

Stability of sports, 30, 234 ; of charac-
teristics in a people, 163

Statistics, are processes of blending, 1 7 ;

charms of, 62
Stature, discussion oe Data, 83
Strength, Scheme of, 37
Structure, incipient, 18
Sweet peas, 79, 225
Swiss guides, 23

Temper, Appendix D., 236, 85

Traits, 9

Transmutation of female measures, 5,

42, 78
Trustworthiness of the data, 130, 167,

231
Types, 24 ; a marked family type, 234

Uncles, 133, 191

Variability of Stature, in population,
93 ; in Mid-Parents, 93 ; in Co-Fra-
ternities, 94 ; in Fraternities, 124 ;
in a pure breed, 189

Yariation, individual, 9

Watson, Rev. H. W., 242
AVeissman, 193

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