BUREAU OF — 
AMERICAN ETHNOLOGY 
4 


0049 


NATURAL INHERITANCE 


/BY 
FRANCIS danron, F.R.S. 
a €© Oo 
AUTHOR OF 
“ WEREDITARY GENIUS,”’ ‘INQUIRIES INTO HUMAN FACULTY,’’ ETC. 


_ BUREAU OF 
AMERICAN ETHNOLOGY 
O 
LSS 
LIBRARY 


Pondon 
MACMILLAN AND GO. 


“AND NEW YORK 


1889 


The Right of Translation and Reproduction is Reserved 


RIcHARD CLAY AND Sons, LIMITED: 
LONDON AND aie ke 


ERRATA. 


P. 70.—Correct the first four lines so as to make them read as follows :— 


Now if the lateral distance of a particular green mark from M is given 
and called @, what is the most probable distance from M of the red mark 


ce 
ae é a ae 
at which it was aimed? It is eae x 


P. 127, line 17.—In the formula (2) omit the sign of the square root. 
[Mem. The work in the numerical example is correct. | 


P. 98, line 20. —Insert the following sentence after the words ‘‘ one-third ” :— 

We might otherwise state it thus. Let /, including its sign, stand 

for the deviation of the Father’s stature, and // for that of the transmuted 

stature of the Mother. Then 4(/'+ J) is the deviation of the Mid- 

Parental stature. As the average Mid-Filial deviation is two-thirds of 
this, itis 3 x 4(F+ M), or $F + 3M. 


P. 157.—Paragraph on Marriage Selection. It is true that a slight dis- 
inclination is shown to marry within the same caste, if we lump together the 
artistic marriages with the artistic, and the non-artistic marriages with the 
non-artistic. I lumped them together on account of the paucity of the 
numbers. But if they are treated separately, the inference regarding the 
artistic marriages will be found to be reversed. 


P. 203.—The value corresponding to argument 0°1 should be 0°05, and not 
0°65. 


P, 205.—The value corresponding to Grade 58 should be +0°30, and not 
— 0°30. 


CONTENTS. ane 


CHAPTER JT. 

PAGE 

ENR ODUCT OR VE tice cami feta Seer me yc pnt reece Se ialhs are ae ke eG ee 1 
CHAPTER IT. 

ROCHSSHSMTNGs Ein RMD LT Wicun viv nome cuskrant yy “bree oh SRG Tiere 4 


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. 
OG ANT CH SWAB UMD Yasue ye ett orate o ct ceaunt to op ree ay 2 COM ara ecu eal 
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 OF FREQUENCY ......... 390 


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. 


NoRMAL VARIABILITY . 


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 I]lustration of the Cause 
of Curve of Frequency, 63.—Order in Apparent Chaos, 66.—- 
Problems in the Law of Error, 66. 


CHAPTER VI. 
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 svelte 


DISCUSSION OF THE DATA OF SVATURE 


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 ; 
b, 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; Fowth Method, 128; Trustworthiness of the 
Constants, 180 ; General view of Kinship, 182.—Separate Con- 
tribution of each Ancestor, 134.—Pedigree Moths, 136. 


CEEAP TERS svi) lil, 


DIsctussIoN OF THE Data oF Eyr Cotour 


Preliminary Remarks, 138.—Data, 139.— Persistence of Eye 
Colour in tke Population, 140.—Fundamental Eye Colours, 
142.— Principles of Calculation, 148.—Results, 152. 


PAGE 


Ol 


71 


CONTENTS. Vil 


CHAPTER IX. 


PAGE 
SU BPAR DIS TICWMEA CULT Yes Me Pik. ts cio ke el laa oh. wl oy ae oe, LOS 
Data, 154.—Sexual Distribution, 156.— Marriage Selection, 157.— 
Regression, 158.--Effect of Bias in Marriage, 162. 
CHAPTER X. 
IDISHASE Efe po sae : ‘ reteset Gra) ore odo: 


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


CHAPTER XI. 


AUTH NEUMANN) ies ee? leh onc eee ha te meres Sela! tek at Gee Mia rete iif 


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


CHAPTER XII. 


SIT NTNTRISY 5, ered ae ge as iE une Oa op Js mn ee nou pe eel as val {Oy 


vill 


CONTENTS. 


TABLES. 


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


No. of the 


SUBJECTS OF THE TABLES. 


Tables. 

1. Strengths of Pull arranged for drawing a Scheme 

2. Data for Schemes of Distribution for various Qualities and 
Faculties . 38 HAS 5 esta | Nome 

3. Evidences of the general ranean of the Law of ieguees 
of Error A cuemhe ere ee : 

4. Values for the Normal Curve of Frequency (extracted from 
the well-known Table) ide secs oe De 

5. Values of the Fecketally oe Saas from the well- 
known Table) . SPS SIAR eres ene 

6. Values of the Probability Integral when the scale eo which 
the Errors are measured has the Prob: Error for its Unit . 

7. Ordinates to the Normal Curve of Distribution, when its 100 
Grades run from — 50°, through 0°, to ++ 50° 

8. Ditto when the Grades run from 0° to 100°. (This Table is 
especially adapted for use with Schemes) . 

9. Marriage Selection in respect to Stature . 

9a. Marriage Selection in respect to Eye Colour 

9b. Marriages of the Artistic and the Non Artistic . 

10. Issue of Parents who are unlike in Stature 

11. Statures of adult children born to Mid Parents of Various 
SIC UU Re: ee OER TT MRR ara sarc H Git nco. AC 

12. Statures of the Brothers of men of various Statures, from 


AR SHE (CGA se. Males OE Ac Se arc ee ee 


PAGE 


199 


200 


201 


202 


202 


203 


204 


205 
206 
206 
207 
207 


208 


209 


CONTENTS. 


No. of the 
Tables. 


13. Ditto from the Special data 


SUBJECTS OF THE TABLES. 


14. Deviations of Individual brothers from their common Mid- 
Fraternal Stature 


15. Frequency of the different Eye Colours in 4 successive Gene- 
TEMGOME) 5 14 6 Be 


16. The Descent of Hazel-Eyed families 


17. Calculated contributions from Parents and from Grandparents, 
according as they are Light, Hazel, or Dark eyed 


18. Examples of the application of Table 17 
19. Observed and calculated Eye Colours in 16 groups of families 
20. Ditto in 78 separate families . 


21. Amounts of error in the various calculations of anticipated 
Eye Colour . 


22. Inheritance of the Artistic Faculty . 


APPENDICES. 


A. Memoirs and Books on Heredity by the Author 

B. Problems by J. D. Hamilton Dickson 

C. Experiments on Sweet Peas, bearing on the law of Regression. . 
D. Good and bad Temper in English Families . 

E. The Geometric Mean in Vital and Social Statistics . 

F 


Probable extinction of Families, 214; Discussion of the Problem 
by the Rev. H. W. Watson, D.Sc. 


Orderly arrangement of Hereditary Data. 


a2 


INDEX . 


1x 


219 
221 
225 
226 
238 


241 
248 


257 


Wed 


NATURAL INHERITANCE | 


NATURAL INHERITANCE. 


CHAPTER I 
IN TRO D-ULe WOR, Ye 


I HAVE long been engaged upon certain problems that 
lie at the base of the 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, with 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 INHERITANCE. [CHAP. 


generations. ‘The large do not always beget 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, 1s, how much less ? 

The last of the problems that I need mention now, 
concerns the nearness of kinship in different degrees. 
We are all agreed 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 


ra INTRODUCTORY. 3 


sustained effort, need not feel much regret that the 
road to be travelled over is indirect, and does not 
admit of being mapped 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 which 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. 


CHAPTER IL. 


PROCESSES IN HEREDITY. 


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


A CONCISE account of the chief processes in heredity 
will be given in this chapter, partly to serve as a 
reminder to those to whom the works of Darwin especi- 
ally, and of other writers on the subject, are not 
familar, 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 speak 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. I1.] PROCESSES IN HEREDITY. 5 


in features and disposition from their earliest years, 
though brought into the 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 11 may seem impossibie 
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 meaning can we attach to the word “ Average ’ 
when it is applied to the stature of two such different 


6 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 
eroup 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 


11. | PROCESSES IN HEREDITY. 7 


6 feet, as 6 feet + 6 inches; if 54 feet, as 54 feet + 
54 inches ; that is to say, as 5 feet + 114 inches." 

Similarly 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- 
transmuted, 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 living beings 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, and which have been combined under influences 
that 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, while 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 avery easy operation to those who possess that 
most useful 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 known 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 fupene 
which is as much as it will bear. Suppose we were 
building a house with second-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 
might have been moved and much shuffled together 
in the yard, yet pieces from the same source would 
frequently remain in juxtaposition and it may be 
entangled. They would he 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 perhaps 


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 
agoregates, 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 lodgement. 
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 Inkeness and Individual Variation.—Natural 
peculiarities are apparently due to two broadly different 
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 heads, but as different effects of the 
same underlying causes. 

The origin of these and other prominent processes 
in heredity is best explained 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 agency 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 
shioht 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- 


11. | | PROCESSES IN HEREDITY. 11 


sponding variety in the results. In some islets one 
plant would prevail, in others another; nevertheless 
there would be many traits of family hkeness 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. We are told that buried seeds 
may le 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 débris, after the 
cliffs had tumbled into the sea. Again, many plants on 
the islands may maintain an olscure 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 other 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. 


Feritages that Blend and those that are Mutually 
Eaxclusive.—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 : 
wholly black, neither are they piebald, but of a fairly 
uniform mulatto brown. The quadroon child of the 
mulatto and the white has a quarter tint; some of 
the children may be altogether darker or lighter than 
the rest, but they are not piebald. Skin-colour is 
therefore a good example of what 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 general view. 

Next as regards heritages that come altogether from 
one progenitor to the exclusion of the rest. Hye-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 wild 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 white 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 would make their appear- 
ance during an indefinite time, giving it repeated 


14 NATURAL INHERITANCE. [cuAP. 


chances of holding its own in the struggle for existence, 
and of establishing itself if its qualities were superior 
to those of the black stock under any one of many 
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 Acquired Faculties is used in perfect 
strictness and all imheritance is excluded that could be 
referred to some form of Natural Selection, or of 
Infection before birth, or of peculiarities of Nurture 
and Rearing. Moreover, a large deduction from the 
collection of rare cases must be made on the ground 
of their being accidental comcidences. 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 positive kind, that was formerly relied upon, has 
been since found capable of being interpreted in another 
way, and is nolonger adduced. On the other hand there 
exists such a vast mass of distinctly negative evidence, 
that every instance offered to prove the transmission 


a? Pe 


>. 


11.] PROCESSES IN HEREDITY. 15 


of acquired faculties requires to be closely criticized. 
For example, a woman who 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 aremany. 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 O, Priestley, M.D, (Churchill, 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 incalculable number 
of petty accidents that concur to produce variability 
among brothers, make it impossible to predict the 
exact qualities 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. 


C 


CHAPTER III. 


ORGANIC 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 in forming 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 affects 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 
C2 


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. XJ.) 


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 The 
Modern Cell Theory, and Theories as to the Physiological Basis of Heredity, 
by Prof. John Gray McKendrick, M.D., F.R.S., &. (R. Anderson, Glasgow, 
1888.) 


11. | ORGANIC STABILITY. 21 


likings of each individual inscet in a flying swarm may 
be supposed to determine the position that he occupies 
init. Every particle must have many immediate neigh- 
bours. Even a sphere surrounded by other spheres of 
equal sizes, hke 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 effects of chance in producing stable 
results are common enough. ‘Tangled strings variously 
twitched, soon get themselves into tight knots. Rub- 
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 leneth so come into collision as to wedge themselves 
into a sort of arch across the tube, and effectually 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 
pecuhlar 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 
Governments, 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 will 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 tu 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 the 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. 

Hvery variety of Crowd has its own characteristic 
features. Ata 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 Red River 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. [CuAP. 


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 : 
“T have constantly kept in view the leading principles 
of this work, namely, to give in these domestic recipes 
the most exact quantities. ... 1 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 indifferent 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 

1 The Royal Cookery Book. By Jules Gouffé, Chef de Cuisine of the Paris 


Jockey Club ; translated by Alphonse Gouffé, 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 


d 


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. 


Subordinate 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 into 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 work 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 
offer 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- 


11. | 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 oe structure of, eee 
living things. 


Model.—The distinction between oe mary” + aX 


ordinate positions of stability will be made clearer by the 


FIG I. 


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. - [enar, 


intended to illustrate the 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 4 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 dif_i- 
eult 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 (, 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 cD, 
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, 1s 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 different 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 


111. ] ORGANIC STABILITY. dl 


electrical batteries was that which 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 
appled 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 by Minute Steps Only.—The theory 
of Natural Selection might dispense with 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 must be small are 
very different views; it 1s 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 1s 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 were 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 ilus- 
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 being 
“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 

D 


34 NATURAL INHERITANCE. [CHAP. IIT. 


that Evolution need not proceed by small steps only. I 
have largely used metaphor and illustration 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. 


CHAPTER IV. 


SCHEMES OF DISTRIBUTION AND OF FREQUENCY. 


Histermities and Populations to be treated as Units.—Schemes of Distribu- 
tion and their Grades.—The Shape of Schemes is independent of the 
number of observations.—Data for Eighteen Schemes.—A pplication 
of the method of Schemes to sees Measures.—Schemes of Fre- 
quency. 


Fraternities and Populations to be Treated as Units.— 
The science of heredity is concerned with Fraternities 
and large Populations rather than with individuals, and 
must 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 we 
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. [CHAP. 


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 Rank 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 


the 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 Grade 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 
illustration, while its small size makes it all the more 
intelligible. | 

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 Fig. 3. The scale of 


Ibs. is given at the side of both Figs.: and the com- 
partments a to g, that are shaded with broken 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 
Ibs. 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 begin with the third line in the Table for 
iulustration: it tells us that 87 per cent. of the group 
had Strengths less than 70 lbs. Therefore, when drawing 
the figure, a perpendicular must be raised at the 37th 
erade 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 differs sensibly 
from a flowing curve, but when working with double 
minuteness, as mentioned above, the connecting lines 
differ 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 Rank (on a scale reckoned from 0° to 100°) of any 
person in the group to which he belongs. The measured 
streneth 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 Grade on which it falls is 


FIG .4. ihe FIG .5. 
109 
! 
| 
| 
! 
| 
| 
| 
- 50 | 
I 
M 
a 
| l 
0 a7 
0 50 200 0 50 wo 60 50° 100° 


the one required. For example: let us suppose the 
Strength of Pull of a man to have been 74 Ibs, 
and that we wish to determine his Rank 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 


tv.| SCHEMES OF DISTRIBUTION AND OF FREQUENCY. 41 


position will be exactly Middlemost, after the Strengths 
of all the men in the group 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 wu 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 —4w) and 
(N+4u), is greatest when N=M. 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 1s 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 
poimts 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 compare 
the values at the 50th Grades in the two schemes. For 
even if the Medians differ considerably from the Means, 


1v.| 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 Vig. 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 poimt at which the same 
values are to be found. In Vig. 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: “ Very 
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 shapes 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 rreeularity would have been less conspicuous, 
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] SCHEMES OF DISTRIBUTION AND OF FREQUENCY. 45 


limits, but they will never actually touch them. A chess 
board has eight squares ina 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 
orade 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, with much correctness, may 
be printed in a single line of a Table, and according to 
a uniform plan that is suitable for any kind of values. 
The measures to be recorded are those at a few definite 
Grades, 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 


1v.| SCHEMES OF DISTRIBUTION AND OF FREQUENCY. 47 


from the 18 Schemes, and find it is easily understood 
and much 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. 

T 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 Reports, 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 five 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 little from the inferences of the author, but the matter 
is here of small importance, so I need not go further into 
detauls. 

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 II., 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, 1t 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 be 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 Grade 
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 

1D 


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 V. 


NORMAL VARIABILITY. 


Schemes of Deviations.—Normal Curve of Distribution.—Comparison of 
the observed with the Normal Curve.—The 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 quality among a 
multitude of men, either by a simple diagram or by a line 
containing afew figures. In this chapter it will be shown 
that a considerably briefer description is approximately 
sufficient. 

Every measure in aScheme is equal to its Middlemost, 
or Median value, or M, 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 M in any particular case, 
every measure in a Scheme may be expressed in the 

E 2 


52 NATURAL INHERITANCE. [cHaP. 


form of M+(+£D).. lt M=O, or if it 1s ‘subtragned 
from every measure, the residues which are the 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 18 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.,, L., be the lengths of 
the perpendiculars at two specified grades in Scheme 4., 
and K., K., 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 ae a 

-1— Kee 
series of transmuted data will be obtained for drawing 
a new Scheme pB’., 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.J 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 
mace perpendicular at 25, OF; and that at 7a5, Q:,. 
then the unit by which every Scheme will be defined 
is its value of $(Q.,—Q.,), 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 differ- 
ent Schemes, numbered I., IT., IIL, &c., whose respective 
values of Q are q1, q2, qs, &c., to others whose values of Q 
are in each case equal to q, then all the data from which 


Scheme I. was drawn, must be multiplied by a those 
Onl 


from which Scheme II. was drawn, by 2 and so on, and 
2 


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 differ 
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 x Q 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, &c., 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. 5d 


accuracy of measurement, and without the 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 familar Table of the Probability Integral, 
given in Table 5, wd 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. [cHaAP. 


inside out, as it were, deriving the “arguments” for 


Tables 7 and 8 from the entries in the body of Table 6, 
and making other easily intelligible alterations. 


Comparison of the Observed with 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 18 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 M. Although the several series in Table 3 run 
fairly well together; I should not have dared to hope 
that their regularities 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 


J 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 
apples 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 Prob. Error is taken as unity, and 
their corresponding Gr'rades. 


TPRO) 04 1B) AKO so sgocsbocc0008 1:000 ; corresponding Grades 25°'0, 75°:0 
Modul wsirsceeeeeecceeeees 2:097 ; ns 5 a, 
Meany Barocas esters 1188 ; x AN SES} 


Error of Mean Squares 1483 ; % . 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 M. Ina 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 
safeouard against its misinterpretation. Moreover the 
term Probable Error is absurd when applied to the 
subjects now in hand, such as Stature, Hye-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 language. 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 
M—Q, and that at Grade 75° is M + Q, but all this is 
superimposed upon the primary conception. Q stands 
essentially on its own basis, and has nothing to do with 
M. 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 M 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 the 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 formule 
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 Grade. 
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 the 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 0°78; 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 
(ae 1s) 12000. 

Two Measures at known Grades deternune a Normal 
Scheme of Measures.—If we know the value of M as 
well as that of Q we know the entire Scheme. M 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 M 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 be the given Deviation, and d the 
tabular Deviation at the same Grade, as found in Table 8; then multiply 


every entry in Table 8 bys. As the tabular value of Q is 1, it will become 


changed into ae 
0 


62 ' NATURAL INHERITANCE. [cuar. 


The Charms of Statistics.—It is difficult to under- 
stand why statisticians commonly mit 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 A, B be the two given 
Measures of which A is the larger, and let a, b be the values of the tabular 
Deviations for the same Grades, as found in Table 8, not omitting their 
signs of plus or minus as the case may be. 


Then the Q of the Scheme = SS. (The sign of Q is not to be re- 
a— 


garded ; it is merely a magnitude.) 


M=4—aQ;orM=8B- 69. 


Example : A, situated at Grade 55°, = 14°38 
B, situated at Grade 5°, = 9:12 
The corresponding tabular Deviations are :—a = +0:19; b= —2°-44. 
Therefore Q = Peee = oe _ Bp —s0 
O19 + 244 2-63 
M = 14.38 — 0°19 X 2 = 14:0 
or= 9124+244xX%2=140 


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 .&. FIG .9. 


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 the back- 
board, and below these again are a series of vertical 
compartments. A charge of small shot 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 was 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 shot 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 Deviation 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 will still fall 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 M or Q. To do so, we 
must divide its strangely shaped area into four equal 
parts by vertical lines, which is hardly to be effected 
except by a tedious process of “Trial and Error.” On 
the other hand M and Q can be derived from Schemes 
of Distribution with no more trouble than is needed to 


divide a line into four equal parts. 


66 NATURAL INHERITANCE. __ (omar. 


Order in Apparent Chaos.—I know of scarcely any- 
thing so apt to impress the imagination as the wonderful 
form of cosmie order expressed by the “ Law of Fre- 
quency of Error.” The law would have been personified 
by the Greeks and deified, if they had known of it. It 
relons with 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. Itis 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-ordaimed 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. 


Problems in the Law of Hrror.—All the properties of 
the Law of Frequency of Error can be 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 retaim 
a clear geometric view of the facts when we are dealing 
with statistical problems, which abound with dangerous 


v.] NORMAL VARIABILITY. 67 


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 AA, 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 
effect 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 perpendicu- 

F2 


68 NATURAL INHERITANCE. [crap 


lar line drawn from its starting point, and each shot 
will have a Prob: Error that we will call 6. Do this 
for all the AA compartments in turn; b 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 gq. 

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 b, and the result of the two acting together is 
that each shot has a Prob: Error of g. What is the 
relation between a, b, and gq? Calculation shows that 
g=a’+b*. In other words, g corresponds to the hypo- 
thenuse of a right-angled triangle of which the other two 
sides are a and b respectively. 

(2) It is a corollary 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 g, and the Q of the A and B systems respectively, 
a and b, then g=a°+b’. 

1 We may see the 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 Problem 1. 


ee | 


v.| NORMAL VARIABILITY. 69 


(8) Suppose that a row of compartments, whose upper 
openings are situated like those in Fig. 7, page 63, are 
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 Vig. 9. The effect of this will be to 
compress the heap of shot laterally ; its outline will still 
be a Curve of Frequency, but its Prob: Error will be 
ciminished. 


The foregoing three properties 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 Mr. 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 M 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 b. Now, if the lateral distance of a particular 
ereen mark from M is given, what is the most probable 
distance from M of the red mark at which it was aimed ? 


It is 9/ et 


(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 


Ls be 
value is 
VA 


) 


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 1f 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. 


CHAPTER VI. 
| DATA. 


Records of Family Faculties, or R. F. F. data.—Special Data.—Measures 
at my Anthropometric Laboratory.—Experiments on Sweet Peas. 


I wap 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 [ 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 obtained, 


G2 NATURAL INHERITANCE. [cHAP. 


to say nothing of its being more interesting by far than 
one of sweet peas or of moths. 


Record of Family Faculties, or R.FE. Data.—The 
source from which the larger part of my data is derived 
consists of a valuable collection of ‘‘ Records 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 the own Family Records. 

“These Extracts will be treated as confidential docu- 
ments, to be used for statistical purposes only, the 
insertion of names of persons and places bemg 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 
‘Record of Family Faculties.’ 

‘More especially : 

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

‘““(b) By including brief notices of the brothers and 


vi] DATA. 73 


sisters (if any) of each of those ancestors. (Importance 
will be attached both to the completeness with which 
each family of brothers and sisters 1s 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 which 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 obyious that uniformity in the arrangement of docu- 
ments is of primary importance to those who examine 
and collate a large number of them.) 

“Hach 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, 
SW. It will be convenient if the letters ‘ R.H.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 the donor of 
the prizes, aided by competent examiners. 

‘The value of the individual prizes cannot be fixed 
beforehand. No prize will, however, exceed 50/., nor be 
less than 5/., 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 Records sent in reply to this 
offer, that deserved to be seriously considered before 
adjudginge 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 followmg 7 classes had 20 or somewhat fewer 
representatives: (1) Titled persons and landed gentry ; 
(2) Army and Navy; (8) 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 Records; the remainder 
are land agents, farmers, artisans, literary men, school- 
masters, clerks, students, and one domestic servant in a 
family of position. 


ey 


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. 

Hvery 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 
orandparents, and 8 great parents; also that he and 
each of those 14 progenitors had usually brothers and 
sisters, who were included in the inquiry. ‘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 equal 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 AWARDS. 


A Prize oF £7 WAS AWARDED TO EACH OF THE 40 FOLLOWING 
CONTRIBUTORS. 


Amphlett, John, Clent, Stourbridge ; Batchelor, Mrs. Jacobstow Rectory, 
Stratton, N. Devon; Bathurst, Miss K., Vicarage, Biggleswade, Bedford- 
shire; Beane, Mrs. C. F., 3 Portland Place, Venner Road, Sydenham ; 
Berisford, Samuel, Park Villas, Park Lane, Macclesfield ; Carruthers, Mrs., 
Brightside, North Finchley ; Carter, Miss Jessie E., Hazelwood, The Park, 


Cheltenham ; Cay, Mrs. Eden House, Holyhead; Clark, J. Edmund, 


76 NATURAL INHERITANCE. [ CHAP. 


Feversham Terrace, York ; Cust, Lady Elizabeth, 13 Eccleston Square, 8. W.; 
Fry, Edward, Portsmouth, 5 The Grove, Highgate, N. ; Gibson, G. A., M.D., 
1 Randolph Cliff, Edinburgh ; Gidley, B. Courtenay, 17 Ribblesdale Road, 
Hornsey, N. ; Gillespie, Franklin, M.D., 1 The Grove, Aldershot ; Griffith- 
Boscawen, Mrs., Trevalyn Hall, Wrexham ; Hardeastle, Henry, 38 Eaton 
Square, S.W.; Harrison, Miss Edith, 68 Gloucester Place, Portman Square, 
W.; Hobhouse, Mrs. 4 Kensington Square, W. ; Holland, Miss, Ivymeath, 
Snodland, Kent; Hollis, 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 Kast, 
Richmond, Middlesex ; Leathley, D. W. B., 59 Lincoln’s Inn Fields (in 
trust for a competitor who desires her name not to be published) ; Lewin, 
Lieutenant-Colonel T. H., Colway Lodge, Lyme Regis; Lipscomb, R. H., 
East Budleigh, Budleigh Salterton, Devon ; Malden, Henry C., Windlesham 
House, Brighton; Malden, Henry Elliot, Kitland, Holmwood, Surrey ; 
McCall, Hardy Bertram, 5 St. Augustine’s Road, Edgbaston, Birmingham ; 
Moore, Miss Georgina M., 45 Chepstow Place, Bayswater, W.; 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, 8.W.; Smith, Mrs. 
Archibaid, Riverbank, Putney, S.W.; Strachey, Mrs. Fowey Lodge, 
Clapham Common, 8.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 £5 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.C.); Drake, Henry H., The 
Firs, Lee, Kent; Ercke, J. J. G., 13, Brownhill Road, Catford, S.E. ; 
Flint, Fenner Ludd, 83 Brecknock Road, N.; Ford, William, 4 South 
Square, Gray’s Inn, W.C.; Foster, Rev. A. J., The Vicarage, Wootton, 
Bedford ; Glanville-Richards, W. 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 Russell 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., Boscomb 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., 
Viney Hall Vicarage, Blakeney, Gloucestershire ; Smith, Mrs. F. P., Cliffe 
House, Sheffield; Staveley, Edw. 8. R., Mill Hill School, N.W.; Sturge, 
Miss Mary W., 17 Frederick Road, Edgbaston, Birmingham ; Terry, Mrs., 
Tostock, Bury St. Edmunds, Suffolk; Utley, W. H. Alliance Hotel, 
~ Cathedral Gates, Manchester ; Weston, Mrs. Ensleiyh, Lansdown, Bath ; 
Wodehouse, Mrs. E. R. 56 Chester Sqnare, S.W. 


The material in these Records is sufficiently varied to 
be of service in many inquiries. The chief subjects to 
which allusion will be made in this book concern 
Stature, Hye-Colour, 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 Records 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 ageregate 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 shehtly 
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 R.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. Still, speaking from a know- 
ledge of many of the contributors, | 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 “Special observations,’ concern the 


v1] DATA. 79 


variations in stature among 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 obtaimed returns of 295 families, containing in 
the aggregate 783 brothers, some few of whom also 
appear in the R.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. Haeperiments on Sweet Peas.—Vhe last of the data 


80 NATURAL INHERITANCE. [CHAY. 


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 different sizes, but of 
the same species, conducted for the following reasons. 
I had endeavoured to find a population pessessed 
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 VIII. 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 officer would treat 
a large population. Then I selected with great pains 
several sets for planting. Hach set contained seven 
little packets, numbered K, L, M, N, 0, Po anduge 


each of the seven packets contained ten seeds of almost 


vu] 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 | 
ascertained by laying 100 peas of the same weight in a 
row. ‘The weights run in an arithmetic series, having 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 
erain; 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. All this is shown in the 
Appendix, where it will be seen that I 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 14 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 difficulties 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 well-known 
statistical operation. Suffice it to say that I took im- 
mense pains, which, if I had understood the general 
conditions of the problem 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. 


\ 
/ 
ee 
ase 


CHAPTER VII. 
DISCUSSION OF THE DATA OF STATURE. 


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


Stature as a Subject for Inqury.—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 
differences of bringing up, and its inconsiderable influ- 
ence on the rate of mortality. Other advantages 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 accumulated lengths or 
G 2 


84 NATURAL INHERITANCE. [CHAP. 


thicknesses of more than a hundred bodily parts, each 
so distinct from the rest as to have earned a name by 
which it can be specified. 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 square root of 


vit. | 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. 


Marriage 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 Temper 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 1s 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 VIII, 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 ight and 
the other hazel-eyed, they give 23 observed against 15 
calculated ; and where one parent is ight and the other 
dark-eyed, they give 24 observed against 32 calculated. 


Vit. | 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 
equdance or Eroblem 2, page 68: Ii find) the OF 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 
/2 x 1:7 inches = 2°41 inches. Therefore the Q in a 
eroup 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, by 


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 which 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 lkeness. 
I do not regard this difference as of consequence, 
because the numbers are small, and because a sheht 
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.—We 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 


vil. | DISCUSSION OF THE DATA OF STATURE. 89 


that ideal personage to whom we have already 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- 
worthy 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 cases 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 difference 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. [cuap. 


of Like Parents; (b) those who are the progeny of 
Unlike Parents. Next we write the statures of the 
individuals in each Fraternity under the form of 
M+(+D) (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, ito one Scheme of 
deviations, and all those that belong to the group b 
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 Group than there is in the b Group, and such 
proves to be the case. J 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 im all cases they have 


borne the test successfully. 


Hilden» * 


vit.] DISCUSSION OF THE DATA OF STATURE. of 


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


Description of the Tables 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 formule that will 
be used. ; 

Table 11, R.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 from the R.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 R.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 that 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 
68°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, 
although it amounts to more than 0°15 inch. The 


vii. | DISCUSSION OF THE DATA OF STATURE. 93 


series in question refers to R.F.F. brothers, who, owing 
to the principle on which the Table is constructed, are 
only a comparatively small sample taken out of the 
R.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 
reoular a Scheme for the general R.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. 


Variability 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 
data. 


Variability of Mid-Parents.—The value of Q in a 
Scheme drawn from the Statures of the R.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 equal 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 inch, which agrees excellently with the observed 
value.’ 


Variability 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 growp of Mid- 
Parents who have the same Stature (reckoned to the 
nearest inch) will be termed a Co-Fraternity. Hach 
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 differed 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 differ 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 
differences between town and country-folk, and those 
between persons of different social classes, are con- 
spicuous in the data contaimed in the Report of the 

1 In all my values referring to human stature, the second decimal is 
rudely approximate. I am obliged to use it, because if I worked only to 


tenths of an inch, sensible errors might creep in entirely owing to arith- 
metical operations. 


Vit. ] 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 quite 
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 Geometric 
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 difficulty 
of explanation, and introduced extra trouble through- 
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 offspring must on the whole, 
be more mediocre than the stature of their Parents ; 
that is to say, more near to the M of the general 
Population. Table 11 enables us to compare the 
values of the M in different Co-Fraternal groups 
with the Statures of their respective Mid-Parents. 
Fig. 10 is a graphical representation of the meaning of 


96 NATURAL INHERITANCH. [cHAP. 


the Table so far as it now concerns us. ‘The horizontal 
dotted lines and the graduations at their sides, cor- 
respond to the similarly placed lines of figures and 
eraduations in Table 11. The dot on each line shows 
the point where its M 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 


ans ee 
| --REGRESSION — |---— ae 
FROM 7 

. ek DIIPAREN Tien |wanny ann ce hea 


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 1s 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- 


vil. | DISCUSSION OF THE DATA OF STATURE. 97 


Statures of the Sons would be, if they were on the 
average identical with those of their Muid-Parents. 
Most obviously A B does not agree with C D; therefore 
Sons do nof, on the average, resemble their Mid- 
Parents. On examining these lines more closely, it 
will be observed that AB cuts CD at a pomt M that 
fairly corresponds to the value of 684 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, HE M F, through M, and 
let EHC A be any horizontal line cutting ME at E, MC 
at KH, and MA at A. Then it is obvious that the ratio of 
EA to EC is constant, whatever may be the position of 
ECA. This is true whether EC A be drawn above or 
like F DB, 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 
Fihal 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 Regression.” 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 Regression, on the average of many 
cases, from the Mid-Parental to the Mid-Fihal 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 Regression 
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 im its appropriate place, but they are 
too scattered and irregular to make it useful to give 


vit. | DISCUSSION OF THE DATA OF STATURE. 99 


the results in detail. They seem to show a Regression 
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 
average Reeression from either of the Parents to the 
Son. 


b. 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 2 as 
widely as his Mid-parent, it does not in the least follow 
that the Mid-parent should deviate on the average from 
P, 3 or 14, 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 11, 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 the man 
himself. This value of 4} is four and a half times 
smaller than the numerical converse of 3, since 44, or 
3, being multiplied into 4, is equal to 3. 


c. Parental: As a Mid-Parental deviation is equal 
to one-half of the two Parental deviations, it follows 
that the Mid-Parental Regression must be equal 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 4, the 
average Parental Regression must be 4 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 appear in the Table. I found it hard at first 
to catch the full significance of the entries, though I 
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- 


vit. | DISCUSSION OF THE DATA OF STATURE. 101 


tical one, the 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 684 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. 


the ratio of 2, and those where the ellipses were touched 
by a vertical tangent, lay in a straight line inclined to 
the horizontal in the ratio of 4. 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 Ratios 
of Regression, already obtained by a different method, 
namely those of # from Mid-Parent to Son, and of 


102 NATURAL INHERITANCE. [cHAP. 


4 from Son to Mid-Parent. These and other re- 
lations were evidently a subject for mathematical 
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 (1) the value of Q in the General 
Population, which was found to be 1°7 inch; (2) the 
value of Q in any Co-Fraternity, which was found to be 
1°5 inch; (3) the Average Regression of the Stature of 
the Son from that of the Mid-Parent, which was found 
to be 3. I wrote down these values, and phrasing the 
problem in abstract terms, disentangled from all refer- 
ence to heredity, submitted it to Mr. J. D. 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, imasmuch 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 Regression from 4 to 7%; the 


vir. | 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 Regression 
in Stature refers primarily to Deviations, that is, to 
measurements made from the level ef mediocrity to the 


1 The following is a more detailed comparison between the calculated 
and the 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.) 

Ratio of mean filial regression = 2. 

“ Prob. Error” of each Co-Fraternity = 1°50 inch. 


Sections of surface of frequency parallel to XY are true ellipses. 
(Obs.—Apparently true ellipses.) 
MEXe MO) 16 Web aor nearly le-3, 
(Obs.—1 : 3.) 
Major axes to minor axes = ,/ 7: ,/ 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.—A pparently so.) 
‘Prob. Error”, the Q of that curve, = 1.07 inch. 
(Obs,—1-00, or a little more.) 


104 NATURAL INHERITANCE. [CHAY. 


crown of the head, upwards or downwards as the case 
may be, and not from the ground to the crown of the 
head. (In the population with which I am now dealing, 
the level of mediocrity is 684 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 + (+ D) be the 
Stature of the Parent, the Stature of the offspring will 
on the average be P + (+ 4D). | 

If this remarkable law of Regression had been based 
only on those experiments with seeds, in which I first 
observed it, it might well 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 


Vil. | DISCUSSION OF THE DATA OF STATURE. 105 


parents, partly from his ancestry. In every population 
that intermarries freely, when the genealogy of any man 
is traced far backwards, his 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 M 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, 1s 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 
effect resembles that of pourmg 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 them is to weaken the original 
alcoholic strength in a constant ratio. 


The law of Regression 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 
oifted 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 
oifted 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 
oifted as the ablest of all the children of a very great 
many mediocre pairs. 

The constancy of the ratio of Regression, 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 


vil. | DISCUSSION OF THE DATA OF STATURE. 107 


contrived more than one form of apparatus by which 
the probable stature of the children of known parents 
can be mechanically reckoned. Fig. 12 1s 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 
FIG 12. 


o r P inel 
together so as to form a single SG ESRECAETISTINURE 


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 


alr 

1 

Wess 
im 


eroove 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 


= z 
e | a 
G 

=| 
alm 
al) es 


ry 
a 


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, 
I’ 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. 


Thus 56 is written in the position of 60°48 inches, which 
is equal to 56x 1:08. 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 versd, 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 2 of that amount. 

The weights M oa F have to be set cmpastte to the 
heights of the mother and father on their respective 
scales ; then the weight SD will show the most probable 
heights of aSon 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 leneth 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 he 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, 


vil. | DISCUSSION OF THE DATA OF STATURE. 109 


I obtained the value for Fraternal Regression of 2; 
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 


FRATERNAL REGRESSION | 


R.F.F. SPECIALS 
64 66 68 70 72 64 66 68 70 v2 


unknown brother has two difterent 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 Reeression from either Parent to the 
Son is twice as great as that from a man to his Brother, 
aman is, generally speaking, only half as nearly related 


110 NATURAL INHERITANCE. [CHAP. 


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 Regression 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 P4D be the 
stature of the known man, and P+D’ 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 1s 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 might marshal them one behind the 
other in successive ranks, and thereby form a “ Squad- 
ron,” numbering 1000 statures each way, and standing 


vit. | DISCUSSION OF THE DATA OF STATURE. iui 


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 


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 NATURAL INHERITANCE. [cHAP. 


Throw 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 different 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 
different 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 
refets. 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 are rect- 


vu. | 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 


FIG 1S, 
' | 
| 


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 which 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 f. Then if p be the Q of 
I 


114 NATURAL INHERITANCE. — [CHAP. 


the general Population, we arrive at a general equation 
that is true for all degrees of Kinship; namely— 
Te = (1) 

but 7, the curvature in rank, is a regressed value of p, 
and may be written wp, w being the value of the 
Regression. Therefore the above equation may be put 
in the form of 

wepe+ fP=p (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 p. 

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 affords 
an excellent diagramatic representation, true to scale, 
of the action of the law of Regression in Descent. © I 
should like to have given in addition, a perspective 
view of the Squadrons, but failed to draw them 


an 


Vit. | DISCUSSION OF THE DATA OF STATURE. 115 


clearly, after making many attempts. Their curvatures 
are so delicate and peculiar that the eye can hardly 
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 Royal 
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 Generations 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. 


116 NATURAL INHERITANCE. [CHAP. 


In each 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 Regression 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 lfe-histories 
are recorded in the R.F.F. data. 

The Males and Females in Generation I. whose M has 
the value of P (viz., 684 inches), and whose Q is 1-7 
inch, were found to group themselves as it were at 
random, into couples, and then to form a system of 


vil. | DISCUSSION OF THE DATA OF STATURE. 17, 


Mid-Parents. This system had of course the same M 
as the general Population, but its Q was reduced to 
v&x1-7 inch, or to 1:2 inch. It was next found 
when the Statures of the Mid-Parents, expressed in the 
form of P+(+D), were sorted into groups in which 
D was the same (reckoning to the nearest inch), that a 
Co-fraternity sprang from each group, and that its M 
had the value of P+(+2D). The system in which 
each element is a Mid-Co-Fraternity, must have the 
same M as before, of 684 inches, but its Q will be again 
reduced, namely from 1:2 inch to 2x1°2 inch, or to 
0°8 inch. Lastly, the individual Co-Fraternals were 
seen to be dispersed from their respective Muid-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 I]. Consequently the members of 
Generation II. constitute a system that has an M of 
684 inches and a Q equal to ,/ [(0°8)?+(1°5)7], = 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 heights to their 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 comcides with that 
drawn from male Statures. Marriage selection was found 
to take no sufficient notice of Stature to be worth con- 
sideration ; neither was the number of children in 
Fraternities found to be sensibly affected by the 
Statures of their Parents. Again, it was seen to be 
of no consequence 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. (1) 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 1n 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 different Co-Fraternities. Strictly 
speaking, that value was found to slightly rise or fall as 
the Mid-Stature of the Co-lraternity 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 


vu. | 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 inquiry 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 that in which the mediocre members 
of a population are those that are most nearly in 
harmony with their circumstances. The harmony ought 
to concern the ageregate 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, imas- 
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. We already know that if we 


vil. | DISCUSSION OF THE DATA OF STATURE. 121 


call this value P, and write each stature under the 
form of P+ (in which « includes its sign), and if the 
number of times with which any value P+ occurs, 
compared to the number of times in which P occurs, 
be called y, then « 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 would be most favour- 
able to some particular stature, and whatever the value 
of « might be, it is possible that the stature P+a 
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+, and the frequency 
of the latter occurrence will diminish rapidly as a 
increases. If the number of times with which any 
particular value of P+ is most favoured, as compared 
with the number cf times in which P is most favoured, 
be called y’, we may fairly assume that y’ and «& are 


122 NATURAL INHERITANCE. [cHap. 


connected by the law of Frequency of Error. But 
though the system of y values and that of y 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 N’, 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 $8; these being the final survivors. 
We have seen that :— 

y=the number of individuals who have the stature 
P+, counting those who have the stature P, as 1. 

y’ =the number of times in which P+ is the most 
favoured stature, counting those in which P is the 
most favoured, as 1. 

Then yy’=the number of times that individuals of 
the stature Px are selected, counting those in which 
individuals of the stature P are selected, as 1. 

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


vil. | DISCUSSION OF THE DATA OF STATURE. 123 


that law is expressed, that the relation between yy’ and 
% 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 hable to 
be hunted by beasts of prey, if no other useful faculty 
was thereby diminished. 

But a-too free use of this “if” 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 obtainmg 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 fleetness 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. 


accommodation. Hvolution 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 apply each of them to both 
the Special and to the R.F.F. data; this will give 8 
separate estimates of its value, which in the meantime 
will be called 6. The four methods are as follow: 

First method; by Fraternities each containing the 
same number 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 ; 1t will be seen that 
the results justify the assumption. 


Vii. | DISCUSSION OF THE DATA OF STATURE. 125 


The value of the M 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 true M, 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 M of any small 
Fraternity (MF’), and that of the corresponding true 
M (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 (ME”’) of our large 
ideal Fraternity will therefore be identical with its (MF), 
and its Q will be the same as b. 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’,), (ME"’.), &. It can easily be shown 
that (ME), (MF’,), &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 =b x = If n=1, then the Prob. Devia- 


Jn 
mow becomes! b,-as ite should, If 7 = 2) the Prob 


126 NATURAL INHERITANCE. [cHAP. 


Deviation is determined by the same problem as that 
which concerned the Q of the Mid-Parentages (page 87), 
where it was shown to be b x ae By similar reasoning, 
Tt 
soon. When » is infinitely large, the Prob. Deviation 


is 0; that is to say, the (ME’) values do not differ at 
all from their common (MF). 


when n = 3, the Prob. Deviation becomes b x and 


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 6b in terms of d, as follows :— 
The (ME’) values are distributed about their common 
(MF), each with the Prob. Deviation of 5x —, 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 }, 


b? 


consequently b? = d’?+ —, or = 
n 


n—l 


n 
d’ 


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 b, which are respectively 
1°01, 1°01, 1:20, and 1:08; the mean of these is 1°07. 


Second Method; from the mean value of Fraternal 
Regression :—We may look on the Population as com- 
posed of a system of Fraternities. Call their respective 
true centres (see last paragraph) (MF,), (MF), &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 0. 

Then (1:7)?=c’+ 0? (1) 

Let P+(+F,) be the stature of any individual, and 
let P+(4+MF,) be that of the M of his Fraternity, 
then Problem 4 (page 69) shows us that :— 


| (MF,,) . Cc 
the most probable value of r 8 VPLe (2) 

This is also the value of Fraternal Regression, and 
therefore equal to 2. Substituting in (2), and replacing 
c by the value given by (1), we obtain 6=0-98 
inch. | 


Third Method; by the Variability in the value of 
individual cases of Fraternal Regression :—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. 


individual brothers in each Fraternity are dispersed 
from ther own (MF) with a Q equal to 0. 
ence (1:24)? = +07. 


Poe be 
But it is shown Problem 5 that v= ee) ; 
“DA\2 2 Oe 
therefore (1:24)? =b?+ Pare 


Substituting for c° its value of (1°7)’—b? (see last para- 
graph), we obtain 6=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 / 2x0. 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 


vil. | DISCUSSION OF THE DATA OF STATURE. 129 


four brothers, and therefore giving 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 
yen, 2 eves 6 —1-10 inch. 


Thus far we have dealt with the special data only. 
The less trustworthy R.F.F. give larger values of 6 in 
every case. An epitome of all the results appears in 
the following table :— 


Values of b obtained by different methods 


Metodecanabdatat and from different data. 
From Special Data. From R.F.F. data.t 

(1) From Fraternities each 

containing the same number of 

|QCINSTOLS ARE ato ReeHec nse rina a eo EO 1:38 
(2) From the mean value of 

Fraternal Regression............ 0:98 1-31 
(3) From the Variability of 

Fraternal Regression......... .. 1:10 1:14 
(4) From Pairs of Brothers 

bakeneat randoms.) «seh eee 1:10 1:35 

Mean’ J... Sse 1:06 


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


ties, so all were disregarded that contained fewer than 
four individuals. In (2) and (8) 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 
R.F.F. data accord less well together. The R.F.F. 
measures are not sufficiently exact for use in these 
delicate calculations. Their results, being compounded 
of 6 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 b 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. 


Trustworthiness of the Constants.—There is difficulty 
in correcting the results obtamed from the R.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 imaccuracy 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 R.F.F. would be greater 
than that of one of the Specials, whereas it proves to 
be the same. It is likely that the accuracy is a com- 
pound first of the uncertaimty above mentioned, whose 
effect would be to increase the value of the Prob. Error, 


vit | DISCUSSION OF THE DATA OF STATURE. 131 


and secondly of a tendency on the 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 R.F.F. data in Table 12 run so 
irregularly that I cannot interpret them with any 
assurance. The value they give for Fraternal Regression 
certainly does not exceed 4, and therefore a correction, 
amounting to no less than 4 of its amount, is required 
to bring it to a parity with that derived from the 


Special data (because $+4x+4= 2). Hence it 
might be argued, that the value of Regression from 
Mid-Parent to Son, which the R.F.F. data gave as 2, 
ought to receive a similar correction. If so, it would 
be raised to 2 + 2 = 8; but I cannot believe this 
high value to be correct. My first estimate made 
from the R.F.F. data, was 2, as already mentioned. If 
this be adopted, the corrected value would be ¢, or 58) 
instead of $, which might possibly pass. Curiously 


enough, this value of + for Regression from Mid-Parent 
to Son, coincides with the value of 2 for Regression 
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 Regression from entirely 
different and more accurate groups of data, the pro- 
visional value already adopted of 2 from Mid-Parent 
to Son may be accepted as being near enough for the 
present. It is impossible to revise one datum in the 
K 2 


132 NATURAL INHERITANCH. [CHAP. 


R.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 not 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 fwas found to be equal to 
1:50 inch. We deduce the value of f from that of w by 
means of the general equation p*w°+/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 / as follows: A Nephew 
is the son of a Brother, therefore in this case we have 
w=1x2=2; whence f=1°66. 

The Regression, which we call w, 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 w would be 1. 


vu. | DISCUSSION OF THE DATA OF STATURE. 1 


se) 


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, Mean Q =r 
to their Kinsmen in various near degrees. regression=w. =px/v (1 -w?). 
| Mid-parents to Sons............ 2/3 1:27 
_ Brothers to Brothers ......... Qed Le 
Fathers or Sons to | ; 
Sons or Fathers- { "°°" Lye LOD 
Uncles or Nephews to 
9 ° 
Nephews or Uncles \ sets /9 H66 
Practically 
Grandsons to Grandparents... 1/9 that of Popu- 
; : lation, or 
Cousins to Cousins ............ 2/27 ( 1-7 inch, 


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 Regression to P would be complete. The M of the 
Kinsmen, which is expressed by P+w(+D), would in 
that case become P, whatever might have been the value 
of D; therefore wmust=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 45 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 that 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 P42D, 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 imphed 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 
Regression, it was shown that a peculiarity in a Man 
impled a peculiarity of 4 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 4D, that of the Mid- 
Great-Grand-Parent would be 4D, and so on. Hence 
the total bequeathable property would amount to 
D(1+44+4+4 &.) =D3. 

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 


Vit. | DISCUSSION OF THE DATA OF STATURE. 155 


to be equally taxed ; then, as an accumulation of ances- 
tral contributions whose sum amounts to D3 yields an 
effective heritage of only D%, it follows that each piece 
of heritable property must have been reduced to ¢ of its 
original amount, because 3 x 4=2. 

Secondly, suppose the ee 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. : ee case the oa heritage would be 


i Para tors ;+ —)=D eo , which must, as 


before, be equal to D2; whence “ == 

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, (1) that the Mid-Parental peculiarities, 
pure and simple, influence the offspring to ¢ of their 
amount ; (2) that they influence it to 38 of their amount. 
These values differ but slightly from $, and their mean 
is closely 4, so we may fairly accept that result. Hence 


136 NATURAL INHERITANCE. [cHAP. 


the influence, pure and simple, of the Mid-Parent may 
be taken as 4, and that of the Mid-Grand-Parent as 1, 
and so on. Consequently the influence of the individual 
Parent would be 4, and of the individual Grand-Parent 
zs, 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 member 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 eut their wings. Their families 


VII. | DISCUSSION OF THE DATA OF STATURE. 157 


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 VIIL. 


DISCUSSION OF THE DATA OF EYE COLOUR. 


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


Preliminary Remarks.—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 (1) 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 
peculiarity 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- 
harity im each ancestor taken singly, is reduced in 
transnussion according to the following average scale ;— 
a Parent transmits only 4, and a Grand-Parent only 75. 

Stature and Eye-colour are not only different as 
qualities, but they are more contrasted in hereditary 


cH. vut.] DISCUSSION OF THE DATA OF EYE COLOUR. = 189 


behaviour than perhaps any other common qualities. 
Parents of different Statures usually transmit a blended 
heritage to their children, but parents of different Hye- 
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 Hye- 
colour and the other a dark Eye-colour, some of the 
children will, as a rule, be hght 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 ageregate of the quasi- 
independent inheritances of many separate parts, while 
Hye-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 ‘Records of Family 
Faculties” (“ R.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 INHERITANCE. [CHAP. 


Stature, and shown that they were fairly trustworthy. 
I think they are somewhat more accurate in respect to 
Hye-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 population, 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 R.F.F. data are compiled. Those persons who 
ranked in the Family Records as the “children” of the 
pedigree, were counted as generation [.; their parents, 
uncles and aunts, as generation II. ; their grandparents, 
ereat uncles, and great aunts, as generation IIJ.; 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 1s 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 n 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 that some cases of young children 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 Records” to express Hye- 
colours. I began by classifying them under the follow- 
ing eight heads ;—1, light blue; 2, blue, dark blue; 
83, 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 
eight in number, the observations are far from being 
sufficiently 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 of. 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 imternal 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.i.F. data must have been so 
curiously distributed as to preserve the concurrence. 
‘If these curves were not concurrent, then the errors 
in the R.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.E.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 ageregate 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 12°7 per 
cent. of all the observed cases. In medium tints, the 
outer portion of the iris is often of a dark grey colour, 


DISCUSSION OF THE DATA OF EYE COLOUR. 145 


vill. | 


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


“yovtq ‘UMOIq yIVp “A | 


‘uMOoIg yrvq | 


“umoIg | 


“UMOIG YUSIT | 10 


‘Tezey ‘Aois yareq | 


‘users-ontq ‘Aor | o° 


‘ong yep ‘ontg | A 


‘onqg yausry | 77 


Number 
of 
cases 


> 
i= 
=I 
= 
= 
3 
q 
i>) 
Oo 


913 


Pee 


1515 


Til Ness seeses 


” 


1477 


22 


585 


Total Males .........00. 


Females ......00 


»” 


7 


i 
A 
N 


2213 


4490 | Total cases 


144 NATURAL INHERITANCE. [CHAP 


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 lght 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-thirds 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.,1s 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 absorbing 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 
oiven 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 Candolle’ has 


1 Heérédité de la Couleur des Yeux dans l|’Espéce humaine,” par 
M. Alphonse de Candolle. “ Arch. Sc. Phys. et Nat. Geneva,” Aug. 1884, 
3rd period. vol. xii. p. 97. 

L 


146 NATURAL INHERITANCE. [CHAP. 


also shown from his data, that yewx 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, contaming 
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;” 6, the parents; c, the grand- 
parents. Group 2 contains a, the father of the 
“children” and his brothers and his sisters; b, 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. Out 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 Hye-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 group, and individual peculiarities 


V1it. | 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 Hye-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 heht-eyed Grand- 
Parents are proportionately very numerous. 

The question of marriage selection in respect to 
Hye-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 Hye-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 L., 
II., and III, and are placed in juxtaposition with 
the observed facts entered in the column headed 
“Observed.” These three columns contain calculations 
based on data limited in three different 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; Il. 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;” G, for “a grandparent of 8;” G, for “a great 
orandparent of 8,” 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 pos- 
sessed by F is equal to D, and that nothing whatever 


Vill. | DISCUSSION OF THE DATA OF EYE COLOUR. 149 


is known with certainty of any of the 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 G, to §) will on the average possess $D. Similarly 
that each of the four grandparents of F (who will stand 
in the order of G, to S$) will on the average possess 
4D, and so on. Again we have seen that I, on the 
average, transmits to 8 only 4 of his peculiarity ; that 
G, transmits only 7; G, only gy, and so on. Hence 
the ageregate of the heritages that may be expected 
to converge through F upon 8, is contained in the 
following series :— 


Dis +2(5 <5) +4(5+ 5p) + &e. 


ee satagt &e. | =D x 0°30. 
That is to say, each parent must in this case be 
considered as contributing 0°30 to the heritage 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 8. 

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 KHye- 
colour, must be taken to mean that that same fraction 


150 © NATURAL INHERITANCE. [CHAP. 


of the total number of children 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 Hye-colour, in the proportion 
in which those Hye-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 2 of 
his total contribution of 0°30, ze, 0°20 to light, and 
4, ze. 0°10 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 ealculated 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 G, and that nothing 
whatever is known with certainty of any other ancestor 
of 8. Then it has been shown that the child of G, 
(that is F) will possess $D ; that each of the two parents 
of G, (who stand in the relation of G, to S) will also 
possess 4D; that each of the four grandparents of G, 
(who stand in the relation of G, to S) will possess 4D, 
and so on. Also it has been shown that the shares 
of their several peculiarities that will on the average 


be transmitted by F, G,, Ge, &c., are & ae) eee 


Vit. | DISCUSSION OF THE DATA OF EYE COLOUR. 151 


respectively. Hence the aggregate of the probable 
heritages from G, are expressed by the following 
series -— 


i la ye nee 
Disx at! mines i> A song) mS ete. 
| aie 1 1 Nos. (ae BN ; 
= gs) (G+ + a =Dx 12 +2 )=D x06. 


So that each grandparent contributes on the average 
0:16 (more exactly 0°1583) of his peculiarity to the 
heritage of §, 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 1 in the columns II. of Tables 17 
and 18. 

III. Eye-celours 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 G, 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 Dx 3=Dx0-075. For the con- 
venience of. using round numbers I take this as 
Dx0°08. So the two parents contribute between 


152 NATURAL INHERITANCE. [ CHAP. 


them 0°50 of the peculiarity of 8, 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 lght, 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 03 to dark. All this is tabulated in 
Table 17, and its working explained by an example in 
the columns headed III. of Table 18. 


Fesults—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 L., IL, 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 «dividual 
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 


Vul. | 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 IL, we find I. to 
be shghtly 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 more 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 Hye-colour. 


CHAPTER [Xx 
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- 
cditary Genius. The inheritance of much less excep- 
tional oifts 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 mm 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 
ereat Painters and Musicians, whose biographers usually 
say little or nothing of their non-artistic relatives. 


fas 


CHAP. IX. | THE ARTISTIC FACULT\ 155 


The object of the present chapter is not to givea 
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 Hye-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 began 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 whole 
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 show 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 women, 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 
9p show that the number of Artistic to Non-Artistic 
persons in the general population is in the proportion 


IX. | THE ARTISTIC FACULTY. 157 


of 304 to 694. The data used in Table 22 refer to a 
considerably larger number of persons, and do not 
include more than 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 R.F.F. 
correspondents, three on the average are artistic and 
seven are not, 


Marriage Selection.—Table 9B 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 shght 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 INHERITANCH. [CHAP. 


moderately artistic people do not. A man of highly 
artistic temperament must look on those who are 
deficient in it, as barbarians; he would continually 
crave for a sympathy 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. 


Regression.—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 numerous 
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 
Kye colour; in other words, that the value of Fihal 
Regression would in this case also be 2. 

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 + (+ 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 


160 NATURAL INHERITANCE. [cHapP. 


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 
approximation 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 1°71. Therefore an artistic 
person has, on the average, an art-measure of 
P +4171. 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 M of the Co-Fraternity born of a group of 
Mid-Parents whose measure 1s P + 1°71 will be 
P+ (2 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 1:7. 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 + 0°78}. 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, which 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 may be 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 

dy {((40 x P) + 30 (P — 171)} 

= P — 38x 171 = 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 M the value of P—{§ 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 the re- 
mainder of 17 per cent. will be Artistic. Observation 
gives the values of 79 and 21, which 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 + 83), or 614 
per cent. of their children would be Non-Artistic, and 
4 (60 + 17), or 384, would be Artistic. The observed 
numbers are 61 and 39, which agree excellently well. 

We may therefore conclude that the same law of 
Regression, and all that depends upon it, which governs 
the inheritance both of Stature and Hye-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 with 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 subsequent 
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 with 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 Regression and of Co-Fraternal 
expansion 1s due to the Regression increasing with the 
Deviation. Its effect 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. ; 


i) 


M 


CHAPTER X. 


DISEASE, 


Preliminary Problem.—Data.—Trustworthiness of R.F.F. Data.—Mixture 
of Inheritances.—ConsumMpPTIon : General Remarks; Parent to Child ; 
Distribution of Fraternities; Severely Tainted Fraternities ; Con- 
sumptivity.—Data for Hereditary Diseases. 


THE vital statistics of a population are those of a 
vast army marching rank behind rank, across the 
treacherous table-land 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 repose 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. The 


xe DISEASE. 165 


well understood cause of such 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 which the 
wind 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 toa 
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 well 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 Records 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 valuable in future years; but they must 


xe] DISEASE. 167 


bide their 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 14 direct ancestors, up to the 
great-erandparents inclusive, making in all 15 persons. 
Also, to the Fraternities of which each of these 15 per- 
gons was a member. Reckoning 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 
Records that I am able to use, is about 160; so the 
agoregate of the returns of disease ought to have been 
about twelve thousand, and should have included the 
causes of death of perhaps 6,000 ofthem. Asa matter of 
fact, I have only about one-third of the latter number. 


Trustworthiness of RFF. 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 
the 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 with ; otherwise the returns might be 
accepted as being on the whole honest and outspoken. 
I find the latter to be the case. Sixteen per cent. of 
the causes of death (or 1 in 64) 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 insufficiency 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. 169 


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


Mixture of Inheritances.—The first thing that struck 
me after methodically classifying the diseases of each 
family, in the form shown in the Schedule, was their 
great intermixture. ‘The Tables A and B in Appendix G 
are offered as ordinary specimens of what is everywhere 
tobe 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 which their children would be lable! ‘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 inheritabie 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 no 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 well 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 Records, 


170 NATURAL INHERITANCE. [ CHAP. 


the one of an obvious hereditary 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 leneth 
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. 
T 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 
eancer. 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. ial 


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, differing only in petty details, 
This is far more important than adding to the number 


172 NATURAL INHERITANCH. [CHAP. 


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

In sorting my cases, I included under the head of 
Consumption all the 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 ; Hemorrhage 
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) Suspi- 
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- 


| DISHASE. 175 


sumption feared, and died of bad chill. Chest colds 
with pleurisy and congestion of lungs. Died of an 
attack on the chest. Always delicate. Delicate lungs. 
Hemorrhage 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; anemic. 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 66 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 average 


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, 1t 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 whole 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 in line A of 
the following table :— 


PERCENTAGE OF CASES HAVING VARIOUS PERCENTAGES OF TAINT. 


Percentages of Taint. 


0 10 20 30 A0 
and and and and and Total. 
under | under | under | under above 
9 19 29 39 


A. 66 cases, one 
parent con- 27 20 9 15 29 100 


sumptive. 


B. 84 cases, one 
brother con- | 49 14 10 13 14 100 


sumptive. 


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 


176 : NATURAL INHERITANCE. [cHAP. 


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 1s small when there is no accom- 
panying “malformation.” This last phrase is intended 
to cover not only a narrow chest and the lke, 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 Hratermities.—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. vie 


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. 


mn fe Order of 
: : e at : e at | ages at death. 
Father. aes Mother. d S ah 8 
F. M. 

PAS Gia ygenmiccs. eaunc svete? ie 8 40) Consumption. ).. 1. AOD) oil 40 
IBLONCHIULISH see ee 89 | Consumption. .... 43 | 62 42 
Inf. kidneys and bronchitis. 73 | Consumption. ....47/| 59 43 
Abscess of liver through lung(alive)) Consumption. .... 55 | 62 44 
Jalen Ss Sate a are cuca erie 68) | Consumption’ — . : 2. 65 | 68 47 
Ileantmeier Perc. eatecwen a asic (4)\{Consumptiony..= =): 66 | 70 50 
/TVODINS fe G25 26! 0-0 One O G2nWiaterronychestienssi O0N eas 58 
ATOOMIEESo 2 4 G 0d) 010.6 75 | Weak chest. . . .  (alive)| 74 60 
Mpoplexyeiny ces. chialye mulls 78 | (1 br. and 2 ss. d. of cons.)_| 74 65 
IWecayemrer ste teme ss goers) 74 | Hemorrhage of lungs . 44 | 75 66 
(CHING. 6.58 aaa neh ko pout om 52 | Ossification of heart . . 50 | 76 73 
Senile gangrene... 1. . 76 | Nose bleeding. . . . . 83) 78 74 

(2 bros. d. of cancer). Cancers mrmioe eatan: 42 | 89 83 
Wigner OiWees 5°46 4 4 Ge) | Aieraomhy G5 6 bo Bo 6 73 
FAC Cidentae Sexcte ioe a seh ee iL ANC eb memes Weta “sear si 74 

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


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 I had no idea of the extraordinary tendency on 

N 


178 NATURAL INHERITANCE, [omap. 


the part of the mother to transmit consumption, as 
shown 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 
cousumption on the Fathers’ side. 

Another way of looking at the matter is to compare 
the ages 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 affected, 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.]J 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. 


Order of 


Ages/at death. ages at death. 


| Causes of death. 
| Father. Mother. F. | M. 
Whleartwreia sss 9 os 59, 70 61, 63, 74 53 61 
| Apoplexy and paralysis . 74, 78 OA 10, (2A || 85 62 
Consumption 9. 2. = - 53 aie 59 63 
ANS IITES Se gaia oe nan 70 a 70 70 
COME S36hig as Cuenarees 55 has 70 72 
Senile Gangrene .. =. igs 81 74 74 
Tumourinliver .... 2 ih 75 GG 
RC@anceracateres) © 4s "eo 5 al) Be 78 81 
jeliivsmoe 7) 3s 5: eile old. fe old. 85 
| Winlkangyyat obese Be 85 
| 2 bros. and 1 sis. 
d. of heart disease 
and 1 of paralysis 
at, 40. 


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 
eroups run alike. 

1 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- 
harly exposed during all the time of its existence 
before birth, to contagion from its mother. During 
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 


<a DISEASE. 181 


rooms. The explanation of the fact that we have 
been discussing appears therefore to be summed up 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 more 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 les 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 
work, at least for practical purposes; for whether they 
transmit it equally or not would not affect the results 
materially. Our lst 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 the 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 1s measured be 
such that the Q of the general population = 1. Let 
its M = 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, we 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 
orades above 84°. The Co-Fraternity descended from 
such a group will have an M whose value according 
to the law of Regression ought to be [N + 4 (2°23)] 
or [N + 0°74 units.| — 

Those members of the Co-Fraternity are consumptive 
whose consumptivity exceeds N + 1°47; these are the 
same as those whose deviation from |N+06°74] which 
is the M of the Co-Fraternity, exceeds + 0°73 unit. 


184 NATURAL INHERITANCH. [CHAP. 


Let the 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 0°73 divided 
lO ; 
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 15 to 17. 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 vigorous, 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 n, are + 0.78, 
+ 0°81, and.+ 0°91. Referring 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-Fraternity 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 different faculties 
as yet examined, appears to govern that of consump- 
tivity also, although the constants of the formula differ 
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, the discussion on a memoir by G. Humphreys, 
Actuary to the Eagle Insurance Company, read before 
the Institute of Actuaries.—Insur. Mag. xvii. 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 theory, 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 that 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 
orandparents, 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 dropping 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 im 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 


XI. | LATENT ELEMENTS. 189 


not all of them. 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 Klements 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 INHERITAN CE. [CHAP 


variously after different and unlike progenitors. But 
the difference between 6 in a mixed breed such as we 
have been considering, and the value which we may 
call 8, which 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 1-7 
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 /4x 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 b’ is a trifle ereater than 6’+0°04. But b=1°0; 
therefore 8 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. 


X1.] LATENT ELEMENTS. 191 


When the “children” in the pedigree are from 40 to 
55 years of age, the 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 alive, 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 hght. 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. 


CHAPTER XIf. 
SUMMARY 


THE investigation now concluded is based on the fact 
that the characteristics of any population that is in 
harmony with its environment, may remain statistically 
identical during successive generations. ‘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 1t 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. 195 


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 1t requisite to take Weissmann’s views into account, 
unless I am mistaken as to their scope. It is freely 
conceded that particulate inheritance 1s 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 

© 


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 im a man 
is shared by his kinsmen, but on the average in a less 
degree. 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 


X11. | SUMMARY. 195 


kinship 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 

02 


196 NATURAL INHERITANCE. [cHap 


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

The ratio of filial Regression 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 R.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 
eroups 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 Regression 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 Regressions was given. 


x11. | SUMMARY. 197 


Finally, considerations were offered 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. Reason 
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 Regression, 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 measures made at the International Health Exhibition in 1884. 


Percentages. 
Strength of Pull No. of cases 

i 4 observed. No. of cases Sums from 
observed. beginning. 

Under 50 lbs. 10 2 2 

55 60) 55 42 8 10 

5 Sire yO 140 27 37 

9° 80 99 168 33 70 

» 90 5, 113 21 91 

pee ALO) One 22 4 95 

Above 100 ,, 24 5 100 

Total nse errs. 519 100 


oe 1g 66 KE 9% FG 
29 as 0g 86 9% GS 
6-9L | €-9L | L.GL | G-PL | 0-FL | F-8T 
9-€% | SS | 6.06 |} 0-06 | I-6L | I-8E 
ol 19 rat) 8g Gg og 
POL | OOL | &6 16 88 G8 
ea mo | 1¢ | sp | oe | oF | OF 
7, 96 68 68 08 ny PL 
sl OS ey ialeerOm (hls thE |) Sek 
a 066 | 246 | 8F%| 986 | 926] 612 
= 6VL | @FL | 9ST | SSL] GOLF Ser 
2 Gita con soc | 0S. | Lr WV! s7L 
ay 
= 0-89 | 4-99 | #49 | &-F9 | 2.99 | 0-89 
a 8-74 | 9-€4 | &-GL | PTL | 9-04 f 6-69 
faa} 0-98 | 9.G2 | 6.F8 | 9-78 | Z-FE | 6-88 
=) 6-8 | 2-48 | L248 | 2-98 | 8.98 | 0-98 
= ¢.19 | ¥-99 | ¢.¢9 | 9.79 | 6-89 | 8-99 
Zi y-GL .| &-TL | 0-04 | 69 | &.89 | 6-29 
G6 | 08 | 08 | 02 | 40 3) 08 


(6 
&6 


8-61 
&- LT. 


67 
G8 


8& 
TZ 


TéL 
ILG 


SIL 
661 


¥-69 
0.69 


9-86 
¥-GE 


1-69 
6-19 


OP 


61 
6G 


L6G. 
6-91 


LV 
62 


96 
89 


VoL 
661 


VIL 
GéI 


1-19 
6-89 
&-8& 
6.96 


IL GL 
06 LT 
6-IL | £-0L 
GGL | LPT 
&Y 36 
92 TZ 
PS 6S 
bo 09 
CTL GOL 
J81. LLT. 
OT GOT 
T&I Gol 
1.09 | 4.6 
6-49 | L-99 
6-68 | 66S 
6-78 | 6VS 
6-19 | 6.69 
8-99 | G79 
006 OF 


200 


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oso | rie [ae |) Se] Tee 
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of =f nord ; 

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jo ‘ON jo FU) 


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201 


TABLES. 


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ad 44-4803 puout 
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ssouudey = ‘JUST 
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18-3 | 44-1 | SLT | 08. | GF. 0 | re. | 08. | GT | 89-1 | 90-6 | 9T9 | IW |J 10d AW} Lé.2 
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suosiod ‘xg UL qUaTIE Q jo “quoul 
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“2 JO SPIUL WL PpotlOso0I STOTPCTAD(T youn i : a ae 


“08 pur SOY 608 °.0% Sopely oY} 4B SUOTILIAR, poAdosqo 
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°@ TIAV], 


202 NATURAL INHERITANCE. 


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. 


Splee 
The equation for the Probablity Curve’ is y = ke Wx" in which 


his “the Measure of Precision.” By taking & and A each as 
unity, the values in Table 4 are computed. 


TABLE 4. 


Data for a Normal Curve of Frequency. 
Yi 


— 72 
YE AC 
x y wy y c y 7 ty] 
| TeOO| Sa Ik | ORV eae) | Oxy |) 2s SO 0°0001 
2e (7) OMG) | ves > | O83 |) ea Bsn O07 o 
= 0840 0-85) Sa aS Opa te 4020082) [ie =enmitie 0:0000 
SOG | O70) ea 1 | O73 |i es ZO |) Ovule nity 
=) 058 | O53), = 18) | O40] S228? 070004 ; 
TABLE 5. 
t 2 
Values of the Probability Integral, if aa dt, for Argument 7. 
Tt 
it (=ha)| “0 a | op 3 “4 5) 6 7 oe) “9 
[Ete | Sgt ee Bae 
0 | 0°00 | O-11 0-98 0°33 | 0°48 | 0°52 |0°60 |0°68 | 0°74 | 0°80 
1:0 | 0°843 | 0°880 | 0-910 | 0°934 | 0°952 | 0-966 | 0-976 | 0-984 | 0-989 | 0-923 
2°0 | 9953 | -9970 | -9981 | ‘9989 | -9993 | -9996 | 9998 | 9999 | -9999 | -9999 
infinite] 1-000, 


When ¢ = ‘4769 the corresponding tabular entry would be eve 
therefore, ‘4769 is the value of the ‘‘ Probable Error.” 


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


TABLES. 205 


TABLE 6. 


t a és 
Values of the Probability Integral for Argument 0.4769° that is, when the unit 
of measurement = the Probable error. 


Multiples 
of the ; ; : ; : ; : 5 3 5 

Praienl 0 1 2 3 4 5 6 7 8 9 
Error. 


0:00) 0:65) O11) 0°16} 0:21] 0:26] 0°31} 0°36] 0°41] 0:46 
‘50 “BA ‘58 62 60 69 72 “75 “78 “80 
82 84 "86 .88 °89 eh 92 93 94 395 

"957 | .964] -969] :974) :978| -982] -985| °987} -990| -992 

“9930 | .9943 | -9954 | -9968 | -9970 | 9976 | 9981 | °9985 | -9988 | -9990 
9993 | -9994 | -9996 | -9997 | -9997 | -9998 | 9998 | -9999 | -9999 | -9999 


oni © bo Ht 
oogodgo 


infinite | 1:000 


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 1:0. 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, andthat 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 1:0. 

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 6. Lastly make a converse 
Table to 64; one in which the arguments of 64 become the entries, 
and the entries of 66 become the arguments. From this the Table 7 


202 NATURAL INHERITANCE. 


is made. For example, in Table 6, opposite to the argument 1:00, 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. 
ORDINATES 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 | O-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 USO Ysy pea bSiiCd) |) salorsy || 110240) 
30 1-25) 1230) | W360) 2249) 1-479) 1545) 160" Ci ee eS 
40 1°90 | 1-99 | 2:08 | 2:19) 2°31 | 2°44) 9:60) 2°79) | S20b al moneo) 


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. 


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2 WIV, 


| 


| 


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 §, and ¢, m, and s, respectively—that is, Tall, Medium, and 
Short (medium male measurements being taken as 67 inches, and upwards to 70 
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 82 cases of the one to 


inches). 


27 of the other. 


Sho 1 
12 cases. 


Shy ally 
25 cases. 


Sho & 
9 cases. 


Wey te Theat 
20 cases. 18 cases. 
M.; m. ems 
51 cases. 28 cases. 

M., s. ss} 
28 cases. 14 cases. 


stature. 


Short and tall, 12 + 14 = 32 cases. 
Short and short, 9 


Tall and tall, 18 


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 


TABLE QA. 


27 cases. 


MARRIAGE SELECTION IN RESPECT TO EYE-CoLouR 


in 78 Parental Couples. 


Eye Colour of ees 
cases 
| served. 
| Husband | Wife. OpSse ive 
Light Light 29 
Hazel | Hazel 2 
Dark Dark 6 
Light | Hazel} ) ag 
Hazel | Light | f 
Hazel | Dark | ) i 
Dark | Hazel | J 
Light | Dark |) i 
Dark | Light | § 


Per Cents. 


| Obs. | Chance. 
37. | 37 
3 2 
8 7 
23 15 
5 7 
24 32 


Observed. | Chance. 
| } AS) ae 
28 22 
24 | 32 


Eye Colour 
of Husband 
and Wife. 


Alike 


| { Half-con- 
| trasted 


| 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 261 of Dark. 


TABLES. 207 


TABLE QB. 
MARRIAGES OF THE ARTISTIC AND THE Nor ARriIstic. 


Percentages. 


Pairs of artistic and not artistic 


persons, 
No. of} Males. | Females. MEGEAE 2 Ch: 
Rank in Pedigrees. per- OCS SENG 
sons. observed, combinations. 


both}1 art.| both] both|1 art.| both 
art. | not. | art. | not. f art. |1 not.| not. | art. |1not.| not. 


AME TIS eee tachiel coed soca 826 | 32 | 68 | 39 | 61 | 14 | 31 | 50 | 12 | 46 | 42 
Paternal grandparents ..| 280 | 27 | 73 | 30 | 70 | 12 | 81 | 57] 8 | 41 | 51 
Maternal grandparents..| 288 | 24 | 76 | 28 | 72] 9 | 41] 50] 7 | 39 | 54 


| Totals and means...| 894 | 28 | 72 | 33 | 67 | 12 | 36 | 52 9 | 42 | 49 


Tastes of Husband and Wife—alike ............... 12+ 52=64 | 9+ 49= 58 
3 5 sé contrasted....... 36 42 
TasLe LO. 
EFFECT UPON ADULT CHILDREN OF DIFFERENCES 1N HEIGHT OF THEIR 
PARENTS. 
Proportion per 50 of cases in which 
the Heights! of the Children 
deviated to various amounts from 
the Mid-filial Stature of their Number of 
Difference in inches respective families. Children whose 
between the Heights Heights were 
of the Parents. eS aia ll ete ieee ye observed. 
aes Spas po. Ses (Total 525.) 
oS + eS) + O cies) aS) 
pest || lcs eee acer || tage 
3 ay S| a 5 30 I =H 5 10 
Winderalsinichyessen.ce 21 35 43 46 48 105 
1 and under 2 ...... 23 37 46 49 50 122 
2 ap Sine sece 16 34 Al 45 49 i) 
3 a eee craine 24 35 41 47 49 108 
| 5 and above.. ......... 18 30 40 47 49 78 


1 Every female height has been transmuted to its male equivalent by multi- 
plying it by 1:08, and only those families have been included in which the 
number of adult children amounted to six, at least. 

Notre.—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 heights of the Parents have on the 
whole an inconsiderable effect on the heights of their Offspring. 


NATURAL INHERITANCE. 


208 


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I al Se Sr cece gee ene an ree lta ee ea Te: * Mopog 
8.69 G ez “e Se ere tec a |e ee ie ass lec ae ec eer [A I 6.59 
1.99 6L 99 oa pepe leg G G L 1 JE TIE WZ G 6 i L “"G.g9 
G19 06 84 ; s ; io | tole aE AEN AME 6 WS oe "G.99 
9.29 && L1G / i v IL | 6T | 88 | 86 | 88 | 98 | ST | FL |G |e ais 2L9 
6.89 6P 616 : & y IL WSN ASH? EAS IS |) 5 OME HT EWE) 2 i "9.89 
6.89 If 68 g p ER ROG ESCRSSN OG AGe ie |p Sik er oe om “"¢.69 
G69 GG 89 & SUZ WA NGL I IE Se ieee alld I "G.0L 
6-69 IL &D G G 6 1h | OL |S Sani & {lL Ziel luge |e Ae Sb. 
za! 9 61 Zo Ae Niger alee ler elise Fal eee fenecal laces Se re) 
c i fs @ ae ise || 2 aller ; Pec ecrtot eee fieace ite 6.3) adoqy 
‘squared | Metp[ryo SOND aT BPS geod ee speed ( Cagis. fi ! FA ae 
g : PAOTW 16-81) 6-6) G-TL| G-0L| G69] +89] 3-19] 5-99) G-49) G-F9) -89| SSO] MOjog *soyour 
“IN jo PHA | SIepy ime PON era |) squared 
sale A I0 E “prar_ouy 
PON | yo zoquinu peyoy, “UOIPTIYO F[NpV oy} Jo sp Sry jo yqS10 FT 


("80.1 Aq pordiyjnur uaeq aavy syySiozy o[ewmoay Try) 
“SHUMLVLG SHOIUVA JO SINTUVY-Cifl G0G@ 1O NUOT SHUMALVIG SAOIUVA vO NUUCTIHY) LIAGY AO WAAAY 


(eed WWM) Il wavy 


209 


TABLES. 


6-19 
6-19 
6-19 
1.19 
6-89 
9.89 
6-69 
6-69 
6-04 


“‘SULIPOT 


"gaseg 
[e701 


St Ge tel GN oe tl 


Epa) 88-4] COL | 19l | Gon | s1Or | ore 
; ely me : ie 
: ether ; ea eS ; 
S 7 7 9 g g L 
I if g or | 8 6 
I 7 1 i, lt 2 rae (lh Al 
OAR 9 Gly | Giese elvan 
8 te | ee GS] Of i ee TL 
9 oh te I We Ge | QL fat 
8 ie PS Wwe A eee IP 1 
i | 8 ee | Ge | ie |G 7 
q te 8 9 8 at: 
7 g i z I i e 
5 é : ; Sane a 

GGL | BIL | OL | 3-69 | 3-89 | ZL9 | 3-99 


to um 


mt oO Om © ©O OG CO SH mm rH 
rm 


6-49 


68 61 G 
9 O06 I 
v T T 
L I . 
@ F ne 
9 7 ae 
V G a 
F 550 ws 
z I 36 
G-F9 | G-E9 | 6-69 


“"/.19 MOpO 
"6.69 
"6-89 
"6.19 
"6-G9 
6.99 
a G22 9 
bo ae 
6.69 
bf a4 
CTL 
T [6.6L 
eS ent 
“+ | 97 oA0qy 


1-19 
MOlOT 


ooo 


*sat[OUL UT 


“SOTPOUL UL SLOT JOIG Io] JO SPYSto Fy 


uoul oy 
JO s}ySta Hy 


“(UGCA TOXY ONIWE 


SaUV Md iL 


GNV SUMHLOUWG XIG JO SUITINV AT ‘SLILD IO FL SHOWUVA FO NAT OL SLHOIGE, SQOIUVA JO SUMMLOUG &O UMTNAN WALL WIA 


‘(eed WAM) 31 Tay 


Ay 


NATURAL INHERITANCE. 


210 


66ET 
&G 
06 
9.99 v9 
g.99 OL 
0-29 GGT 
1.19 661 
1.89 606 
9.69 861 
9.69 TL 
6.0L 88 
LT Lv 
1 
VG 

"soso 

“SURIPOTL [e107 


GG 


ON Oo tH Ot OO MF 


Po) 
ian) 
i~ 


XEd) “ICO, (00 (Oo) 13) AS) SO art orl 


G64 


691 10G | vOG} 006} G&L} OLL 
a0 ae 880 c 7 @ 
a [ T V & 6 
I G g 8 oO. ST 
i G 8 96 && 8I 
L 6. 0G GS 86 && 
8. 0G 86 8s GS 96 
06 96 i 8& 8T 6 
UY ise} 96 0G It i 
96 Siig 0& 61 L i 
tL 8T II 8 G T 
6 G 9 iL I ae 
8 v & II ‘ 

I I 500 200 : 
G02 | 4-69 | G-89 | G.29 | 4.99 “G9 


GTZ 


79 | 66) 86 | IspEOn, 
2 4 g fo gg moog 
9 Z G BE OUR DRO OCON EE (a(8), 
3 Z Pe 
a A gl egg 
xs A ee 
4 < go pee eng 
: : Heteteiees @ gg 
4 ; a laccts: 8g 
: seseeee @ gy 
af I + [eee @ py 
aa ue ‘ SEN i A) 
. veonreenesan gigi 
: I I aANGe pues pL 
G.79 | 9-€9 aaiee ‘sotpour 


‘SOTPOUL UL SLOT OL, ALITY} JO SPYSto Fy] 


Ur Toul ogy 
Jo sqm yy 


ANV SUTHLOVG AAT] IO SAITINVYG ‘SLHOINET 


“adUdNTOXH ONITA SsauvMdo 


SNOLIVA AO NUT OL SLHOIUM;T SQOOIUVA HO 


‘(eyeq yemody) ¢] wavy, 


SUMMLOUG LO ULANWON GATLV TAY 


TABLES. 


TaBLE 14 (Special Data). 


DEVIATIONS OF INDIVIDUAL BROTHERS FROM THEIR Mip-FRATBERNAL 


STATURES. 


Amount of Deviation. 


Winydlere WL. hive), .ccesonbdecaq onsen 0dobecoDauEr 
il aml WANG We ccauccoodeseadenesoaupotn0n oob 
PD) enayol HII? Br cocodes cagdosoddcaoHddnsoceoGde 
3 eqn smunelere Ce icedoaeonocoaadodoseaesooonbG 


AM ATVI OWES aciscee eee ene sere oe eeelateie 


Number 
of cases. 


88 
49 


23 


Number 
of cases. 


8 


Number 
of cases. 


20 


P 2 


211 


6 


Number 
of cases. 


21 


NATURAL INHERITANCE. 


212 


; 

Z-00L|&-¢ | 2-0 | 9-TL | 4-0] 2-31 | 7-0 | 1-82 | 2-0 || O67 | OFT] 647) GTS) TE | 69S GOST | 09ST | L6T| ~~ [Btottoy) 
doll z| 6 | zt| tr) st| 82) 62| tise |*t| eo] 0/9 | sor | FOL | 29 | 6 |" T) somos 
OOL i 6 Tat I las G& 96 @ || LAPL | 09 | VEL) T9L| LL | 9026 LLV LLE WE TUL pue 
OOT & GL GL i Il Is LG @ || GIGSLE | LP | O61) 621) OL | SZT DLV LOF Lv | III sole 
OOL 6 Tals lb |) 5 |b OL KG VS G || S16 IS | GOT) 601) 7 88 OFG 606 06 | AI 

6-66 |6-6| GOL | 4-60 | 8-0] T-€L | 9-08 8.9% | G.Z || S1ZS | G9 | SSG} L8G} ZT | 062 819 664 9g |“ [Btolos) 

0-66 | 2-1} 4-4 Git | 2-0 G-6b | £86 | &4e | 1-6) 98¢ G G6 | && | G Gq 68 82 SY SP rer all 

I-00L| $-€ | 6-8 9.0L | F-0| SL | 8-68 | 9-86 | 6.6 || GeZ VG 09 82.) & 86 LhG OLZ WA ye Wu soyvuto 

0-00L| 2% | G-SL'| G&L [6-0] L-GL | 4-68 | 6.66 | 6.6 || GP 11 | 2 OOT) 2 68 LPG SLT GG | III 

6.66 |G P| 6-CL | 9-GL | F-0] £01 | $46 | &.66 | 4.T |) 097 6L | 89 | 04) 4 8P PIT GEL Phe WIXI 

0-001! 9-2 | 8-0L | F-OL |9-0| &-3L | 6-08 | &-66 |.6.6 || L266 | 18 | 976) 8&S) FL 616 189 189 gg |" [Btette,) 

0-001 0-8 F-0OL | ¥-2L | &-0 -GL |'P-16 | 6-86 | 0-L || 666 6 IBS |) VAS We Lt G8 68 Sale 

0-001] 8-7] 0-OL |6-IL | TT 9-1 8-18 | 4-66 | 0.F || GhZ KS WVHA | SE tS SOT &@ LOT. OS | solv 

6-66 |1-¢| 9-6 | LOL |¥-0] 6-OL | 1-08 | 6-08 | 7-@ ELL AO || PAM 4 tS v8 S66 VSG ie jy UII 

6-66 | 9-6] 9-6 V8 7-0] 9-8 7-66 | G8S |8-G || S9P AIL W717 || XS: || 1 Ov 961 LLT. ait |i AMI 

a Eo! BN ge mA os we ca re CH ES GOs | Gx - ae od Li 
<< iw) o tS IS} (op) ey) lea lS ee) iy Oo cep) to eS 

we) & S Cao & || «Gey ce | 6 | 09. 4 3 = | 03. 

asi 4 Er | lar a e ey =| a | 8 Be ar a 2 St 

‘S[RJOT, Pe z : Seleiee bd = & l'sjejor| Se] & | ° o| 3 = = | -noyrioues 

wl = g & a 5 = > Ia) S 4 = 9 & (Suipudose) 
s| 5 Sela E cial eles 4 Bi Seas ! 
S| 5 5 2 a Sle 5 © ra oy JO "ON 
Z sa 8 2; g = 8 S oly pure xog 
© iS 8 e - S g ® 

‘sanuqMedda gq “paadasyo mozoo-aXo Jo sesvo Jo ‘ON 


‘SNOILVUUNDY WAISSHOONG UNOY NI SUNOTOO-AAGY LNAUALIIG 10 AONTAOAAY 


‘GI @IaVL 


TABLES. 213 


TABLE 16, 
Tue Descent oF HAZEL-EYED FAMILIES. 
Observed. Percentages. 
Total 
cases. 
Light.) Hazel. Dark. | Light.) Hazel.| Dark. 
General population ...... 4490 | 2746 | 569 | 1175 | 61:2) 12°7) 26-1 
III. Grandparents... ..... 449 267 Gil |} aaa | GO 13 27 
JUL, TERIREUS panscesaobcn0cad 336 165 85 86 | 49 26 26 
IL, Chautll@beein.nosroco0conane 948 430 302 216 45 32 23 
TaBLe 17. 


CALCULATED CONTRIBUTIONS OF EYE-COLOUR. 


Data limited to the eye-colours of the 


2 parents and 


2 parents. 4 grandparents. | 4 grandparents. 


Contribution to the 
heritage from each. 


II, Il II. 


Light.) Dark. || Light. | Dark. || Light. | Dark. 


Light-eyed parent......... OBO WP soo en Ss 0°25 ee 
Hazel-eyed parent......... 0°20 | 0°10 ue 066 0-16 0-09 
Dark-eyed parent ......... ie 0°30 o6e a0 0665 0°25 
Light-eyed grandparent..| ... Sa: 0°16 ie 0°08 aa 
Hazel-eyed grandparent.| ... He 0°10 0:06 0°05 0-03 
Dark-eyed grandparent...| ... ae, os 0°16 ai 0°08 


Residue, rateably as- 
Some Cee rd scenes anne 0°28 | 0:12 0°25 0-11 0°12 0°06 


214 NATURAL INHERITANCE. 


EXAMPLE OF ONE 


TABLE 18. 


CALCULATION IN EACH OF THE THREE CASES. 


I ‘ II. 
=I g |g 
2 HS) oe See 
Ancestry and their | Contribute |= %| Contribute = Bz 
eye-colours. 2k to 2k to 2 
B28 28 ies 
oa as <3 
fo) | =) ° 
|4 | Light.| Dark. 4 | Light.| Dark. Ai 
Light-eyed parents.| 2 | 0°60 ie 
Hazel-eyed parents. ue 1 
Dark-eyed parents . | il 
Light-eyed grand- 
TOENRELMES o oc cnboconnS 1} 0-16 1 
Hazel-eyed grand- | 
Palentss...cse-eeses|| =| 2| 0°20 | 0-12 2 
| Dark-eyed grand- | 
JOEHRSNWESHG! Syqor-ogeon|) >= 1 0°16 1 
|Residue, rateably as-| 
SISMEM ced sagesisie so5. |) Oss |) OP 0:25: )) <0 
| Total contributions) ... | 0°88 | 0°12 0°61 | 0°39 || 
1:00 1°00 


INN, 


Contribute 
to 


TABLES. 


‘TABLE 19, 


OBSERVED AND CALCULATED E.YE-coLOoURS IN 16 GRouUPS oF FAMILIES. 


215 


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 


Parents. Grandparents. 


Light.| Hazel.| Dark. | Light.| Hazel. 
2 as cas 4. aes 
2 aes S60 3 1 
2 aes ane 2 1 
ot “fs 2 2 oie 
1 il was 3 i 
1 1 000 3 a 
iL il oto 2 2 
1 1 ve 2 te 
i 1 at 2 1 
i nog = 1 3 606 
1 af il Bl ces 
1 fine 1 Diese esc 
I 600 1 Wii ee 
1 200 1 1 1 
500 1 1 1 1 


Dark. 


MS poet ets: 


NNW WEDPHE Dp? 


Number of the light eye- 
coloured children. 
Total 
child- Calculated. 
ren. | QOb- 
served. 

I II. Ill 
| 183 174 161 163 172 
(ays) 46 47 44 48 
92 88 81 67 79 
27 26 24 18 22 
22 11 6 12 6 
62 52 48 51 51 
42, 30 33 38l 32 
él 28 24 24 20 
49 35 38 28 34 
31 25 24 21 23 
76 45. 44 55 46 
66 30 38 38 35 
27 15 16 18 16 
20 9 12 8 9 
22 8 13 ata ial 
24 9 14 12 10 
629 623 601 614 


NATURAL INHERITANCE. 


216 


TABLE 20. 
OBSERVED AND CALCULATED Eyr-CoLours IN 78 SEPARATE FAMILIES, EACH 


OF NOT LESS THAN SIx BROTHERS OR SISTERS. 


1 3 
_ 
= iS | IDIDIDIHOOGOOVNN LLL ASASCSOKN KL HSH BOHAAANHAHH HONS 
w, A 
| us} 
qo & 
80,5 P=) F DO OANAAAANT HAHA HAhONSHHDOOOMHNONNOSHMIBBSoDONOMN 
(Sh 3 fel IDIDIDADOOOOCON NNN NN SHDN SHGOSOON WN HOWHWAA HAG IDONH 
>) Ss) 
2° | , 
ean) 2 z WODOADANANNSSSSSSSNDONSAADMHONOMHONHHNONHNONMBNSS 
us ll IDIDIDIGOOOOCONL NNER SOHSONKNN HOH HOBAAAD AA HIG hc 
oy) 
Fore | 
ES a 
e ey OO OID I YK DODD OERKAMAHANDODARDNOhAWOOCHIONNHHwM :HOOOrMO 
On rH - a a S = 
ic) 
ie) 
au | 
pod OOOO EEE DDDDDDANE-ONLRARARDOrnCHDONnDORDOHnAOrMOrnRADH: 
org 2 : al rr. cn - al rH rt 
AS 
od 
5 : toa ts ERR RNTANMOMANN : 
mi ‘ . . . . 
£ A 
q = 
2 i 
Se S Oli FOR O80) ERO Oe altel eal ial al 
2 6 Ls 
re 4 43 
A o a SSH OSH SH SH OSH OSH SHH HHH HH HHH HOD OD OD OD OD OD OD COD OOD NAA AA AN 60 Ar ri rir 6 60 68 60 00 
oes] 
B 4 
= rd 
2 H OO OTS SON EO | 
S) is sPedlsMigsplensomtey ce et aust aleimas 
® A 
a | 2 ime 
a 8 | (ede teks ets AN Hooded 
Fan o 
Cs} a5} | 
iv aA = = = 
45 
Sh NANNANNANNNANANANNANNANNNNANANNNANN : 3: 1: titi in#enine 
re] 


217 


TABLES. 


Taste 20—continuwed. 


ght eye- 
dren, 


coloured chil 


Number of the li 


OU. 


DAD HI DA HID A HHO ONO AM BDIDIO NN A 9 HH 19, OO HH 
6 60 Hb © HH HS OH RG Ho HH HH 1 19 Go HO RH dO OD DAI HH cd 


Children. 


BC OO Es CAND EEC I AICS ID WON 15S CO C5 ED -IIND CO SI SIGN EA. GO ICD COLO — 


| 
| 


SOHIWSOOSHMEHASCHDOANAWAOOOANIOIVNO DANO O19 OMS 19 
18 Ro HHO RH 2 SH G9 HH HH 19 69 69 HID 00 SH SH SH SHH GD HIS O 1G 


Ob 
served. 


CD HO HID LR C OD H 1G OD SH OD 6 1D H 6 10 10 OD SH AI OD 10 OD SH SH 0D OD OD SH OOO NT 


Total 
child- 
ren. 


DAY RAADODROOAHAWDErOLnDDDADARDOGOWDOCHAHEDrEeDDOOHMOYr 
il Tod ri Tonto il 


Eye-colours of the 


Fs t tNNNANN AA EN EARTH HANNANAN TIAN OOOO AN 4 OD 


Oo BONGICU 9 Bes Si -hiaiGeital 85 8 8 B98 S19 S898 8.8 Bi bOiab 8 Biol bial oe 


Grandparents. 


MDONAAANAAAATAANAATAHWMAMAMMAMAMMANANNANANNT NH : NANT 


CO Ta ST SU TUCO aD 


Parents. 


rol ml ted ee al lle el le ofa! sareul seh a ieh (teva tebe cong SASs wcities ter ake Recah ad attired 


Light.) Hazel.| Dark. | Light.) Hazel.) Dark. 


Ps et De FO OD Oe OD nO OO Oe 


218 


NATURAL INHERITANCE. 


TABLE 


ile 


ERROR IN CALCULATIONS. 


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


Amount of Errors. 
é Total 
Data employed referring to 0-0 0-6 1-2 1:8 Be | Crsae. 
to to to to and 
Ov5= |) tel 1% 2°3 | above. 
lp ihe parents onliye-n-cqeoss 19 30 18 5 6 78 
II. The 4 grandparents only...:. | 16 28 10 10 14 78 
III. The 2 parents and 4 grand- 
| OEIC capaodosdeenaddaooseE oes 41 LG, 8 4 8 78 
TABLE 22: 
INHERITANCE OF THE ARTISTIC FACULTY. 
Children. 
Observed. Per cents. 
Parents. 
iSeenthon eee Observed. Calculated. 
of os Total es a 
Fraterni- children. arate i ane ate 
ties. art. 4 art. 
ants art. 
Bobhvartishie 5. - sce. 30 148 95 64 36 60 40 
One artistic; onenot..| 101 520 201 39 | 61 39 61 
Neither artistic......... 150 39 173 Dil 79 17 83 
Motalssc.acsccseee 281 1507 469 100 | 100 | 100 | 100 


The “‘ parents ” and the ‘‘ children” in this Table usually rank respectively as 
Grandparents and Parents in the R.F.F. pedigrees. 


APPENDIX. 


A. 


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. Proc, Reyal Soc., No. 136, 1872, p. 394. 

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

Statistics by Intercomparison. Phil. Mag., Jan. 1875. 

*On 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 English 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. 
English Men of Science. 1874. 
Inquiries into Human Faculty. 1883. 


Record of Family Faculties! 1884. . 2s. 6d. _ 
Life History Album 2 (edited by F. Galton). 1884. 3s. 6d. and 4s. 6d. 


1 The Record of Family Faculties 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. Therest consists of blank forms, with printed questions and blank spaces to 
he fil'ed with writing. The Record is designed to facilitate the orderly collection of 
such data as are important to a family from an hereditary point of view. It allots 
equal space to every 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 scheduies are followed by Summary 
Tables, in which the distribution of any characteristic throughout the family at 
large may be compendiously exhibited. 

2 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 history of each 
member of the near ancestry of the owner. 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 hy charts on which 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 4s. 6d. edition contains a card of variously aplenne. wools to 
test the sense of colour. 


*,* 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 trustworthy life-histories 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 DICKSON, FELLOW AND TUTOR OF 


ST. PETER’S COLLEGE, CAMBRIDGE. 
(Reprinted from Proc. Royal Soc., No. 242, 1886, p. 63.) 


Problem 1.—A point P is capable of moving along a straight line 
P’OP, making an angle tan-!2 with the axis 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 p, whose mean posi- 
tion at any time is P, is capable of moving from P parallel to the 
axis of aw (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 
“2, y, 2, the 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, 

oF (3a — 2y)? fis At a (2) 
(1-22)2" ~ 9-50) 


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, 

YQ», (Cee ae 

(22) ES GES 0)2 


=) @,-a constant s9.) ..9(2) 


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


222 NATURAL INHERITANCE. 


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


Y a 9 Bae — 2y = (0) 
(1:22)2 *9(1 BOP 
6 eee = 3 
y_ —-9(150)2 6 ; 
that i A= = 
so mee ge, Le | 


(1-22) 9(1-50) 


or, approximately, on the liney =4.a. Let this be the line OM. 
(See Hig: 1p. 1012) 

From the nature of conjugate diameters, and because Pp is the 
mean position of p, it is evident that tangents to these ellipses 
parallel to the axis of « meet them on the line x = 2y, 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 
les 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 «constant. The result is 
simplified by taking the origin on the line OM. Thus putting «= a, 
and y = y, + y', where by (3) 


Tite Pica =U 
(1:22)? 9(1-50)? 
the exponential takes the form 
il 4 d ape Cae EE (3x, — 2y,)? 
+ : 24 3 tf ——— Ams (4: 
1 (022)? ~ 9(1-50)? 5 cae: \ (1-22) ar 9(1°50)? (4) 
whence, if e be the probable error of this section, 
il if 4 


e (122 ' 9150p - 
or [on referring to (3 = 150) — 
[ ing 0 ( )] é Je 
that is, the probable error of sections parallel to the plane of yz is 
1 
nearly a times that of those parallel to the plane of xz, and the 


locus of their vertices lies in the plane zOM. 


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, 


al? yf? 


30°68 599 


= CONSE 5 5 5 6 we (GO) 


the major axis being inclined to the axis of # at an angle whose 


tangent is 05014. [In the approximate case the ellipses are 
2 2 
=i _ = const., and the major axis is inclined to the axis of x at 
an angle tan 11, ] 
5. The question may be solved in general terms by putting 
YON = 6, XOM = 4, and replacing the probable errors 1:22 and 
1:50 by a and 6 respectively ; then the ellipses (2) are, 


P , (wy tan 6? _ 


3 R ten er se aecuR nie) 
equation (3) becomes 
y2 x—y tan 6 
5 +tan — = 0 
or Y —tan d= een a) ae 
Zz 62 + a? tan26 
1 il tan?6 
and (5) becomes = + Hie rl ena apa hatte ye eH (48) 
(5) e at b2 (9) 
tan @ _ é 
whence a ea aay NY weer ney vue (JUG) 
tan’ 6  /62 (HO) 


If ¢ be the probable error of the projection of p’s whole motion 
on the plane of az, then 


c2 = a tan? 6 + 62, 


which is independent of the distance of p’s line of motion from the 
axis of « Hence also 


Ba fon Ue te eh AN 


Problem 2.—An index g 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 the 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 g, required the most probable position 
of Q (which cannot be observed) ; it being known that the probable 
error of qg relatively to Q in all positions is 6, and that of Q rela- 
tively to Mise. ‘The ordinary law of error is to be assumed. 

If in any one observation, MQ = a, Qqg = y, then the law of error 
requires 


ee . (12) 


to be a minimum, subject to the condition 
x + %¥ = a, a constant. 


Hence we have at once, to determine the most probable values of 
a’, y', 
Ma Oe tC] 


z 5 ‘ 2 
2a 2 ears 


(13) 


and the most probable position of Q, measured from M, when q’s ob- 
served distance from M is a, is 
@ 


It also follows at once that the probable error v of Q (which may 
be obtained by substituting a —za for y in (12)) is given by 


1 le eee 
ve C2 62 b2 4 C2 ° e ° e 


BO) 


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


APPENDIX C. 225 


C 
EXPERIMENTS ON SWEET PEAS BEARING ON THE LAW OF REGRESSION, 


The reason why Sweet Peas were chosen, and the methods of 
selecting and planting them are described in Chapter VI., p. 79. The 
following Table justifies their selection by the convenient and accu- 
rate method of weighing, as equivaient to that of measuring them. 
Jt will be seen that within the limits of observed variation a 
difference of 0°172 grain in weight corresponds closely toan average 
difference of 0:01 inch in diameter. 


TABLE 1, 


COMPARISON OF WEIGHTS OF SWEET PAS WITH THEIR DIAMETERS. 


Diameter of one 


Weight of one seed in hundredths 


Distinguishing seed in grains. | Length of row of 


letter of 100 seeds in Cues 
seed. Common difference inches. Gomimonnaiiorenca 
= 0172 grain. =) (OI Satan 
K 1:750 21:0 21 
L 1°578 20°2 20 
M 1:406 19°2 19 
N 1:234 eo) 18 
O 1°062 EO il? 
IP *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 showing 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 Regression 
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. 


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


| : =e Mean Diameter 
Be Diameters of Filial Seeds. A iiiell Seals. 
of Parent Total. | _ 
Seed. , 
pera ade GeV ee) ie) OG Observed |Smoothed 
Alt 22 3 PU) AUS} |) Bk | als} 6 2 100 lied 17:3 
20 23 1K) |} Ly) ale) BO) a8 3 2 100 7B WO 
19 35 IaH} WA |) kes |} TLL UL@ 2 AL 100 16°0 16 6 
18 34 WA |) USS |) I |) AE 6 2, 0 100 16°3 16°3 
ie oF UG |) ales |} Ike. als} 4 if 0 100 15°6 16°0 
16 34 US || AUS} |] AUG > As} 3 1 0 100 16:0 157 
15 46 14 yt) aka jy alZ 4. 2 0 100 IUSo33 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 


1 Reprinted after slight revision from Fortnightly Review, 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 Records, 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 temper.—Amiable, buoyant, calm, cool, equable, forbearing, 
gentle, good, mild, placid, self-controlled, submissive, sunny, timid, 
yielding. (15 epithets in all.) 

Bad temper.—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- 


2Q 


228 NATURAL INHERITANCE. 


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

T 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 those 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 L 
must call neutral. Jam 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 


‘ 
Te 


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. 

Next 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? 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 may be half unconsciously, by the compilers of the Records. 
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 
more 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.) 


| 


. as 3 E g 

= ae & 8 g go 

Relationships. ay A cet ea) aes 2 Ey Eee |= = 

a) 8) eb lei Sees 

=F ot od <i iS BH | As 
a. Fathers and Sons ..... 35 12 32 12 9 100 188 
b. Mothersand Daughters | 39 18 31 8 4 | 100 | 179 
Cr NCLES sees reat oe 32 13 25 18 WO A, | B72 
COBAIN ES #4 8 eect tere aoe | 39 14 29 9 9 | 100 | 238 
a+ 6. Direct line.......... 74 30 | 63 20 13 200 367 
e +d. Collaterals.......... 71 Qi aiewoe 27 21 | 200 | 510 

Good. Bad Temper. 

| @ 4-0. Direct lines......... 104 96 200 | 367 
| c +d. Collaterals. ......... 98 102 200 510 


APPENDIX D. 231 


On comparing the entries, especially the 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. 


IDABIE Oh 


COMBINATIONS OF TEMPER IN MARRIAGE (per cents.). 


A.—Observed Pairs. B.—Haphazard Pairs. 
Tempers of Wives. Tempers of Wives. 
Tempers 
of Husbands. 
Good. Bad Tempers. Good. Bad Tempers. 
1 2 3 4 5 1 2 3 4 5 
Goodeyee-: 1 6 10 9 6 2 13 5 10 3 2 
ee near | ON etry also |e olla oe sl Oem aus Vee 
Bad escce 3 | It 4 Yh 8 2 11 5 8 2 2 
Se cg eaicils Ao 3 3 2 1 6 2 5 1 1 
Spat eee Bt a ll OA Wie i 4 2 3 1 1 
Goodrrenccrct: 22 24 25 21 
IBEVGL -enenageeced bl 23 30 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 tv 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 
cannot 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 capenent 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 10, as against a caleulated 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. | are as (6), 2, 9, 2, 1, im the observed cases, 
against (13), 2, 8, 1, 1, in the calculated ones ; here the irregularity 
of the 6 and 13, Se aek are put in brackets for distinction sake, is 


Ba s5: iad 


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 were, 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 upon 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 IIT). 
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 


1 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. 


DISTRIBUTION OF TEMPER IN FRATERNITIES. 


A.—Observed. B.—Haphazard. 

All All All All 
pe | y umaper good- Intermediate bad- || good- Intermediate bad- 
peter tomes. | Some | eases | tee | Rome) cen | te 

2 42 10 20 12 10 21 11 

3 55 ial 15 21 8 7 20 21 7 

4 29 5 Gg g 8 1 2 3 1 8 2 

5 6 1 Ogee Die ok 2 0 DRO OR Ae sl 0 

6 14 1 8 B 4 0 abe ty Gh WD 0 

4 to 6 49 d Uf 2 2 


236 NATURAL 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 er 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? After some consideration of the materials, I defined—rightly 
or wrongly—a good-tempered Fraternity as one in which at least 
two members were good-tempered and none were bad, anda _ 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 635 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, we 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 vitaland 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 
T 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 


1 Reprinted, with slight revision, from the Proceedings of the Royal 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 portions, 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 example, in judging 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, 6, c, when taken successively in the hand, 
appear to differ by equal intervals when a:6:: 6: c, and not when 
a—b=b-c. Inall 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 Jaw 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. Itis 
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 
one 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 field 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 Proc. Royal Soc., No. 198, 1879, 
following my own. It should be referred to by such mathematicians 
as may read this book. 


APPENDIX F. 241 


FE. 
PROBABLE EXTINCTION OF FAMILIES.! 


Tue 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 Jowrn. Anthropol. Inst. 1888. 

2 “Au milien des renseignements précis et des opinions trés-sensées de 
MM. Benoiston de Chateauneuf, Galton, et autres statisticiens, je n’ai pas ren- 
contré la réflexion bien importante qu’ils auraient dfi faire de extinction inévitable 
des noms de famille. Hvidemment tous les noms doivent s’éteindre.... Un 
mathématicien pourrait caleuler comment la réduction des noms ou titres aurait 
lieu, d’apres la probabilité des naissances toutes féminines ou toutes masculines 
ou mélangées et la probabilité d’absence de naissances dans un couple queleonque,” 
&c,— ALPHONSE DE CANDOLLE, Histoire des Sciences et des Savants, 1873. 

1B 


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 fewsteps, 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. 
1 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;, 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 problem by the Rev. H. W. Watson, D.Sc., F.RB.S., 
Sormerly Fellow of Trinity College, Cambridge. 


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, a, the percentage that have two, and so on up to 
a,, the percentage that have qg such sons, g being so large that it is 
not worth while to consider the chance of any man having more 
than g adult sons—our first hypothesis will be that the numbers 


APPENDIX F. 243 


Go Gy, Gy, etc., 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 asif 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. Very 
probably accurate statistics would discover variations in the values 
of a,, 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 Taine a aw etc., up to ca be denoted by the sym- 
bols ¢, ¢,, f, etc., up to ¢,, in other words, let 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 N 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 


«  (& +te+t,0?+, etc. +t,07)? 


Let then the expression ¢, + ¢,% + t,x? + etc. + ¢,27 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—l1th generation is ,.,m) N, the 


R 2 


244 NATURAL INHERITANCH. 


number with one representative ,.m,.N, the number with two 
y-[y. 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 «* in the expression 


| py + 3M T +,4mMel7*-+ ete. + mh } N 


If, therefore, the coefficient of N in this expression be denoted by 
J, (x) it follows that ,.,721, ,7/, and so on, are the coefficients of a, 
x? and so on, in the expression f,, («). 

Tf, therefore, a series of functions be found such that 


f,(a)=t)+te+ ete. +¢,0% and f, (x) =f,_, (fp +e, ete. +t?) 


then the proportional number of groups of surnames with s represen- 
tatives in the rth generation will be the coefficient of a in f, (#) 
and the actual number of such surnames will be found by multiplying 
this coefficient by N. The number of surnames unrepresented or be- 
come extinct in the rth generation will be found by multiplying 
the term independent of a inf, (x) by the number N. 

The determination, therefore, of the rapidity of extinction of sur- 
names, when the statistical data, f, ¢,, etc., are given, is reduced to 
the mechanical, but generally laborious process of successive substi- 
tution of t)+¢,e+¢t,x?+ etc., for w in successively determined values 
of f. («), 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 g=2 and ép, t,, ¢, are each equal to 3. 


l+et+a" 1b 1 ) 
Here /, (2 (= fil) = a le (l+a+a?)+ 4 L+ataryy 
and so on. 


Making the successive substitutions, we obtain 


fh. oes 15995 45 
2 Oo Ocoee a 


249 | 2652 , 3482? , 16628 10924 | 3408 16x8 | da? | af 
sist aisy * 2187 * 2187 2187 2187 2187 2187 
Bos og 08306x + "1063522 + ‘0780423 + 0648924 + 054430 + °0143728 


+ °0169227 + °0114428 + -00367x9 + -00104x! + 00015" + °00005x12 
+ 0000129 + -00000x'4 + -00000z! + :00000z'6 


APPENDIX F. 245 


and the constant term inf, (#) or ,m, is therefore 


6°3183 4. 08306 , 10685 , *07804 06489 | 05443 01437 , 01692 , 01144 
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 7, f, up tof; when reduced to 
decimals, are in this case 33333, °48148, 57110, 64113, and 65628 
respectively. Thatis 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¢,, and this 
quantity is in the present case equal to one. 

If axes Ox and Oy 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 population curve will, in this case, be a straight 
line parallel to Oz, while the swrname 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 ¢)+4,%+ 
ete.+t,2, are proportional to the terms of the expanded binomial 


246 NATURAL INHERITANCE. 


J 
(a+bx,? @.e. suppose that ¢ a Rr Sg and so on. 
4 0= (G8) (a+ 6)? 
: _- (a+bzx)2 eos 
Here /, («)= (a+b) and jm = Gee 


A= aap rr 


1 
pe epee 
PULL al a + OM j 


Generally ,m) = on | a+ b,.1Mq \ U ig G & \§ OF, Ali } q 
q 


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 


power of g,and multiply by ——— 
C Car 


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 fp, t,, ete., ¢, are 
ascertained, values of a, 6, and g may be found, which shall render 
the terms of the expansion (a+ 6x)! approximately proportionate to 
the terms of f, (z). If this can be done, we may approximate 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 g 
might be 5, while é), ¢, vb might be ‘237, 396, 264, 088, -014, -001, 


or nearly, 4, 4, 34, and soo: 


a, Te 
a\5 5 
(3 +2) pe 9 


1 Cie 


Should that be the case, we have, f, («)= 


Bers slg! 1 
and generally ,m)= j; [ 3 + 1M i 
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. 
Lea ea 
3 
viz., that while 237 names out of a thousand disappear in the first 


We observe the same law noticed above in the case of 


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 

t, +2t, + 36, + 4¢,-+- 58, 
is greater than one. 
Whenever jf, («) can be represented by a binomial, as above sug- 
gested, we get the equation 


il 
1 = (a+ by { a+b,.m } q 


whence it follows that as r increases indefinitely the value of ,m, ap- 
proaches indefinitely to the value y where 


ery \et | 
_ a+b 
Gaaeh alts ee 
that is where y=1. 


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, + 2¢, + ete. 
+qt,>1, and, therefore an indefinite increase of male population. 

The true interpretation is that each of the quantities, ,m,, ,m., 
etc., tends to become zero, as r 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., representatives 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 of /, (x), but the reason- 
able inference is that such is the case, seeing that it holds whenever 


+ ba) 


J, (%) may be compared with iG 2 whatever a, b, or q may be. 


(a+) 


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 ; 8 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 :— 


Order Numerical Values 
: : of 
Kinship. Genera- . : 3 
tion. in Binary Notation. a: ede Nota- 
ion. 
Cin dees. csc: (0) 1 1 
JER WIGTONS) pagecesseoe 1 10 iL 2 3 
Gree ari sesu. 2 100 101 it@ |} aati 4 5 6 7 
1000 | 1010 |} 1100 | 1110 SEO | eae a 
Gr, (Cats 12eHe = coco 
1001 | 1011 |} 1100 | 1111,)) 9 | 11 jj 13 | 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. 


BS: M, 3. 

FF, 4. M5. MF, 6. MM, 7. 
FFF, 8. EME, 10. MFF, 12. MME, 14. 
FEM, 9. FMM, il. MFM, 13. MMM, 15. 


Tt 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 
plus 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 r, sr, and in 
the plural brs, srs ; also for the long phrase of “ brothers and sisters,” 
to write brss. ; 

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 FE’, 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 
adelphic 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 


251 


APPENDIX G. 


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252 NATURAL INHERITANCE. 
Example A. 
Hathers name). sya ee JAMES GLADDING. 
Mother’s maiden name . . . . MARY CLAREMONT. 
Initials.| Kin. Principal illnesses and cause of death. fee 
J.G. | Father | Bad rheum. fever; agonising headaches; diar- 
rhea; bronchitis ; pleurisy. . Heart disease 54 
R. G bro. Rheum. gout . . . . . Apoplexy 56 
W.G.| bro. | Good health except gout ; : paralysis later Apoplexy 83 
105 be sis. Rheum. fever and rheum. gout . . . Apoplexy 73 
C. G. sis. Nelicatepe nw reer (inoculated) Small pox 
M. G. | Mother | Tendency to Jung disease ; biliousness; fre- 
quent heart attacks . Heart disease and dropsy 63 
| A.C. bro: \|Good.health-.. sien re eee Accident 46 
W. O. rosa eledvaywaldulifers pee erme Premature old age 62 
E. C. bro. | Always delicate... ... . . Consumption 19 
i. R. | ‘sis. Small-pox three times . . . . General failure 85 
its INIA sis. Bilious ; weak health . ..... . . Cancer 50 
L. C. S1SS a henge tS varies” Semreiligd cy 8 rae ei . Hever 21 
M.G.| bro. | Inflam. lungs; rheum. fever . . Heart disease 7 
K. G. bro. | Debility ; heart disease; colds . Consumption 40 
G. L. |- sis. | Bad headaches ; coughs; weak spine ; hysteria ; 
apoplexy . . . . Paralysis 50 
F. S. sis. Bad colds ; inflam. ‘lungs ; hy Sie. Cee living 
R. F. sis. Infantile paralysis ; colds ; ; nervous depression . | living 
L. G. sis. Inflam. brain, also lungs ; neuralgia ; nervous : 
LEVER: io sal Be Sompimcmi Jun eee eee living 


— 


APPENDIX G. 


253 


EXAMpLe B. 
Hathersmamess.. 4. se JuLius Firzroy. 
Mother’s maiden name. . . AMELIA MERRYWEATHER. 
Initials.| Ki Principal illn d f death Nee at 
nitials. in. tincipal illnesses and cause o 3 AeAthn 
R. F Father | Gouty Habit. . Weak Heart and Congest. Liver 73 
L. F.i LOLEOY, 7 llss Meiers Paty acca Gout and Decay 88 
PATA Cram ER DLO [Sore feel cter, azo} ney meat! encore os Mes eens al te Accident 48 
We 20s [OTRO 8) F eee mie et ee ied Wore at et IMA em Er Typhoid 16 
Mother} Gallstones. . . . Internal Malady (?) Cancer 55 
vir DLO aes Pein Aocnincih oh Sun cas Vist yo eta val, Paralysis 86 
A. M. RO NmiY We ceret ay senti t rer at ee aruba waels Paralysis 85 
We JE bro. Still living. 
R. B. SIS SIR esate erent arse a a Sam ed an Syeieee Consumption 33 
C. M. SUS Sic | peek Se a eee ek cece ise Lon mene Rheum. in Head 88 
1m I SiSeeee etsy cer coe a Sey crane ec Softening of Brain 76 
1 died an infant. 
G. F. bro. | Gout: tendency to mesenteric disease ; eruptive 
disorders . . . Blood poisoning after a cut 46 
lel, ID, bro. Liver deranged ; bad headaches ; once supposed 
COMMTNOGVO 5 4 5 4 ¢ Gradual Paralysis 45 
S.T.F.| bro. | Eruptive disorder; mesentery disease; inflam- 
mation of liver . . Inflammation of Lungs 42 
Fe Gre sis. Eruptive disorder ; liver. . . Inflam. of Lungs 47 
Tale 183 J8|| = BIE Delicate ; tend. to mesent. disease . Conswmuption 29 
Neer sis. Coldsieliverndisonders sys ee) ee Consumption 30 
1Dg Iby Lo) Re Mesenteric disease ; grandular swellings . Atrophy 16 


2 died infants. 


(Space left for remarks.) 


254 NATURAL INHERITANCH. 


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 and B 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 overflow 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 suffice, placing ‘‘Children” where ‘“‘ Father” now stands, 
“ Father’s Father” for “ Father,” and so on throughout. 


INDEX. 


Accidents, 19, 55, 65 

Acquired peculiarities, inheritance of, 
14 

Album for Life History, 220 

Ancestral contributions, 134 

Adelphic, 250 

Anthropometric Committee of the 
British Assoc., 95; anthrop. labo- 
ratory data, 43, 46, 79 

Apparatus, sce Models 

Acquired faculties, transmission of, 16, 
197 

ARTISTIC FAcuLTY, 154 

Averages tell little, 36 ; comparison of 
with medians, 41 

Awards for R.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 ; intemper, 233 ; have 
no effect on statistical results, 17 _ 


Cabs, 26, 30, 31 

Candolle, A de, 142, 145, 241 

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 » 

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 CoLouR, 138 


Families, extinction of, Appendix F., 
241 


Family Records, sce 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 

Ss) 


258 


Frequency, Scheme of, 49 ; model, 63 ; 
surface of, 102 


Geometric Mean, 118, Appendix E, 238 

Gouffé, cookery book, 24 

Governments, 22 

Grades, 37, 40; of modulus, mean 
error, &c., 57 

Grove battery, 31 


Hazel eyes, 144 
Hospital, St. Bartholomew’s, 47 
Humphreys, G., 186 


Incomes of the English, 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 

Maealister, 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, 15; in 
consumption, 177. Sce Parent 

Mulatto blends, 13 


INDEX. 


Museums to illustrate evolution, 33 
Music, 155, 158 


Natural, its meaning, 4; natural selec- 
tion, 32, 119 

Nephews, 133 

Nile expedition, 23 

Nomenclature of kinship, 248 

NoRMAL VARIABILITY, 51 


O’Brien, 84 

Omnibuses, 26, 32 

Order in apparent chaos, 66 
ORGANIC STABILITY, 4 


Paget, Sir J., 47 

Palmer, 48 

Pangenesis, 19, 198 

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, naturai 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., sce 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. 


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 consumptivity, 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; 
effect 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; 
nate, 25 

Stability of sports, 30, 234 ; 
teristics in a people, 163 


subordi- 


of charac- 


259 


Statistics, are processes of blending, 17 ; 
charms of, 62 

STATURE, DISCUSSION OF DATA, 83 

Strength, Scheme of, 37 

Structure, incipient, 18 

Sweet peas, 79, 225 

Swiss guides, 23 


TemMpPER, 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 

Variation, individual, 9 


Watson, Rev. H. W., 242 
Weissman, 193 


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