Most noble Professors and Students of Girtham College,--Since last 'I
wandered 'twixt the pole and heavenly hinges, 'mongst encentricals,
centres, concentricks, circles, and epicycles,' like the great
Albumazar, and found them full of life and wisdom for the guidance of
our States and laws, I have turned my attention to the Applied
Mathematics, in order to determine what other truths this shaft may
yield.
The strength of all sciences, according to Bacon, consists in their
harmony; and it is truly marvellous how perfect this harmony is, if our
ears are tuned aright to hear it. We have observed how the beautiful
and regular laws of curves and cones correspond to the social laws of
States and nations, guiding them as if by word of counsel, admonishing
them on what principle they ought to regulate their governments and
inter-relations. We have seen that the laws which govern thought and
light and sound are almost identical, and that harmony pervades not
merely the ordinary sciences, but extends her benign influence over
these newly discovered fields of scientific research, which I claim to
have discovered.
All this may appear at first sight surprising; but the real philosopher,
who knows that all kinds of truth are intimately connected, will receive
such revelations of science with satisfaction rather than astonishment;
for this new science, which has opened itself out before me, is only an
extension of other well-known laws and discoveries which have come down
to us from the remote past.
If my investigations should appear to you, most noble professors,
somewhat novel and imaginary, remember the maxim of the sage, that in
the infancy of science there is no speculation which does not merit
careful examination; and the most remote and fanciful explanations of
facts have often been found the true ones. Perhaps some
'self-opinionated particle' (I speak mathematically) may have been
inclined to laugh at our theories and discoveries, as the wise fools of
the day laughed at Kepler and his laws; but time has changed the world's
laughter into praise, and a century hence our discoveries may rank among
the achievements of modern science. As Cicero says, 'Time obliterates
the fictions of opinions, but confirms the decisions of nature.'
I have not shunned, most noble professors, to enlist Imagination under
the banner of Geometry; for I am fully persuaded that it is a powerful
organ of knowledge, and is as much needed by the mathematician as by the
poet or novelist. It is, I fear, often banished with too much haste from
the fields of intellectual research by those who take upon themselves to
give laws to philosophy. We need imagination to form an hypothesis; and
without hypotheses science would soon become a lifeless and barren
study, a horse-in-the-mill affair ever strolling round and round,
unconscious of the grinding corn. In my previous investigations my
imagination pictured the symmetry of curves and States; the hypothesis
followed that the laws which regulated them were identical, and you have
observed how the supposition was confirmed by our subsequent
calculations.
In this lecture I propose to examine some of the forces which exist in
our social system, and shall endeavour to estimate them by methods of
mathematical procedure and analogical reasoning. We will begin with the
old definition of Force as _that which puts matter into motion, or which
stops, or changes, a motion once commenced_. When a mass is in motion,
it has a capacity for doing work, which is called _Energy_; and when
this energy is caused by the motion of a body it is called Kinetic
Energy (in mathematical language KE = 1/2 MV^2). Another form of kinetic
energy is called Potential Energy, which is in reality the capacity of a
body for doing work _owing to its position_. For example we may take an
ordinary eight-day clock. When the weights are wound up, they have a
certain amount of potential energy stored up, which will counteract the
friction of the wheels and the resistance of the air on the pendulum.
Or, again, we have the example of a water-wheel: first the water in the
reservoir, being higher than the wheel, has an amount of potential
energy. This is converted into kinetic energy in striking against the
paddles, and after this we have potential energy again produced by the
action of the fly-wheel.
By the principle of conservation of energy, if we consider the whole
universe, not our planet alone (for its heat and energy are continually
diminished to some slight degree), we find that _no energy is lost_.
Force is recognised as acting in two ways: in _Statics_, so as to compel
rest, or to prevent change of motion; and in _Kinetics_, so as to
produce or to change motion; and the whole science which investigates
the action of force is called _Dynamics_.
All this is of course pure mathematics, and I have made these elementary
observations for the benefit of my younger hearers, the students of this
University. My grave and reverend seniors will pardon, I am sure, the
repetition of facts well known to them for the sake of those who are
less informed than themselves.
Now before I proceed further, I will endeavour to point out that these
elementary truths of physical science hold good in our social system.
Each individual is a mass, acted on by numerous forces, capable of
'doing work,' which work can be measured and his velocity calculated.
Some individuals have a vast _potential energy_; that is to say, from
their position and station in the social system, they have a power which
is capable of producing work which a less exalted individual has not.
Like the weights in an eight-day clock, or the water in a reservoir,
they have a capacity for doing work, owing to the position to which
they have been raised. How vast the influence of a Primate or a Premier,
a General or a King! And yet their power is chiefly potential energy,
arising from the position they occupy, not from the individuals
themselves. Schiller has described this in poetical language, which,
strange to say, is mathematically correct:
'Yes, there's a patent of nobility
Above the meanness of our common state;
With what they _do_ the vulgar natures buy
Their titles; and with what they _are_, the _great_.'
Other forces may have raised these men to their exalted positions; but
their influence is due to their height, their potential energy. Placed
on a lower level, they would cease to have that power. How calm the
dignity of this potential rank! The water in the reservoir is scarcely
ruffled or disturbed, as if unconscious of its power; when it has lost
its force it rushes along with a sullen murmur and a roar, howling and
hissing and boiling in endless torture, until--
'It gains a safer bed, and steals at last
Along the mazes of the quiet vale.'
So the vulgar crowd rushes on, with plenty of kinetic force, making
noise enough and looking very busy; while those who seem to sleep in
calm forgetfulness, exercise their potential energy, and do the real
work of turning the great engine of the State.
There are attractive and repulsive forces (more commonly the latter, the
cynic will say) in our social system, but each individual is the centre
of various forces acting upon him. In nature all matter possesses the
force of gravity, and whatever the size of two particles may be, they
mutually attract each other. The earth attracts the moon; the moon
attracts the earth. A stone thrown up into the air exercises an
infinitesimal force upon the earth; so in the social system every
individual, however small and insignificant he may be, exercises some
attractive force upon his neighbour. There is no one in the world who
does not exercise some influence for good or for evil upon his fellows.
The force of _cohesion_ is manifest in society as in nature, that force,
I mean, which resists the separation of a body's particles. Different
bodies possess different powers of cohesion, _e.g._, the cohesion of
chalk is far less than that of flint embedded in it; even the same body
possesses different powers of cohesion in different directions, _e.g._,
it is easier to split wood in the direction of the fibres than
perpendicular to them. If by our old principle of continuity we change
the words 'bodies' into 'States' or 'individuals,' we shall see that the
same laws hold good in social science as in natural philosophy.
These are a few analogous laws which I have taken almost at random; but
it must strike the most casual listener to my remarks that it is
wondrous strange that men, regarded as social beings, should possess the
same qualities, and be governed by the same laws, as the rest of
_matter_. As Bishop Butler says, 'the force of analogy consists in the
frequency of the supposed analogous facts, and the real resemblance of
the things compared.' It appeals to the reasoning faculty, and may form
a solid argument. Hence, if we can prove the similarity of various laws
and conditions, we may not be wrong in assuming by analogy the identity
of those laws and conditions.
I have stated my case in this manner in order to convince the
gainsayers, if any such there be, and to banish any doubts or
questionings which may have arisen in your minds. I will now proceed
with some further investigations, full of the most profound interest
and importance.
Doubtless many of the lady-students present are in the habit of
welcoming peaceful evening in with a potent draught of 'the cup which
cheers but not inebriates;' and as men are great flatterers (for
imitation is the greatest flattery), I believe the male portion of my
audience have been known to follow that excellent example. Some perhaps
are in the habit of burning the midnight oil, and keep their eyes open
by means of this fruit of the hermit's pious zeal, endowed by high
omnipotence with the power of hindering sleep;[6] but that practice I
do not advise, as that delicate portion of our system, the nerves,
especially of women, often becomes injured by such stimulating doses.
However, you will have observed (if you do not follow the modern
pernicious fashion of taking tea without sugar) that numerous bubbles
are formed upon the surface of the liquid. After a few moments these
unite into one central mass of bubbles by the force of mutual
attraction.
It appears from considerations which are detailed in works on physical
astronomy, that two particles of matter placed at any sensible distance
apart attract each other with a force directly proportional to the
product of their masses, and inversely proportional to the square of
their distance.
Now, suppose that we have a number of circular masses situated upon a
plane surface, they will attract each other with a force which may be
determined with exactitude; and the greater the masses the greater the
force. We will now apply this to polemical science. The agricultural
settlement is the first stage in the civilization and formation of a
State. How did this arise? First, a single family immigrated to some
uncultivated parts of the country, perhaps accompanied by others, who
formed a little colony. Other settlements were made in other parts of
the land; and thus the country became overspread with these detached and
separate communities. An eminent writer declares that these settlements
can be traced in the beginnings of every race which has made progress;
that they were characteristic of those races in Greece and Italy, in
Asia and Africa, which grew into the opulent and famous cities in which
so much in the early history of civilization was developed. The colonies
of England have been formed in the same way, just as in olden time
England itself was occupied when the Roman power ceased.
These settlements correspond to the circular masses situated on the
plane surface; they were quite separate from each other, each having its
own laws, its own headman or ruler, its own assembly or parish council.
But as time elapsed, the force of mutual attraction set in; by degrees
these separate settlements were drawn together by force which increased
in proportion as the settlements increased; until at last one united
kingdom was formed under one king, governed by uniform laws and
regulations. The bubbles have blended, the circles have come together,
and one large circle or other curve is the result. This may be called
the _Law of Social Attraction_. In accordance with the results of one
of my previous lectures, I have taken the circle as representing the
simplest form of government, which figure, in the case of the elementary
settlements, must have been small.
Many of you, most noble professors, are doubtless accustomed to make
experiments with the microscope. I will suggest a simple one, which
illustrates very forcibly what I am endeavouring to show you. Take some
particles of copper, and scatter them at intervals over the surface of
an object-glass, and pour some sulphuric acid upon the glass. Now, what
is the result? A beautiful network of apparently golden texture spreads
itself gradually over the whole area of the glass. Steadily it pursues
its way, and the result is beautiful to behold. The minute particles of
copper were the original settlements scattered over the land; the
sulphuric acid the civilizing agent; and the final picture of a united
civilized homogeneous nation is well represented by the progressive and
finally glorious network of gold. This example is of course outside our
present subject, but it serves as a beautiful illustration.
As an instance of the attractive force exercised by small communities
upon each other, I may mention the united kingdom of Germany, which is
composed of numerous small States and nations, which have been drawn
together by the power of mutual attraction. Until recently they were
each self-contained, separate constitutions, with their own kings and
forms of government; but the attracting force, assisted by forces from
without, has proved too much for them, and the great and powerful united
kingdom of Germany is the result.
But why, you may ask, have not the people in Hindustan united in the
same way? There the agricultural settlements remain as they did ages
ago; separate petty chieftains rule under the all-governing power of
England. Why have they not united?
To this objection I reply that there is in social science, as in Nature,
a _vis inertia_; that is to say, there is a tendency in matter to remain
at rest if unmoved by any external agency, and also of persisting to
move, after it has once been set in motion. The _vis inertia_ of some
bodies is greater than that of others, and depends upon their weight
and density. Now it so happens that the moral _vis inertia_ of the
Hindustani is very great, hence their tendency to amalgamation is
small. They remain in the state in which they happen to be.
On the other hand the inertia of Englishmen is small, of Englishwomen
smaller, and therefore their power of combining is greater. Here let me
observe that the quality of inertia is one which ought to be removed as
far as possible from each social system. Inertia was regarded as a
capital crime by the Egyptians. Solon ordained that inert persons should
be put to death, and not contaminate the community. As savages bury
living men, so does inertia practise the same barbarous custom upon
States and individuals. Observe the putrid state of inert water, the
clear and sparkling beauty of the moving stream, bearing away by the
force of its own motion aught that might contaminate it. Men more often
resemble the stagnant water than the rivulet. A healthy social state
enforces labour by natural laws, and banishes inertia as much as
possible from the system. If the principles of some noisy English
politicians were fully carried out, and all things made '_free_,'
inertia would be increased, and listless indolence pervade the masses of
our countrymen. I may say that inertia is not entirely unknown in our
sister University of Cambridge.
The existence of social forces is supported by the testimony of Dr.
Tyndall, who plainly recognises their power, though he does not attempt
to expound their origin. 'Thoughtful minds are driven to seek, in the
interaction of social forces, the genesis and development of man's moral
nature. If they succeed in their search--and I think they are sure to
succeed--social duty would be raised to a higher level of significance,
and the deepening sense of social duty would, it is to be hoped, lessen,
if not obliterate, the strife and heart-burnings which now beset and
disguise our social life.' I accept with gratification Dr. Tyndall's
conclusions: to determine, examine, trace, calculate these social forces
which exercise such a powerful influence on our characters, our lives,
our customs, which produce the greatness of the State, or drag it down
with irresistible strength from its pinnacle of glory to an abyss of
degradation; to estimate such forces is the great and noble object of
our lectures and researches in this University. Prosecute, most noble
professors, your studies in this direction with all the energy of your
enlightened intellects, and there is yet hope that this new science,
which I have endeavoured to sketch out, however feebly, may be the means
of saving our beloved nation from degradation and ruin, and raising her
to a higher level of glory and honour. I hope to continue the subject of
social forces in my next lecture.
[6] A Chinese legend relates that a pious hermit, who in his
watchings and prayers had often been overtaken by sleep, so
that his eyelids closed, in holy wrath against the weakness
of the flesh, cut them off, and threw them on the ground. But
a god caused a tea-shrub to spring out of them, the leaves of
which exhibit the form of an eyelid bordered with lashes, and
possess the gift of hindering sleep.--Dr. Ure.