influences by which the magnitudes, etc., of the objects are
determined can seldom if ever be roundly classed into large and small,
without intermediates. He is tantalised by the hope of getting hold
of sub-groups of sufficient size that shall contain no individuals
except those belonging strictly to the same species, and he is almost
constantly baffled. In the end he is obliged to exercise his
judgment as to the limit at which he should cease to subdivide. If
he subdivides very frequently, the groups become too small to have
statistical value; if less frequently, the groups will be less truly
specific.
A species may be defined as a group of objects whose individual
differences are wholly due to different combinations of the same set
of minute causes, no one of which is so powerful as to be able by
itself to make any sensible difference in the result. A well-known
mathematical consequence flows from this, which is also universally
observed as a fact, namely, that in all species the number of
individuals who differ from the average value, up to any given amount,
is much greater than the number who differ more than that amount,
and up to the double of it. In short, if an assorted series be
represented by upright lines arranged side by side along a
horizontal base at equal distances apart, and of lengths
proportionate to the magnitude of the quality in the corresponding
objects, then their shape will always resemble that shown in Fig. 1.
The form of the bounding curve resembles that which is called in
architectural language an ogive, from "augive," an old French word
for a cup, the figure being not unlike the upper half of a cup lying
sideways with its axis horizontal. In consequence of the multitude
of mediocre values, we always find that on either side of the
middlemost ordinate _Cc_, which is the median value and may be
accepted as the average, there is a much less rapid change of height
than elsewhere. If the figure were pulled out sideways to make it
accord with such physical conceptions as that of a row of men
standing side by side, the middle part of the curve would be
apparently horizontal.
[Illustration: Fig. 1.]
[Illustration: Fig. 2.]
The mathematical conception of the curve is best expressed in Fig. 2,
where PQ represents any given deviation from the average value, and
the ratio of PO to AB represents the relative probability of its
occurrence. The equation to the curve and a discussion of its
properties will be found in the _Proceedings of the Royal Society_,
No. 198, 1879, by Dr. M'Alister. The title of the paper is the
"Law of the Geometric Mean," and it follows one by myself on
"The Geometric Mean in Vital and Social Statistics."
We can lay down the ogive of any quality, physical or mental,
whenever we are capable of judging which of any two members of the
group we are engaged upon has the larger amount of that quality. I
have called this the method of statistics by intercomparison. There
is no bodily or mental attribute in any race of individuals that can
be so dealt with, whether our judgment in comparing them be guided
by common-sense observation or by actual measurement, which cannot
be gripped and consolidated into an ogive with a smooth outline, and
thenceforward be treated in discussion as a single object.
It is easy to describe any given ogive which has been based upon
measurements, so that it may be drawn from the description with
approximate truth. Divide AB into a convenient number of fractional
parts, and record the height of the ordinates at those parts. In
reproducing the ogive from these data, draw a base line of any
convenient length, divide it in the same number of fractional parts,
erect ordinates of the stated lengths at those parts, connect their
tops with a flowing line, and the thing is done. The most convenient
fractional parts are the middle (giving the median), the outside
quarters (giving the upper and lower quartiles), and similarly the
upper and lower octiles or deciles. This is sufficient for most
purposes. It leaves only the outer eighths or tenths of the cases
undescribed and undetermined, except so far as may be guessed by,
the run of the intermediate portion of the curve, and it defines all
of the intermediate portion with as close an, approximation as is
needed for ordinary or statistical purposes.
Thus the heights of all but the outer tenths of the whole body of
adult males of the English professional classes may be derived from
the five following ordinates, measured in inches, of which the outer
pair are deciles:--
67.2; 67.5; 68.8; 70.3; 71.4.
Many other instances will be found in the Report of the
Anthropometric Committee of the British Association in 1881,
pp. 245-257.
When we desire to compare any two large statistical groups, we may
compare median with median, quartiles with quartiles, and octiles
with octiles; or we may proceed on the method to be described in the
next paragraph but one.
We are often called upon to define the position of an individual in
his own series, in which case it is most conformable to usage to
give his centesimal grade--that is, his place on the base line
AB--supposing it to be graduated from 0° to 100°. In reckoning this,
a confusion ought to be avoided between "graduation" and "rank,"
though it leads to no sensible error in practice. The first of the
"park palings" does not stand at A, which is 0°, nor does the
hundredth stand at B, which is 100°, for that would make 101 of them:
but they stand at 0°.5 and 99°.5 respectively. Similarly, all
intermediate _ranks_ stand half a degree short of the _graduation_
bearing the same number. When the class is large, the value of half
a place becomes extremely small, and the rank and graduation may be
treated as identical.
Examples of method of calculating a centesimal position:--
1. A child A is classed after examination as No. 5 in a class of 27
children; what is his centesimal graduation?
_Answer_.--If AB be divided into 27 graduations, his rank of No. 5
will correspond to the graduation 4°.5; therefore if AB be graduated
afresh into 100 graduations, his centesimal grade, x, will be found
by the Rule of Three, thus--
x : 4°.5 :: 100:27; x = 450°/27 = 16°.6.
2. Another child B is classed No. 13 in a class of 25 _Answer_.--If
AB be divided into 25 graduations, the rank of No. 13 will
correspond to graduation 12°.5, whence as before--
x : 12°.5 :: 100 : 25; x = 1250°/25 = 50°; _i.e._ B is the median.
The second method of comparing two statistical groups, to which I
alluded in the last paragraph but one, consists in stating the
centesimal grade in the one group that corresponds with the median
or any other fractional grade in the other. This, it will be remarked,
is a very simple method of comparison, absolutely independent of any
theory, and applicable to any statistical groups whatever, whether of
physical or of mental qualities. Wherever we can sort in order,
there we can apply this method. Thus, in the above examples, suppose
A and B had been selected because they were equal when compared
together, then we can concisely express the relative merits of the
two classes to which they respectively belong, by saying that 16°.6
in the one is equal to 50° (the median) in the other.
I frequently make statistical records of form and feature, in the
streets or in company, without exciting attention, by means of a
fine pricker and a piece of paper. The pricker is a converted silver
pencil-case, with the usual sliding piece; it is a very small one,
and is attached to my watch chain. The pencil part has been taken
out and replaced by a fine short needle, the open mouth of the case
is covered with a hemispherical cap having a hole in the centre, and
the adjustments are such that when the slide is pushed forward as
far as it can go, the needle projects no more than one-tenth of an
inch. If I then press it upon a piece of paper, held against the
ball of my thumb, the paper is indelibly perforated with a fine hole,
and the thumb is not wounded. The perforations will not be found to
run into one another unless they are very numerous, and if they
happen to do so now and then, it is of little consequence in a
statistical inquiry. The holes are easily counted at leisure, by
holding the paper against the light, and any scrap of paper will
serve the purpose. It will be found that the majority of inquiries
take the form of "more," "equal to," or "less," so I arrange the
paper in a way to present three distinct compartments to the pricker,
and to permit of its being held in the correct position and used by
the sense of touch alone. I do so by tearing the paper into the form
of a cross--that is, maimed in one of its arms--and hold it by the
maimed part between the thumb and finger, the head of the cross
pointing upward. The head of the cross receives the pricks referring
to "more"; the solitary arm that is not maimed, those meaning
"the same"; the long foot of the cross those meaning "less." It is
well to write the subject of the measurement on the paper before
beginning to use it, then more than one set of records can be kept
in the pocket at the same time, and be severally added to as occasion
serves, without fear of mistaking one for the other.
[Illustration: ]
CHARACTER.
The fundamental and intrinsic differences of character that exist in
individuals are well illustrated by those that distinguish the two
sexes, and which begin to assert themselves even in the nursery,
where all the children are treated alike. One notable peculiarity in
the character of the woman is that she is capricious and coy, and
has less straightforwardness than the man. It is the same in the
female of every sex about the time of pairing, and there can be
little doubt as to the origin of the peculiarity. If any race of
animals existed in whom the sexual passions of the female were as
quickly and as directly stirred as those of the male, each would
mate with the first who approached her, and one essential condition
of sexual selection would be absent. There would be no more call for
competition among the males for the favour of each female; no more
fighting for love, in which the strongest male conquers; no more
rival display of personal charms, in which the best-looking or
best-mannered prevails. The drama of courtship, with its prolonged
strivings and doubtful success, would be cut quite short, and the
race would degenerate through the absence of that sexual selection
for which the protracted preliminaries of love-making give
opportunity. The willy-nilly disposition of the female in matters of
love is as apparent in the butterfly as in the man, and must have
been continuously favoured from the earliest stages of animal
evolution down to the present time. It is the factor in the great
theory of sexual selection that corresponds to the insistence and
directness of the male. Coyness and caprice have in consequence
become a heritage of the sex, together with a cohort of allied
weaknesses and petty deceits, that men have come to think venial and
even amiable in women, but which they would not tolerate among
themselves.
Various forms of natural character and temperament would no doubt be
found to occur in constant proportions among any large group of
persons of the same race, but what those proportions may be has
never yet been investigated. It is extremely difficult to estimate
it by observations of adults, owing to their habit of restraining
natural ill tendencies, and to their long-practised concealment of
those they do not restrain but desire to hide. The necessary
observations ought, however, to be easily made on young children in
schools, whose manifestations of character are conspicuous, who are
simultaneously for months and years under the eye of the same master
or mistress, and who are daily classed according to their various
merits. I have occasionally asked the opinion of persons well
qualified to form them, and who have had experience of teaching, as
to the most obvious divisions of character to be found among school
children. The replies have differed, but those on which most stress
was laid were connected with energy, sociability, desire to attract
notice, truthfulness, thoroughness, and refinement.
The varieties of the emotional constitution and of likings and
antipathies are very numerous and wide. I may give two instances
which I have not seen elsewhere alluded to, merely as examples of
variation. One of them was often brought to my notice at the time
when the public were admitted to see the snakes fed at the
Zoological Gardens. Rabbits, birds, and other small animals were
dropped in the different cages, which the snakes, after more or less
serpentine action, finally struck with their poison fangs or crushed
in their folds. I found it a horrible but a fascinating scene. We
lead for the most part such an easy and carpeted existence, screened
from the stern realities of life and death, that many of us are
impelled to draw aside the curtain now and then, and gaze for a
while behind it. This exhibition of the snakes at their feeding-time,
which gave to me, as it doubtless did to several others, a sense of
curdling of the blood, had no such effect on many of the visitors. I
have often seen people--nurses, for instance, and children of all
ages--looking unconcernedly and amusedly at the scene. Their
indifference was perhaps the most painful element of the whole
transaction. Their sympathies were absolutely unawakened. I quote
this instance, partly because it leads to another very curious fact
that I have noticed as regards the way with which different persons
and races regard snakes. I myself have a horror of them, and can
only by great self-control, and under a sense of real agitation,
force myself to touch one. A considerable proportion of the English
race would feel much as I do; but the remainder do not. I have
questioned numbers of persons of both sexes, and have been
astonished at the frequency with which I have been assured that they
had no shrinking whatever from the sight of the wriggling mysterious
reptile. Some persons, as is well known, make pets of them; moreover,
I am told that there is no passage in Greek or Latin authors
expressive of that form of horror which I myself feel, and which may
be compared to what is said to be felt by hydrophobic sufferers at
the undulating movements of water. There are numerous allusions in
the classics to the venom fang or the crushing power of snakes, but
not to an aversion inspired by its form and movement. It was the
Greek symbol of Hippocrates and of healing. There is nothing of the
kind in Hebrew literature, where the snake is figured as an
attractive tempter. In Hindu fables the cobra is the ingenious and
intelligent animal, corresponding to the fox in ours. Serpent worship
was very widely spread. I therefore doubt whether the antipathy to
the snake is very common among mankind, notwithstanding the
instinctive terror that their sight inspires in monkeys.
The other instance I may adduce is that of the horror of blood which
is curiously different in animals of the same species and in the
same animals at different times. I have had a good deal of
experience of the behaviour of oxen at the sight of blood, and found
it to be by no means uniform. In my South African travels I relied
chiefly on half-wild slaughter oxen to feed my large party, and
occasionally had to shoot one on every second day. Usually the rest
of the drove paid no particular heed to the place of blood, but at
other rare times they seemed maddened and performed a curious sort
of war-dance at the spot, making buck-leaps, brandishing their horns,
and goring at the ground. It was a grotesque proceeding, utterly
unlike the usual behaviour of cattle. I only witnessed it once
elsewhere, and that was in the Pyrenees, where I came on a herd that
was being driven homewards. Each cow in turn, as it passed a
particular spot, performed the well-remembered antics. I asked, and
learned that a cow had been killed there by a bear a few days
previously. The natural horror at blood, and it may be the
consequent dislike of red, is common among mankind; but I have seen
a well-dressed child of about four years old poking its finger with
a pleased innocent look into the bleeding carcase of a sheep hung up
in a butcher's shop, while its nurse was inside.
The subject of character deserves more statistical investigation
than it has yet received, and none have a better chance of doing it
well than schoolmasters; their opportunities are indeed most enviable.
It would be necessary to approach the subject wholly without
prejudice, as a pure matter of observation, just as if the children
were the fauna and flora of hitherto undescribed species in an
entirely new land.
CRIMINALS AND THE INSANE.
Criminality, though not very various in its development, is
extremely complex in its origin; nevertheless certain general
conclusions are arrived at by the best writers on the subject, among
whom Prosper Despine is one of the most instructive. The ideal
criminal has marked peculiarities of character: his conscience is
almost deficient, his instincts are vicious, his power of
self-control is very weak, and he usually detests continuous labour.
The absence of self-control is due to ungovernable temper, to passion,
or to mere imbecility, and the conditions that determine the
particular description of crime are the character of the instincts
and of the temptation.
The deficiency of conscience in criminals, as shown by the absence
of genuine remorse for their guilt, astonishes all who first become
familiar with the details of prison life. Scenes of heartrending
despair are hardly ever witnessed among prisoners; their sleep is
broken by no uneasy dreams--on the contrary, it is easy and sound;
they have also excellent appetites. But hypocrisy is a very common
vice; and all my information agrees as to the utter untruthfulness
of criminals, however plausible their statements may be.
We must guard ourselves against looking upon vicious instincts as
perversions, inasmuch as they may be strictly in accordance with the
healthy nature of the man, and, being transmissible by inheritance,
may become the normal characteristics of a healthy race, just as the
sheep-dog, the retriever, the pointer, and the bull-dog, have their
several instincts. There can be no greater popular error than the
supposition that natural instinct is a perfectly trustworthy guide,
for there are striking contradictions to such an opinion in
individuals of every description of animal. The most that we are
entitled to say in any case is, that the prevalent instincts of each
race are trustworthy, not those of every individual. But even this
is saying too much, because when the conditions under which the race
is living have recently been changed, some instincts which were
adapted to the old state of things are sure to be fallacious guides
to conduct in the new one. A man who is counted as an atrocious
criminal in England, and is punished as such by English law in social
self-defence, may nevertheless have acted in strict accordance with
instincts that are laudable in less civilised societies. The ideal
criminal is, unhappily for him, deficient in qualities that are
capable of restraining his unkindly or inconvenient instincts; he
has neither sympathy for others nor the sense of duty, both of which
lie at the base of conscience; nor has he sufficient self-control to
accommodate himself to the society in which he has to live, and so to
promote his own selfish interests in the long-run. He cannot be
preserved from criminal misadventure, either by altruistic
sentiments or by intelligently egoistic ones.
The perpetuation of the criminal class by heredity is a question
difficult to grapple with on many accounts. Their vagrant habits,
their illegitimate unions, and extreme untruthfulness, are among the
difficulties of the investigation. It is, however, easy to show that
the criminal nature tends to be inherited; while, on the other hand,
it is impossible that women who spend a large portion of the best
years of their life in prison can contribute many children to the
population. The true state of the case appears to be that the
criminal population receives steady accessions from those who,
without having strongly-marked criminal natures, do nevertheless
belong to a type of humanity that is exceedingly ill suited to play
a respectable part in our modern civilisation, though it is well
suited to flourish under half-savage conditions, being naturally
both healthy and prolific. These persons are apt to go to the bad;
their daughters consort with criminals and become the parents of
criminals. An extraordinary example of this is afforded by the
history of the infamous Jukes family in America, whose pedigree has
been made out, with extraordinary care, during no less than seven
generations, and is the subject of an elaborate memoir printed in
the Thirty-first Annual Report of the Prison Association of New York,
1876. It includes no less than 540 individuals of Jukes blood, of
whom a frightful number degraded into criminality, pauperism, or
disease.
It is difficult to summarise the results in a few plain figures, but
I will state those respecting the fifth generation, through the
eldest of the five prolific daughters of the man who is the common
ancestor of the race. The total number of these was 123, of whom
thirty-eight came through an illegitimate granddaughter, and
eighty-five through legitimate grandchildren. Out of the thirty-eight,
sixteen have been in jail, six of them for heinous offences, one of
these having been committed no less than nine times; eleven others
led openly disreputable lives or were paupers; four were notoriously
intemperate; the history of three had not been traced, and only four
are known to have done well. The great majority of the women
consorted with criminals. As to the eighty-five legitimate
descendants, they were less flagrantly bad, for only five of them
had been in jail, and only thirteen others had been paupers. Now the
ancestor of all this mischief, who was born about the year 1730, is
described as having been a jolly companionable man, a hunter, and a
fisher, averse to steady labour, but working hard and idling by turns,
and who had numerous illegitimate children, whose issue has not been
traced. He was, in fact, a somewhat good specimen of a half-savage,
without any seriously criminal instincts. The girls were apparently
attractive, marrying early and sometimes not badly; but the
gipsy-like character of the race was unsuited to success in a
civilised country. So the descendants went to the bad, and such
hereditary moral weaknesses as they may have had, rose to the
surface and worked their mischief without check. Cohabiting with
criminals, and being extremely prolific, the result was the
production of a stock exceeding 500 in number, of a prevalent
criminal type. Through disease and intemperance the breed is now
rapidly diminishing; the infant mortality has of late been horrible,
but fortunately the women of the present generation bear usually but
few children, and many of them are altogether childless.