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                              THE
                    ROMANCE OF MATHEMATICS.




                              The
                    Romance of Mathematics:

                             BEING
                    THE ORIGINAL RESEARCHES
                               OF
              A LADY PROFESSOR OF GIRTHAM COLLEGE
                               IN
      _Polemical Science, with some Account of the Social
           Properties of a Conic; Equations to Brain
               Waves; Social Forces; and the Laws
                     of Political Motion._


                               BY
                       P. HAMPSON, M.A.,
                     ORIEL COLLEGE, OXFORD.


                            LONDON:
               ELLIOT STOCK, 62, PATERNOSTER ROW.
                             1886.




INTRODUCTION.


The lectures, essays, and other matter contained in these pages have
been discovered recently in a well-worn desk which was formerly the
property of a Lady Professor of Girtham College; and as they contain
some original thoughts and investigations, they have been considered
worthy of publication.

How they came into the possession of the present writer it is not his
intention to disclose; but inasmuch as they seemed to his unscientific
mind to contain some important discoveries which might be useful to the
world, he determined to investigate thoroughly the contents of the
mysterious desk, and make the public acquainted with its profound
treasures. He found some documents which did not refer exactly to the
subject of 'Polemical Mathematics;' but knowing the truth of the Hindoo
proverb, 'The words of the wise are precious, and never to be
disregarded,' and feeling sure that this Lady Professor of Girtham
College was entitled to that appellation, he ventured to include them in
this volume, and felt confident that in so doing he would be carrying
out the intention of the Authoress, had she expressed any wishes on the
subject. In fact, as he valued the interests of the State and his own
peace of mind, he dared not withhold any particle of that which he
conceived would confer a lasting benefit on mankind.

Internal evidence seems to show that the earlier portion of the MS. was
written during the period when the authoress was still _in statu
pupillari_; but her learning was soon recognised by the Collegiate
Authorities, and she was speedily elected to a Professorship. Her
lectures were principally devoted to the abstruse subject of Scientific
Politics, and are worthy of the attention of all those whose high duty
it is to regulate the affairs of the State.

The Editor has been able to gather from the varied contents of the desk
some details of the Author's life, which increase the interest which her
words excite; and he ventures to hope that the public will appreciate
the wisdom which created such a profound impression upon those whose
high privilege it was to hear the lectures for the first time in the
Hall of Girtham College.




CONTENTS.


  PAPER                                                             PAGE
    I. Some Remarks on Female Education:

         Cambridge Man's Powers of Application.--Torturing Ingenuity
         of Examiners.--Slaying an Enemy.--'Concentration.'--
         'Tangential Action.'--'Gravity'                               1

   II. Lecture on the Theory of Brain Waves and the Transmigration
       and Potentiality of Mental Forces                              15

  III. The Social Properties of a Conic Section, and the Theory of
       Polemical Mathematics:

        'Circle.'--'Parabola.'--'Ellipse.' 'Eccentricity of Curves'   25

   IV. The Social Properties of a Conic Section (_continued_):

        'Ellipse.'--Most favoured State.--Alarming Result of
         Suppression of House of Lords.--Analogies of Nature.--
         Directrix.--Contact of Curves and States.--'Hyperbola.'--
         Problems.--Radical Axis and Patriotism.--Extension of
         Franchise to Women.--Correspondence                          39

    V. Social Forces, with some Account of Polemical Kinematics:

         The Use of Imagination in Scientific Discovery.--Kinetic and
         Potential Energy.--Social Statics and Dynamics.--Attractive
         Forces.--Cohesion.--Formation of States.--Inertia.--Dr.
         Tyndall on Social Forces                                     71

   VI. Social Forces (_continued_): Polemical Statics and Dynamics:

        'Personal Equation.'--Public Opinion, how calculated.--
         Impulsive Forces.--Friction.--Progress                       89

  VII. Laws of Political Motion:

         M. Auguste Comte on Political Science.--First Law of
         Motion.--The Biology of Politics.--Stages of Growth and
         Decay of States.--Doctrine of Nationality.--Doctrine of
         Independence.--Law of Morality.--Ignorance of Electors and
         Selfishness of Statesmen opposed to Action of Law.--Final
         'Reign of Law'                                              101

 VIII. The Principle of Polemical Cohesion:

         Centralization.--Co-operation of States.--Marriage.--Trade
         Unions.--International Law                                  115

       Extracts from the Diary of the Lady Professor                 125

       Conclusion                                                    129




PAPER I.

SOME REMARKS OF A GIRTHAM GIRL ON FEMALE EDUCATION.


[_This essay upon Female Education was evidently written when the future
Professor of Girtham College was still in the lowlier condition of
studentship, before she attained that eminence for which her talents so
justly entitled her. Its unfinished condition tends to show that it was
probably evolved during moments of relaxation from severer studies,
without any idea of subsequent publication._]

Oh, why should I be doomed to the degradation of bearing such a foolish
appellation! A Girtham Girl! I suppose we have to thank that fiend of
invention who is responsible for most of the titular foibles and follies
of mankind--artful Alliteration. The two _G_'s, people imagine, run so
well together; and it is wonderful that they do not append some other
delectable title, such as 'The Gushing Girl of Girtham,' or 'The Glaring
Girl of Glittering Girtham.' O Alliteration! Alliteration! what crimes
have been wrought in thy name! Little dost thou think of the mischief
thou hast done, flooding the world with meaningless titles and absurd
phrases. How canst thou talk of 'Lyrics of Loneliness,' 'Soliloquies of
Song,' 'Pearls of the Peerage'? Why dost thou stay thine hand? We long
for thee to enrich the world with 'Dreams of a Dotard,' the 'Dog
Doctor's Daughters,' and other kindred works. Exercise thine art on
these works of transcendent merit, but cease to style thy humble, but
rebellious, servant a Girtham Girl!

But what's in a name? Let the world's tongue wag. I am a student, a
hard-working, book-devouring, never-wearied student, who burns her
midnight oil, and drinks the strong bohea, to keep her awake during the
long hours of toil, like any Oxford or Cambridge undergraduate. I often
wonder whether these mighty warriors in the lists--the class lists, I
mean--really work half so hard as we poor unfortunate 'Girls of
Girtham.' Now that I am writing in strict confidence, so that not even
the walls can hear the scratchings of my pen, or understand the meaning
of all this scribbling, I beg to state that I have my serious doubts
upon the subject; and when last I attended a soirée of the
Anthropological Society, sounds issued forth from the windows of the
snug college rooms, which could not be taken as evidences of profound
and undisturbed study.

Sometimes I glance at the examination papers set for these hard-working
students, in order that they may attain the glorious degree of B.A., and
astonish their sisters, cousins, and aunts by the display of these magic
letters and all-resplendent hood. And again I say in strict confidence
that if this same glorious hood does not adorn the back of each
individual son of Alma Mater, he ought to be ashamed of himself, and not
to fail to assume a certain less dignified, but expressive,
three-lettered qualification. But before those Tripos Papers I bow my
head in humble adoration. They sometimes take my breath away even to
read the terrible excruciating things, which seem to turn one's brain
round and round, and contort the muscles of one's face, and stop the
pulsation of one's heart, when one tries to grasp the horrid things.

Here is a fair example of the ingenuity of the hard-hearted examiners,
who resemble the inquisitors presiding over the tortures of the rack,
and giving the hateful machine just one turn more by way of bestowing a
parting benediction on their miserable victims:

'A uniform rod' (it is a marvellous act of mercy that the examiner
invented it _uniform_; it is strange that its thickness did not vary in
some complicated manner, and become a veritable birch-rod!) 'of length
_2c_, rests in stable equilibrium' (stable! another act of leniency!),
'with its lower end at the vertex of a cycloid whose plane is vertical'
(why not incline it at an angle of 30°?) 'and vertex downwards, and
passes through a small, smooth, fixed ring situated in the axis at a
distance _b_ from the vertex. Show that if the equilibrium be slightly
disturbed, the rod will perform small oscillations with its lower end
on the arc of the cycloid in the time

           +-------------------
           | a{c² + 3(b - c)²}
    4[pi]\ | ----------------- ,
          \|    3g(b² - 4ac)

where _2a_ is the length of the axis of the cycloid.'

A sweet pretty problem, truly! And there are hundreds of the same
kind--birch-rods for every back! How the examiner must have rejoiced
when he invented this diabolical rod, with its equilibrium, its
oscillations, its cycloid, and other tormenting accessories. And yet, I
suppose, before my days of studentship are over, I shall be called upon
to attack some such impregnable fortresses of mathematics, when I hope
to be declared equal to some twentieth wrangler, if I escape the
misfortune of sharing a portion of the 'wooden spoon.'

Ah, you male sycophants! You would prevent us from competing with you;
you would separate yourselves on your island of knowledge, and sink the
punt which would bear us over to your privileged shore. Of all the
twaddle--forgive me, male sycophants!--that the world has ever heard, I
think the greatest is that which you have talked about female education.
And the best of it is, you are so anxious about our welfare; you are so
afraid that we should injure our health by overmuch mental exertion; you
profess to think that our brains are not calculated to stand the strain
of continued mental exercise; you think that competition is not good for
the female mind; that we are too competitive by nature--too ambitious!
Yes, we are so ambitious that we would enter the lists with those who
are asked in Public Examinations to find the simple interest on £1,000
for 5 years at 6¼ per cent.; so ambitious that we would compete with
those who are requested to disclose the first aorist middle of [Greek:
tuptô]. Oh, think of the mental strain involved in such questions! How
it must ruin your health to find out how many times a wheel of radius 6
feet will turn round between York and London, a distance of 200 miles!
It is quite wonderful how your brains, my dear male sycophants, can
stand such fearful demands upon your intelligence and industry!

But you are so kind to us, so afraid of our health! Really, we are much
obliged to you. If you married one of us, or became our guardian, or
left us a legacy, we should then recognise your interest in us, and be
very grateful to you for your good advice. But as matters stand, we are
quite capable of taking care of ourselves. We will promise not to work
too hard, if you will promise not to weary us with your paternal
jurisdiction.

But, male sycophants, I want a word with you. Why do you object to our
taking degrees, or going in for examinations in order to qualify
ourselves for our duties in life? You need not speak out loud if you
would rather not. Are you not just a little afraid that we might eclipse
you? And it is not pleasant to be beaten by a woman, is it? And then you
profess to think that we ought to be all housewives and cooks, and
knitters of stockings, and sewers-on of our husbands' buttons; but what
if we have no husbands, no buttons to sew? And is it not a little
selfish, my dear male sycophant, to wish to keep us all to yourself? to
attend upon the wants of the lords of creation, who often distinguish
themselves so much in the domain of science?

Now, look me straight in the face (no shirking, sir!). Is it not
jealousy--green-eyed, false-tongued jealousy--which saps your generous
instincts, and makes you talk rubbish and nonsense about strains, and
brains, and ambition, and the like? And if that is not hypocritical, I
do not know what is.

Well, good-day to you, male sycophant! I really have not time to indulge
myself in scolding you any more. You are a good creature, no doubt; and
when you have shown us what you can do, and can estimate the capacity of
the female brain, and take a common-sense view of things, we will
recognise your privilege to speak; and when I am the presiding genius of
Girtham College, I will grant you the use of our hall for the purpose of
lecturing to us on 'Women's Rights,' or, as you may prefer to entitle
your discourse, 'Men's Wrongs.'

       *       *       *       *       *

Oh, this is shameful! I really am very sorry. Here have I been wasting a
good half-hour in dreaming, and slaying an imaginary enemy with
envenomed words and frequent dabs of ink. If I cannot concentrate my
mind more on these mathematical researches, I fear a dreadful 'plough'
will harrow my feelings at the end of my sojourn in these halls of
learning.

Concentration! How many of our words and ideas and thoughts are derived
from that primal fount of all arts and sciences--mathematics! Here is
one which owes its origin to the mathematically trained mind of some
early philological professor, who had learnt to apply his scientific
knowledge to the enrichment of his native tongue. He quoted to himself
the words of the Roman poet:

            'Ego cur, acquirere pauca
    Si possum, invideor, cum lingua Catonis et Ennî
    Sermonem patrium ditaverit, et nova rerum
    Nomina protulerit? Licuit, semperque licebit.'

His mind conceived endless figures of circles and ellipses scattered
promiscuously over the page, defying the attempts of the student to
reduce them to order. What must he do before he can apply his formulæ
and equations, determine their areas, or describe their eccentric
motion? He must reduce them to a common centre, and then he can proceed
to calculate the abstruse problems in connection with the figures
described. They may be the complex motions of double-star orbits, or the
results of the impact of various projectiles on the tranquil surface of
a pool. It matters not--the principle is the same; he must concentrate,
and reduce to a common centre.

This is the great defect of those who have no accurate mathematical
knowledge; they cannot concentrate their minds with the same degree of
intensity upon the work which lies before them. Their thoughts fly off
at a tangent, as mine do very often; but then I have not been classed
yet in the Tripos; and, O male poetical sycophant, you may be right
after all when you say:

   'O woman! in our hours of ease
    Uncertain, coy and hard to please,
    As variable as the noon-day shade.'

Yes, as variable as the most variable quantities _x_, _y_, _z_. I, a
student of Girtham College, blush to own that my thoughts very often fly
off at a tangent.

'Fly off at a tangent!' All hail to thee, most noble mathematical
phrase! Here is another fine mathematical expression, plainly
exemplifying the action of centrifugal force. The faster the wheel
turns, the greater is the velocity of the discarded particles which fly
off along the line, perpendicular to the radius of the circle. The world
travels very fast now; the increased velocity of the transit of earthly
bodies, the rate at which they live, the multiplicity of engagements,
etc., have made the social world revolve so fast that the speed would
have startled the torpid life of the last century. And what is the
result? Men's thoughts fly off at a tangent; they are unable to
concentrate their minds on any given subject; they are content with
hasty generalisms, with short magazine articles on important subjects,
which really require large volumes and patient study to elucidate them
fully.

What we want to do is to increase the attractive force, in order to
prevent this tangential motion--to increase the _force of gravity_.

'Well,' says the young lady who loves to revel in the 'Ghastly Secret of
the Moated Dungeon,' or the 'Mysteries of Footlight Fancy,' 'you are
_grave_ enough. Pray don't increase your gravity!'

Thank you, gentle critic. I will, in turn, ask you one favour. Leave for
once the 'Mysteries of Footlight Fancy;' seek to know no more 'ghastly
secrets,' and increase _your gravity_--your mental weight; and hence
your attraction in the eyes of all who are worth attracting will be
marvellously increased, by understanding a little about Newton's law of
universal gravitation, and don't fly off at a tangent.

       *       *       *       *       *

At the end of this portion of the MS. the editor of these papers
discovered a photograph which, from subsequent inquiry, proved to be
that of the accomplished authoress of the above reflections. The face
is one of considerable beauty, with eyes as clear, steadfast, and open
as the day. There is a degree of firmness about the mouth, but it is a
sweet and pretty one notwithstanding; and a smile, half scornful, half
playful, can be detected lurking about the corners of the lips, which do
not seem altogether fitted for pronouncing hard mathematical terms and
abstruse scientific problems. This photograph might have been the
identical one which nearly brought an enamoured youth into grave
difficulties by its secretion in the folds of his blotting-paper during
examination. The said enamoured youth had evidently placed it there for
the sake of its inspiring qualities; and it was said that all his hopes
of gaining the hand of the fair original depended upon his passing that
same examination. But the wakeful eye of a stern examiner had watched
him as he turned again and again to consult the sweet face which beamed
from beneath his blotting-paper; and he narrowly escaped expulsion from
the Senate-house on the charge of 'cribbing.' Certainly he took a mean
advantage of his fellow-sufferers, if this were the identical
photograph, for it portrays a most inspiring face. Forgive us, lenient
reader; one moment! There--thank you--we have done. And now we will
proceed to disclose the researches and original problems which the MS.
contains.

Evidently the collegiate authorities were not slow in recognising the
talents of the assiduous student, and elected her without much delay to
a Professorship of Girtham. In this capacity the learned lady delivered
several lectures, of which the second MS. contains the first of the
series.




PAPER II.

LECTURE ON THE THEORY OF BRAIN WAVES AND THE TRANSMIGRATION
AND POTENTIALITY OF MENTAL FORCES.


Professors and Students of the University of Girtham, my Lords, Ladies,
and Gentlemen,--I have the honour to bring before you this evening some
original conceptions and discoveries which have been formulated by me
during my researches in the boundless field of mathematical knowledge;
and though you may be inclined at first to pronounce them as somewhat
hastily conceived hypotheses, I hope to be able to demonstrate the
actual truth of the propositions which I shall now endeavour to
enunciate. It is with some feelings of diffidence that I stand before so
august an assembly as the present; and if I were not actually convinced
of the accuracy of my calculations, I should never have presumed to
appear before you in the character of a lecturer. But '_Magna est
veritas, et prævalebit_.' I cast aside maiden timidity; I clothe myself
in the professorial robe which you have bestowed upon me, and sacrifice
my own feelings on the altar of Truth.

I have been engaged, as you are doubtless aware, for some years in the
pursuit of mathematical research, exploring the mines of science, which
have of late been worked very persistently, but often, like the black
diamond mines, at a loss. Concurrently with these researches, I have
speculated on the great social problems which perplex the minds of men,
both individually and collectively. And I have come to the conclusion
that the same laws hold good in both spheres of work; that methods of
mathematical procedure are applicable to the grand social problems of
the day and to the regulation of the mutual relations which exist
between man and man. Take, for example, the Force of public opinion. Of
what is it composed? It is the Resultant of all the forces which act
upon that which is generally designated the 'Social System.' Public
opinion is a compromise between the many elements which make up human
society; and compromise is a purely mechanical affair, based on the
principle of the Parallelogram of Forces. Sometimes disturbing forces
exert their influence upon the action of Public Opinion, causing the
system to swerve from its original course, and precipitating society
into a course of conduct inconsistent with its former behaviour; and it
is the duty of the Governing Body to eliminate as far as possible such
disturbing forces, in order that society may pursue the even tenor of
its way.

Professors, we have one great problem to solve; and all questions
social, political, scientific, or otherwise, are only fragments of that
great problem. All truths are but different aspects of different
applications of one and the same truth; and although they may appear
opposed, they are not really so; and resemble lines which run in
various directions, but lovingly meet in one centre.

Now, let us take for our consideration the secret influence which men
exert upon each other, apart from that produced by the power of speech
(although that would come under the same general law). As
mathematicians, you are aware that the undulatory theory of light and
heat and sound are now accepted by scientific men as the only sure basis
of accurate calculation. We know that the rays of light travel in waves,
and the equation representing the waves is

         a       2[pi]
    y = --- sin ------ (vt - r),
         r     [lambda]

where _y_ is the disturbance of the ether, _a_ the initial amplitude,
_r_ the distance from the starting-point, [lambda] the wave-length, and
_v_ the velocity of light. Sound and heat likewise have much the same
form of equation. Now, I maintain that the waves of thought are governed
by the same laws, and can be determined by an equation of the same form.
You are aware that in all these equations a certain quantity denoted by
[lambda] appears, and varies for the different media through which the
sound, or light, or heat passes, and which must be determined by
experiment Now, in my equation for brain waves, the same quantity
[lambda] appears which must be determined by the same method--by
_experiment_. But how is this to be done? After mature deliberation and
much careful thought, I have discovered the method for finding [lambda].
This method is _mesmerism_. We find the ratio of brain to brain--the
relative strength which one bears to another; and then by an application
of our formula we can actually determine the wave of thought, and read
the minds of our fellow-creatures. An unbounded field for reflection and
speculation is here suggested. Like all great discoveries, the elements
of the problem have unconsciously been utilized by many who are unable
to account for their method of procedure. For example, thought-readers,
mesmerists, and the like, have unconsciously been working on this
principle, although lack of mathematical training has prevented them
from fully mastering the details of the problem. Hence in popular minds
a kind of mystery has hung about the actions of such people, and excited
the curiosity of mankind.

The development of this theory of brain waves may be of great practical
utility to the world. It shows that great care ought to be exercised in
the domain of thought, as well as that of speech. For example: A man has
made a startling discovery, from which he expects to receive
considerable worldly advantage. He would be careful not to disclose his
discovery in speech to his acquaintances until his plans are
sufficiently matured, lest they should impart it to the world, patent
his device, and reap the reward. But while he is endeavouring to talk
carelessly about it, the wave of thought may be travelling from brain to
brain, suggesting the existence of the discovery; and if the conditions
are favourable, and [lambda] sufficiently small, it is possible that the
idea itself may be conveyed. Of course the more complicated the
discovery, the less likely would the wave convey the conception. Or
suppose that one of the learned professorial body of our sister
university should conceive an attachment for a lady-student of Girtham
College (of course a very improbable supposition!), and the infatuated
_savant_ became somewhat jealous of another learned lecturer of the same
college (another improbability!), the fact of his jealousy would be
imparted to the latter by a wave of thought, and might cause
considerable confusion in the serene course of love or science. The fact
of the existence of the wave is indisputable. What do all the stories of
impressions and double-sight teach us? How could the intelligence of the
death of Professor Steele have been conveyed to his friend and
fellow-student, Professor Tait--the one at Cambridge, the other at
Edinburgh--were it not for the existence of some wave, which, like that
of electricity, wings its rapid flight unobserved by human eyes? Are all
the records of the Psychical Society only myths and legends bred of
superstitious fancy? It were hard to suppose so.

But if, gentlemen, and ladies especially, you wish to keep your secret
discoveries to yourselves, watch over your thoughts as well as your
words; for my researches prove, and the universal experience of mankind
corroborates the fact, that some portion of your inmost thoughts and
secret desires are understood by your neighbours (especially when
[lambda] is small!); that they travel along the waves which I have
attempted to indicate; and if you would desire to extend your influence
in the world, probe the secret instincts of mankind, and prevent
yourself from being deceived and wronged--study the art and science of
Brain Waves.

       *       *       *       *       *

The following verses of rather doubtful merit were found in connection
with the previous MS. They were evidently written by a different hand;
but inasmuch as they were deemed worthy of preservation by the learned
owner of the sealed desk, we venture to publish them. They are closely
connected with the previous lecture, and were evidently composed by an
admirer of the fair lecturer who did not share her love for scientific
research.

    Wavelet,[1] wing thy airy flight;
      Let thine amplitude be great;
    Tell her all my thoughts to-night,
      How I long to know my fate.

    All the fields of Mathematics
      I have roamed at her decree;
    From Binomial and Quadratics,
      To the strange hyperbole.[2]

    I have soared through Differential,
      Deeply drunk of Finite Boole;[3]
    Though its breath is pestilential,
      Reeking of the hateful School.

    I have tried to shape a Conic,
      Vainly read the Calculus;
    But my feebleness is chronic,
      _Morbus Mathematicus_.

    All my curves are cardioidal;
      I confuse my _x_ and _y_s,
    Which they say is suicidal;
      And my tutor vainly sighs.

    Wavelet, tell her how I love her,
      As she mounts her learned throne;
    And that love I hope may cover
      All the failings which I own.

    Wavelet, cry to her for pity;
      Bid her end this bitter woe;
    I might do something 'in the city,'
      But never pass my Little-go.


  [1] We presume this is addressed to an imaginary brain wave.

  [2] We observe here the dash of an indignant pen, and a substituted
      for e. But now the rhyme is spoiled. Gentle Muse, thou art
      sacrificed by the stern hand of Mathematical Truth!

  [3] Query: Does the writer refer to the learned treatise on Finite
      Differences by Professor Boole?




PAPER III.

LECTURE ON THE SOCIAL PROPERTIES OF A CONIC SECTION,
AND THE THEORY OF POLEMICAL MATHEMATICS.


Most Learned Professors and Students of this University,--From the
interest manifested in my first lecture, I conclude that my method of
investigation has not proved altogether unsatisfactory to you, and I
hope ere long to produce certain investigations which will probably
startle you, and revolutionize the current thought of the age. The
application of mathematics to the study of Social Science and Political
Government has curiously enough escaped the attention of those who ought
to be most conversant with these matters. I shall endeavour to prove in
the present lecture that the relations between individuals and the
Government are similar to those which mathematical knowledge would lead
us to postulate, and to explain on scientific principles the various
convulsions which sometimes agitate the social and political world.

Indeed, by this method we shall be able to prophesy the future of states
and nations, having given certain functions and peculiarities
appertaining to them, just as easily as we can foretell the exact day
and hour of an eclipse of the moon or sun. In order to do this, we must
first determine the _social properties of a conic section_.

For the benefit of the unlearned and ignorant, I will first state that a
cone is a solid figure described by the revolution of a right-angled
triangle about one of the sides containing the right angle, which
remains fixed. The fixed side is called the axis of the cone. Conic
sections are obtained by cutting the cone by planes. It may easily be
proved that if the angle between the cutting plane and the axis be equal
to the angle between the axis and the revolving side of the triangle
which generates the cone, the section described on the surface of the
cone is a parabola; if the former angle be greater than the latter, the
curve will be an ellipse; and if less, the section will be a hyperbola.

But the simplest conic section is, of course, a circle, which is formed
by a plane at right angles to the axis of the cone; and the simplest
circle is that formed by a plane passing through the apex of the cone.
All this is simple mathematics; and let beginners consult more
elementary treatises than this one to satisfy themselves on these
points. But if they will assume these things to be true, they will know
quite enough for our present purpose. The simplest conic section of all
has been proved to be a _point_. Now, this represents the simplest and
original form of society, a _single family_. 'It is not good for man to
be alone' was the first observation made by the wise Creator upon the
rational creature whom He had introduced into Paradise as its lord.
Marriage is the rudiment of all social life, from which all others
spring, out of which all others are developed. Around the parents'
knees soon cluster a group of children, and in their relation to each
other we discern the earliest forms of law and discipline--the bonds by
which society is held together. When the children grow up, separate
households are formed; and then the multiplication of families, the
congregating of men together for purposes of security and mutual
advantages in division of labour; and thus is gradually formed a state,
which is only the development of the family--the king representing the
parent, and ruling on the same principle.

Mathematically speaking, our plane no longer passes through the apex.
The point represented the single family; but keeping the plane
horizontal, we move it along the axis, the sections will become
_circles_, which represent mathematically the next simplest form of
society, where the centre is the seat of government, which is connected
with each individual member of the social circle by equal radii. The
social property of a circle is that of a monarchical government in its
purest and simplest form. The larger the circle becomes (_i.e._, the
further you move the plane from the apex), the greater the distance
between the individual and the monarch. Therefore, the more independent
the monarchy becomes, and the less influence do individuals possess over
the ruling power. Hence, we may infer that as years roll on, the
government will become more despotic; but the stability of the country
diminished, and probably some individual particle, when sufficiently
withdrawn from the attraction of the central head, will begin to revolve
on its own account, and spontaneously generate a government of its own.
We may, therefore, conclude from mathematical reasoning that an
unlimited monarchy, though advantageous for small states, is not a safe
form of government for a large or populous country, inasmuch as the
people do not derive much benefit from the sovereign; the mutual
attraction, which ought to exist in a flourishing state between the
ruler and the ruled, is weakened; and the isolation of the monarch
tends to make him still more despotic. As a practical example of the
truth of the foregoing statement, I may mention the present condition of
Russia, which shows that the result of an unlimited monarchy, in a large
and unwieldy social circle, is such as we should have reasonably
expected from mathematical investigations.

Invariably, under the circumstances which I have described, the country
will become disorganized; the sovereign will cease to have any power
over the people, and the country will become a chaos, without order,
influence, or power.

When the centre of a conic section moves along the axis of the curve to
infinity, banished by the mutual consent of the individual particles
which compose the curve, or the nation, a figure is formed, called a
_parabola_. This is the curve which the most erratic bodies in the
universe describe in space, as they rush along at a speed inconceivable
to human minds, and are supposed to produce all kinds of mischief and
injury to the worlds whose courses they wend their way among.

This curve, then, represents the position which the nation assumes when
the constituted monarchy, the centre of the system, has been _banished
to infinity_. A revolution has occurred; the monarch has been dethroned;
and it is not hard to see that the same erratic course which the comet
pursues in its flight, is observable with respect to the social system
which is represented by a parabola. We observe with eager scrutiny the
wanderings of these erratic comets. They appear suddenly with their
vapoury tails; sometimes they shine upon us with their soft, silvery
light, brilliant as another moon; sometimes they stand afar off in the
distant skies, and deign not to approach our steady-going earth, which
pursues its regular course day by day, and year by year. Then, after a
few days' coy inspection of our planet from different points of view,
they fly to other remote parts of the universe, and do not condescend to
show themselves again for a hundred years or so. Such is the erratic
conduct of a heavenly body whose course is regulated by a parabolic
curve.

We may look for similar eccentric behaviour on the part of a community,
nation, or state, whose centre is at infinity, whose constitution has
been violently disturbed, and whose monarchy is situated in the far-off
regions of unlimited space. The erratic course of Republican rule is
proverbial. There is no stability, no regularity. To-day we may observe
its brilliancy, which seems to laugh at and eclipse the sombre shining
of more steady and enduring worlds; but ere to-morrow's moon has risen,
it may have vanished into the regions of eternal night, and we look for
its bright shining light in the councils of the nations, but it has
ceased to shed its rays, and we are disappointed. Sometimes it is asked,
with fear and trembling: 'What would be the effect if our earth were to
come in contact with the tail of a comet? Should we be destroyed by the
collision, and our ponderous world cease to be?' But we are assured
that no such disastrous results would follow. We have already passed
through the tails of many comets, but we have not discovered any
inconvenient change in our ordinary mode of procedure. It is probable
that the comet's tail is composed of no solid substance.

We may therefore infer by analogy that a Republican State would not
offer any powerful resistance if it were to come into collision with a
nation possessing a more settled form of government. A shower of
meteoric stones, like passing fireworks, might take place; but beyond
that nothing would occur to excite the fear, or arouse the energies of
the more favoured nation. As an example of the weakness of a Republican
State I may mention France. There we see an industrious race of people,
endowed with many natural gifts and graces, a country rich and
productive; and yet, owing to the unsettled nature of its government,
all these natural advantages are neutralized; its course amongst the
nations is erratic in the extreme, a spectacle of feeble
administration; and it would offer no more resistance to a colliding
Power than the empty vacuum of a comet's tail. This example will
demonstrate to you the truth of our theory with regard to the
instability of a social system which is geometrically represented by a
parabolic curve.

We will now turn from this picture of insecurity and unrest to another
figure which possesses most advantageous social properties. I refer to
the ellipse. An ellipse is a curve formed by the section of a cone by a
plane surface inclined at an angle to the vertical axis of the cone,
greater than the angle between the axis and the generating line.

Now, this is a curve which possesses most attractive properties. It is
the curve which the earth and other planetary orbs describe around the
centre of the solar system, as if nature intended that we should take
this figure as a guide in choosing the most advantageous social system.
It possesses a centre, C, in view of all the particles which compose the
curve, and connected with them by close ties. It has two foci, S and
S', fixed points, by the aid of which we may trace the curve.

In the interpretation of this figure, the centre of the curve represents
the throne of monarchy. There is no tendency here to revolutionize the
State, to banish the ruling power, and institute a Republican form of
government; but inasmuch as we saw the weakness of an absolute monarchy
in large and populous States, as represented by the circle, the wisdom
of an elliptical social system has ordained that there shall be two
foci, or houses of representatives of the people, who shall assist in
regulating the progress of the nation. Here we have a limited monarchy;
the throne is supported by the representatives of the people; and the
nearer these foci of the nation are to the centre (_i.e._, in
mathematical language, the less the _eccentricity_ of the curve), the
more perfect the system becomes--the greater the happiness of the
community.

In cases where the _eccentricity_ becomes very great, the beauty of the
curve is destroyed, and ultimately the ellipse is merged into one
straight line. Most learned Professors, here we have a terrible warning
of the awful result of too much eccentricity. Whether we regard the life
of the nation or of the individual, let all bear in mind this alarming
fact, that eccentricity of thought, habit, or behaviour may result, as
in the case of this unfortunate ellipse, which once presented such fair
and promising proportions to the student's admiring gaze, in the
'sinister effacement of a man,' or the gradual absorption of a State
into an uninteresting thing 'which lies evenly between its extreme
points.'

The great examples of Bacon, of Milton, of Newton, of Locke, and of
others, happen to be directly opposed to the popular inference that
eccentricity and thoughtlessness of conduct are the necessary
accompaniments of talent, and the sure indications of genius. I am
indebted to Lacon for that reflection. You may point to Byron, or
Savage, or Rousseau, and say, 'Were not these eccentric people
talented?' 'Certainly,' I answer; 'but would they not have been better
and greater men if they had been less eccentric--if they had restrained
their caprice, and controlled their passions?' Do not imagine, my young
students of this university, that by being eccentric you will therefore
become great men and women of genius. The world will not give you credit
for being brilliant because you affect the extravagances which sometimes
accompany genius. Some of you ladies, I perceive, have adopted a
peculiar form of dress, half male, half female; or, to be more correct,
three-fourths male, and one-fourth female. Do not imagine that you will
thus attain to the highest honours in this university by your
eccentricity, unless your talents are hid beneath your short-cut hair,
and brains are working hard under your college head-gear. As well might
we expect to find that all females who wear sage-green and extravagant
æsthetic costumes are really born artists and future Royal Academicians.
It is apparent that many aspirers to fame and talent are eager to
exhibit their eccentricities to the gaze of the world, in order that
they may persuade the multitude that they possess the genius of which
eccentricity is falsely supposed to be the outward sign.

I may remark in passing that the eccentricity of a parabolic curve is
always _unity_. What does this prove? You will remember that a
Republican State is represented by a parabola. Therefore, however such a
nation may strive to alter its condition, and secure a settled form of
government, its eccentricity will always remain the same. It will always
be erratic, peculiar, unsettled; and this conclusion substantiates our
previous proposition with regard to the condition of a social system
represented by a parabola.

With regard to other advantages afforded by an elliptical social system,
we will defer the consideration of this important subject until my next
lecture.




PAPER IV.

THE SOCIAL PROPERTIES OF A CONIC SECTION,
AND THE THEORY OF POLEMICAL MATHEMATICS--(_continued_).


Most learned Professors and Students of this University,--You have
already gathered from my preceding lecture my method of procedure in the
investigation of the corresponding properties of curves and States. You
have perceived that we have here the elements of a new science, which
may be extended indefinitely, and applied to the various departments of
self-government and State control. This new science of polemical
mathematics is in itself an extension of the _principle of continuity_,
for the discovery of which Poncelet is so justly renowned. We can prove
by geometry that the properties of one figure may be derived from those
of another which corresponds to it; and the new science teaches us that
if we can represent, by projection or otherwise, a society of particles
or individuals on a plane surface, the properties of the State so
represented are analogous to the properties of the curve with which it
corresponds. It is only possible for me to touch upon the elements of
the science in these lectures, but I hope to arouse an interest in these
somewhat unusual complications and curious problems, that you may
hereafter make further discoveries in this unexplored region of
knowledge, and that the world may reap the benefit of your labours and
abstruse studies. I have already, in my previous lecture, touched upon
the social properties of the parabola, and examined the constitution of
erratic curves and eccentric nations. It is my intention to-day to speak
of similar problems which arise with reference to elliptical States.

But, first, let me answer an objection which may have occurred to your
minds. Am I wrong in my calculations in attributing too much to the
power and usefulness of forms of government? Does the well-being and
happiness of a nation depend on the government, or upon the individuals
who compose the nation? Most assuredly, I assert, they rest upon the
former. Men love their country when the good of every particular man is
comprehended in the public prosperity; they undertake hazard and labour
for the government when it is justly administered. When the welfare of
every citizen is the care of the ruling power, men do not spare their
persons or their purses for the sake of their country and the support of
their sovereign. But where selfish aims are manifest in Court or
Parliament, the people care not for State officials who are indifferent
to their country's weal; they become selfish too; Liberty hides her
head, and shakes off the dust of her feet ere she leaves that doomed
land, and the stability, welfare, and prosperity of that country cease.

I might refer you to many a stained page of national history in order to
prove this. Compare the closing chapters of the life of the Roman empire
with the record of the brave deeds of its ancient warriors and valorous
statesmen. Grecian preeminence and virtue died when liberty expired. I
agree with Sidney when he writes that it is absurd to impute this to the
change of times; for time changes nothing, and nothing was changed in
those times but the government, and that changed all things. These are
his words: 'As a man begets a man, and a beast a beast, that society of
men which constitutes a government upon the foundation of justice,
virtue, and the common good, will always have men to promote those ends;
and that which intends the advancement of one man's desires and vanity
will abound in those that will foment them.' I may not, therefore, be
altogether wrong in attributing the prosperity and well-being of a
nation to the form of government which it possesses.

We will now proceed to the consideration of the social advantages which
an elliptical State affords. This is the form of government and social
position which we, as a nation, at present enjoy; and from mathematical
considerations I am of opinion that it is the best, and hope that no
change will ever be made in our constitution. You may remember that I
have previously stated that an ellipse has a centre and two foci, in
view of all the particles which compose the curve, and connected with
them by close ties. The centre, in the projected figure, represents the
monarchy, which is limited; and the government is carried on by the aid
of the two houses of representatives of the people, depicted in the
projection by the two foci.

Now the social advantages of the ellipse are given by the fact that the
sum of the distances of any point from the foci is always constant. No
particle is left out in the cold; no one does not possess the advantages
of a social government. Though his distance may be far from the Upper
House, he has the advantage of nearness to the Lower, and _vice versâ_.
The sum of the distances is constant. The extinction of one focus, the
House of Lords, for example, would create a complete disorganization of
the whole system: the other focus would set up a powerful magnetic
attraction, and a curious bulb-shaped curve would be evolved, very
different from the beautiful symmetrical form which the original figure
presented to the eye. The centre of the system would be disturbed; and
it is probable that ere long it would disappear along the axis and be
vanished to infinity. Thus the curve would become a parabola. This is
the alarming result of the extinction of one focus. Abolish the House of
Lords, and you will soon find that the Throne will be disturbed; the
State will become disorganized; the nation will become confused by the
magnetic force of the Lower House, uncounteracted by any other
attraction; and very soon a complete revolution of the whole system
will set in: the monarch will be dethroned, and a Republican form of
government, with all the eccentricities of a parabolic course, will take
the place of a more orderly and settled constitution. This is a plain
deduction from our mathematical investigations; and it behoves all our
statesmen, our philosophers and great men, our fellow-citizens and the
humblest artisans in our manufacturing towns, to weigh well this
alarming result of the abolition of that House which has been threatened
with destruction; and to ascertain for themselves the truths upon which
my proposition and reasoning rest.

I have already observed that the fact that the earth's orbit and that of
other planets are in the form of ellipses; that the curvature of the
earth is nearly the same, ought to guide us in choosing this particular
curve as a model of the projection of a complete and most advantageous
social system.

The circle described on the major axis of an ellipse, is called the
_auxiliary circle_, and affords much assistance in the investigation of
the properties of an ellipse. As we have already shown, the circle
represents the simplest form of monarchical government. Hence, if we
compare the form of government represented by an ellipse (_i.e._, such
as we now enjoy) with that of a system where the king is the only
governing power, we may obtain great assistance in solving complicated
political problems.

In all conics there is a straight line called the 'directrix,' which
represents in social or polemical science the laws of the nation, and
plays a prominent part in the mutual relations of the individual
particles. For instance, in the case of the parabola, the distance of
any particle from the directrix is equal to its distance from the focus.

From this we may conclude that if an individual deviates at all from the
path which the laws (or, directrix) indicate, if he does not show true
respect to the decrees of the focal government, and preserve the true
position between them, directly he is found deviating from his course,
he is quickly banished to a less enlightened sphere. In an ellipse there
is less likelihood of his straying away from the course which the
directrix points out, on account of the two-fold guidance which he
receives from the two foci.

The following curious problem may be noticed. If a parabola roll on
another parabola, their vertices coinciding, the focus of the first
traces out the directrix of the second.

Here we come to the consideration of the international relationship of
States. Two nations have the same form of government (in this example
this form is Republican); their policies coincide: we may conclude from
this proposition that the course which the government of one nation will
pursue, will be that which is prescribed by the laws of the other.

The subject of the contact of curves presents many interesting problems
with reference to Polemical Science, and may be extended indefinitely.
It is well known that there are different orders of contact, which are
designated as the _first_, _second_, or _third_ order. This last order
may be termed the 'marriage of curves,' cemented by the osculating
circle, or 'wedding-ring;' and when two nations have contact of the
third order, they have formed a very close alliance, and by calculation
we can obtain the _radius of curvature_, or size of the wedding-ring, by
means of which they may be united.

The theory and nature of contact constitute a branch of our newly
discovered science which we commend to the careful consideration of
those who have undertaken the difficult and perplexing study of
international law. Alas! too many States refuse this friendly contact,
and, consequently, _cut_ each other, instead of blending in sweet
accord. Their peace is at best an armed neutrality; and if they have
contact of only the _first_ or _second_ order, we can prove
mathematically that they are sure to intersect in some other point or
points; and divergence of policy and disturbed relations are the
results. Contact of the _third, or highest, order_ is the only safe
position for two allied, or contiguous, States.

With your permission I will add a few words to those I have already
uttered with regard to the directrix. As necessary as the directrix is
to the curve, so are the corresponding laws to the State. I will prove
this fact by a few examples. English people have laws, and know how to
obey them; therefore their numbers increase; they thrive and are
prosperous. A friendly critic of another nation has said that the reason
why Englishmen rule the world, is because they know how to obey. On the
other hand, the gipsies have no laws; hence they become fewer and less
powerful. What is the condition of all tribes and nations which are not
governed by laws? They invariably remain poor and miserable. They are in
want of a directrix; and if we could supplement the gift with foci and
centre, they would soon emerge from their savage condition, and become
more civilized.

I have omitted to mention the hyperbolic form of government. The curve
formed by the intersection of the surface of a cone with a plane will be
a hyperbola, when the inclination of the cutting plane to the axis of
the cone is less than the constant angle which the generating line forms
with the axis. It is manifest that the plane will thus intersect the
higher cone, and produce the figure which is known to mathematicians as
the hyperbola.

We may hence deduce the following property of the corresponding
hyperbolic State. We take cognizance of that higher cone with which the
mundane affairs of the lower cone are closely connected. As an example
of this system we may mention the vast temporal rule and power of the
Papal Throne, which formerly exercised such marvellous sway over the
nations of Europe. By an appeal to a Higher Authority than that of
earthly kings and potentates was this rule exercised; but its hyperbolic
form is fast passing away, and degenerating into that of a circle with
indefinitely small radius. We shall not, therefore, discuss the complex
polemical problems which a hyperbolic State suggests.

I will now mention a few problems which are easily capable of proof, and
deduce from them the necessary conclusions which must follow when we
apply our newly discovered principles of polemical science.

1. 'If from any point in a straight line a pair of tangents be drawn to
an ellipse, the chords of contact will pass through a fixed point.'

I will not trouble you with the proof of this proposition, as it is
evident to all mathematicians, and can easily be demonstrated. But mark
well the deductions, when we interpret this mathematical language in
correct polemical terms. A State, through various convulsions of its
own, has merged into a condition represented by a straight line, having
lost its symmetry, its beauty, its curvilinear proportion. An individual
unhappily situated in this unfortunate community regards with longing
eyes the prosperous condition of those who enjoy the social advantages
of a settled form of government, and other blessings which accompany
elliptical jurisdiction and laws. [Two tangents are drawn to an
ellipse.] No matter where the individual may be in the unhappy envious
straight line, the result of his reflection will be the same.
Sympathetic chords are drawn, joining the points of contact of the
tangents with the curve; they all pass through a fixed point. All these
conclusions of the various individuals on the straight line will be the
same. All are of opinion that the elliptical form is the best; and they
mourn in secret over the sad events which have occurred in their own
national life, their eccentricity, their lawlessness, when they see the
advantages which their more staid and sober-minded neighbours so freely
enjoy.

2. The normal at any point of an ellipse bisects the angle between the
focal distances of that point.

The normal is the perpendicular from the point on the major axis; it is
the line of thought directed by the observance of just laws and rules.
Hence this proposition shows that the individual citizen, when guided by
sound judgment, regards with equal favour and entire approval the
existence of both foci, or Houses of Legislature. He considers that both
are necessary to his comfort, and the right regulation of the State's
welfare. He cares not for the _abnormal_ condition of those who talk as
if the existence of either House were unnecessary to his country's weal,
and bestows a pitying glance on those wandering lights, or disturbed
erratic governments, which do not possess the advantages which from
experience he has learned to love and to respect. No matter what his
condition may be, the same opinions are held by all classes, all ranks
and degrees; and if a self-opinionated particle think otherwise, he ought
to be transferred to a less enlightened sphere, and migrate to a
parabolic state, or uninteresting straight line. And when he has changed
his location, he will look back on his old home and old surroundings
with longing eyes and an aching heart, thinking of the blessings he has
lost by his own rash act. This can be proved mathematically. He looks
for an ideal state of society, leaps after the shadow his fancy has
depicted; and when he finds himself outside his former state, he looks
back with longing eyes at the once-scorned focus. What is the focus of a
perpendicular on the tangent of an ellipse from any external point? Can
it not be proved to be a _circle_? That is to say, he will be more
conservative than ever. He would like to return to a primitive form of
government. Farewell to his wild schemes and revolutionary measures!
Farewell to his disestablishments, abolitions, and suppressions! The
throne and government have new attractions in his eyes; loyalty, a new
feeling, asserts its benign influence; and if he could return to his
former position, his normal conduct would be straighter than ever, for
by sad experience he has learned the value of those things which he once
despised.

But we need not depend upon one proof alone. Exactly the same result may
be obtained from the well-known proposition which states that 'the angle
between the tangent from any external point and the focal distance is
equal to the angle between the other tangent and the focal distance.'

3. The same opinions are often held by individuals in quite different
walks and classes of life. Let these individuals be represented by
points on an ellipse. Join these, and we have a system of parallel
chords. Draw a straight line through the middle points of these chords,
and lo! it will always pass through the centre. This shows that the
central thought of all people is directed to the sovereign--that
_loyalty_ is inherent in the hearts of those who recognise elliptical
laws.

I will conclude this lecture with a few remarks on the nature and
properties of the _radical axis_. This name was first given, I believe,
by M. Gaultier, of Tours, and for a full account of its nature I refer
you to the _Journal de l'École Polytechnique_, xvi., 1813. The radical
axis of two circles is the line perpendicular to the line joining the
centres, from any point of which the tangents to the circles are equal.
Let us suppose that one circle becomes a point, and that this point is
situated on the circumference of the first circle. What is the result?
The radical axis becomes the tangent to the circle. Hence we may
conclude that in a social system of monarchical government the radical
axis is perpendicular to the line attaching the individual with the
monarch. Therefore we may conclude that the radical axis indicates a
tendency of particles, or individuals, to fly off at a tangent, at right
angles to the connecting-link between the individual and the king. When
any motion takes place, this is evident, and this tendency is called
centrifugal force. Sad is it for the State when this force is called
into play, and the radical axis is a standing menace to the stability of
States and nations. The only way to counteract its baneful, disturbing
influence is to increase the attraction of the monarch on the
individual, which nullifies the former force, and prevents further
mischief. This is the method which nature itself adopts in the motions
of the planetary worlds; the attraction of the sun prevents any
disturbance which might be caused in the course of the planets by the
action of centrifugal force, and nature suggests this plan for our
adoption. Increase the attraction of the Throne; rigidly connect each
individual by the strong chords of affection, advantage and utility with
the ruling power; and then, though the radical axis may be there, it
will cease to indicate any motion along it, it will not prevail over the
counteracting influence of loyalty, and the stability of the social
system and the happiness of the individuals will be the results.

                 'I would serve my King,
    Serve him with all my fortune here at home,
    And serve him with my person in the wars;
    Watch for him, fight for him, bleed for him, die for him,
    As every true-born subject ought.'

This, most noble professors, is the language of true patriotic loyalty.
Let the monarch be loved and loving, let the laws be just and equal,
happy will be the people, prosperous the realm. There are those who
counsel different things, and preach sedition and the breaking-up of
laws; but those who advocate such doctrines lack that judicial
mathematical training which we, students and professors of Girtham
College, have acquired. If polemical mathematics, the science of the
future, should become more widely studied; if its results were
disseminated far and wide; above all, if the proper position which women
ought to occupy in the counsels of the nation were assigned to them, we
should hear less of these wild schemes and foolish theories, and the
influence of women would tend greatly to promote the stability and
security of the State.

Why, let me ask, should woman be excluded from that position which is so
justly hers? from those duties which she can discharge so faithfully? It
has been said that if we wish to know the political and moral condition
of a State, we must ask what rank women hold in it. We are told that
women have more strength in their looks than men have in their laws.
Why, then, do men debar her from those fields of occupation wherein she
may labour for the nation's good, and use her influence, which they
acknowledge to be great, in those callings wherein she may most easily
benefit the State, and the country she so ardently loves?

At some future time I hope to speak more fully on this subject; and in
concluding this lecture, I will remark that English politics need a
leavening influence which will counteract the evil tendencies and
corrupt theories which, in spite of our advantageous social system, at
present exist; and this leavening influence will be best produced by
the admission of those into the counsels of the nation who are
acknowledged to have a benign and healthy influence--the women of
England. Let women have their proper share in the government of the
country, and I have no fear lest we shall preserve our elliptical
constitution, and all the advantages which we at present enjoy.

       *       *       *       *       *

[Editorial Note.]--In the bundle of papers which contained the foregoing
lectures, some letters of great interest were found, which show that the
fame of the learned Lady Professor of Girtham College had already gone
abroad, and attracted the attention of the leading statesmen of the day.
It is to be regretted that the answers to these letters are not
forthcoming, as it might be proved from them that the science of
polemical mathematics has already influenced the minds of our
legislators in their conduct of affairs at home and abroad. The
following letter is of unique interest, and may be taken as evidence of
the favourable impression which this new science has made on the mind of
one of our greatest thinkers and statesmen:


                    Downing Street,
                            May, 18--

My dear Lady Professor,--The report of the amazing results of your
scientific researches has reached me, and I congratulate you most
heartily on the originality and acumen which you have displayed in your
investigations. A new light has dawned upon our country. Instead of
groping in the darkness of political warfare, ensnared by party ties and
jealousies, the statesmen of the future will be able to calculate and
determine the correct course with mathematical precision and perfect
accuracy. No one can dispute the truth of a proposition in Euclid, or
the genuineness of Newton's laws; and if your method enables men to
calculate and determine the correct political course of action, to solve
political problems as easily as exponential equations, why--then adieu
to the bickerings of party, the querulous complaints of the Opposition!
Nay, joy to the Ministry! There will be no Opposition! Our statesmen
will be able to guide the great ship of the State by means of charts
which know no error; and they will resemble an association of savants
met together to determine the exact moment of the transit of Venus, or
to examine the degree of density of a comet's tail.

This condition of Parliamentary procedure is much to be desired; you
have shown how such an ideal state of things may be obtained. In the
name of the Government I thank you for your endeavours on behalf of your
country's welfare, and look forward to a further development of your
admirably conceived system. As in the domain of ordinary science there
are complex questions which defy the acumen of the philosopher; so in
polemical science there may be questions which present the same
difficulties and complications. But as the first are daily yielding
before the persevering attacks of the mathematician, so I doubt not
polemical science will soon overcome the various problems which may
arise.

But it is mainly on my own account that I venture to address you. I
desire to consult you with regard to certain matters--political
complications--which have recently occupied the attention of Her
Majesty's Ministers. By the help of your new science, can you aid us
in our deliberations? Of course, I am writing to you in _strict
confidence_, and beg that you will keep this communication profoundly
secret. I fear that would be a hard task for many of your sex, who do
not possess your knowledge and powers of mind; but I have great
confidence in your discretion.

These are the problems which are presented to us for solution:

1. Some members of the Cabinet are secretly in favour of Protection, and
the country is rather stirred by the question. Can you, from your
knowledge of the contact of curves and nations, help us to determine
what course we ought to take with regard to Spain, for example? Are the
principles of Adam Smith mathematically correct?

2. I observe that England is represented mathematically by an ellipse.
Are we right in assuming that Ireland is a portion of that ellipse? Or,
on the other hand, in our chart of nations, must we describe that
troublesome country as a rotating parabola, or complex figure,
altogether outside our more favoured State?

3. Do you consider, from your minute observation of our social system,
that the form of our elliptical government is gradually undergoing a
change, and that a revolutionary parabolic tendency is observable in the
action of individual particles?

4. Is it not possible that the differences in the policy of the various
nations of Europe; the difficulties which beset the carrying out of
international law; the jealousies, quarrels, and rivalries of States
might disappear, if the same form of government (_i.e._, elliptical)
were adopted in each?

If you will kindly favour Her Majesty's Ministers with your opinion on
these questions, they will owe you a debt of gratitude, which they, as
representatives of the nation, will do their utmost to repay.

With every good wish for your further success in the regions of
polemical science,

          I beg to remain,
              My dear Lady Professor,
                  Your faithful servant,
                        +----------------------+
                        |                      |
                        |         [4]          |
                        |                      |
                        +----------------------+


[Editorial Note.]--The next letter is not of quite the same pleasing
nature as the foregoing, and shows that it is impossible to please
everyone, even if that happy consummation were desirable. This letter
was evidently called forth by some remarks which the learned Lady
Professor had made in her third lecture with reference to eccentricity
in dress. Our readers will recollect that the professor pointed out that
an extravagant 'bloomer' costume--half male, half female--was no more a
sign of genius than æsthetic dresses, always betokened the artist.[5]
This latter statement evidently gave great offence to the members of a
society which called itself the 'Æsthetic and Dress Improvement
Association,' and the following letter is the result of one of their
solemn conclaves:


                    Oscar Villa, South Kensington,
                            June, 18--.

The Secretary of the Æsthetic and Dress Improvement Association presents
his compliments to the Lady Professor of Girtham College, and begs to
contradict emphatically her statements with regard to a subject upon
which she is evidently in entire and lamentable ignorance, and to
protest against her aspersions upon the artistic studies of this and
kindred societies. He begs to state that true æsthetes are _not_
eccentric (they leave that to lady professors and her Philistine
followers); that to dress becomingly is one of the principal objects of
life, and that true greatness is achieved as much by the study of the
art of dress as by any other noble pursuit or graceful accomplishment.
Are not Horatio Postlethwaite, Leonara Saffronia Gillan, Vandyke
Smithson entitled to greatness? And yet their laurels have been won
solely by the art of dress. Perhaps the lady professor has never read
'Sartor Resartus'! In conclusion, he would ask the Lady Professor to
refrain from casting obloquy upon the work of the Association which he
has the honour to represent; to prevail upon her pupils to abandon the
unfeminine attire which some of them have assumed, contrary to the first
principles of art; to array themselves in flowing robes of sage-green
and other choice colours (patterns enclosed), and to study art, instead
of absurd mathematics, which no one can understand, and do no one any
good.

     (Approved by the Committee of the Æsthetic and Dress
      Improvement Association.)
      June, 18--.


[Editorial Note.]--The next letter, written by a pupil of the Lady
Professor, requires no explanation, and speaks for itself.


                    Jesus College, Cambridge,
                            March, 18--.

My dear Tutor,

You will be glad to hear that after superhuman exertions I have at last
succeeded in passing my Little-go, and I am eternally grateful to you
for all you have done for me. I should never have got through if it had
not been for you. All the coaches in Cambridge would never have managed
it, but you drove me through in a canter. And why? I never could make up
my mind to work for them; but when I coached with you, you made me like
it. I almost revelled in the Binomial when you wrote it out for me; and
then I could not help listening to you; and you looked so grieved when I
would not learn, and made me feel such a brute; so somehow or other you
drove some mathematics into my head, and I pulled through. By-the-bye, I
think you must have tried the 'brain wave' dodge with the examiners, as
five out of the six propositions in Euclid, which you told me to get up
specially, were set! I wish I could read people's thoughts; can you read
mine? If I were a Don, or a Fellow, or something, I would advise the
University to have some lady professors like you to teach the men,
instead of some of these sleepy old tutors. It would be a great
improvement, and I am sure we should get through a great deal more work.

They have given me a place in the Jesus Eight, which I shall take now
that I am released from your professorial ban, and have time for rowing.
But I don't half like giving up mathematics. You see, I have grown fond
of the study. Do you think you could make a wrangler of me? At any rate,
I should like to come to your lectures again. May I?

                    Your Grateful Pupil.
                         *     *     *


  [4] It is to be regretted that this letter has evidently fallen
      into the hands of some autograph collector, who has ruthlessly
      cut off the signature; but the reader will easily determine,
      after careful perusal of the document, from whose pen it emanated.

  [5] Cf. page 36.




PAPER V.

A LECTURE UPON SOCIAL FORCES, WITH SOME ACCOUNT OF POLEMICAL KINEMATICS.


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 = ½ MV²). 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.




PAPER VI.

ON SOCIAL FORCES (_continued_)--POLEMICAL STATICS AND DYNAMICS.


Most Noble Professors and Students of Girtham,--We have embarked upon
a stormy sea of speculation, on a voyage of grand discovery, and the
dangerous waves of adverse criticism, and the deceptive under-current of
prejudice, often make the steersman's lot by no means an enviable one.
But our vessel is sound and perfectly equipped, and therefore I do not
fear to guide her across the great unknown.

It may have occurred to you that the problems which present themselves
for solution in social science are far more difficult and complicated
than those which arise in ordinary mathematics. That is undoubtedly the
case; but this extra degree of difficulty is due to the fact that we
make no assumptions; we take the things as they really are, not as they
are assumed to be. In physical science, if we take into consideration
the resistance of the air, the curvature of the earth, the rigid
connection which exists between particles in the same body, and a host
of other things which are often conveniently neglected in elementary
works, how complicated the various problems become! So we must not be
surprised at some of the difficulties which occur in social science, as
nothing is neglected; the whole problem is before us, and having solved
it we need not make allowances for any falsely assumed _data_.

It is possible that other professors of this science may come to
slightly different conclusions to those which I have arrived at. That
is only to be expected, because their original observations may have
slightly varied. But in physical science allowances are made for
different observers. In astronomy, for example, we find the value of the
'Personal Equation.' One observer on looking through the telescope may
take the meridian of a star rather differently from another watcher of
the heavenly bodies, and the _personal equation_ is used to make
allowances for this quickness, or slowness, of observation. So in social
science there must be a personal equation too, and our object ought to
be, in the ordinary affairs of life as well as in the higher duties of
scientific action, to make our personal equation as small as possible.
But until the old proverb, '_Quot homines, tot sententiæ_,' has ceased
to have any meaning, there will be abundant need of this most useful aid
to accuracy.

The close connection which exists between social forces and material
forces is plainly shown by the doctrine of the conservation of energy.
'This doctrine,' says Dr. Tyndall, 'recognises in the material universe
a constant sum of power made up of items among which the most Protean
fluctuations are incessantly going on. It is as if the body of nature
were alive, the thrill and interchange of its energies resembling those
of an organism. The parts of the stupendous whole shift and change,
augment and diminish, appear and disappear; while the total of which
they are the parts remains quantitatively immutable, _plus_ accompanies
_minus_, gain accompanies loss, no item varying in the slightest degree
without an absolutely equal change of some other item in the opposite
direction.' So do the forces in the social world ebb and flow, rise and
fall, carrying on the same universal law which regulates the energy of
material force.

I will now proceed to enumerate some of those forces which exercise such
a powerful influence on society.

First, let us take the force of _Public Opinion_, which seems to
exercise a relentless sway over the minds and manners of men. This is a
very subtle and secret force, which is most difficult to trace, and
resembles electricity in the science of physics. We cannot see it, but
are only able to judge of its power by its results. Its point of
application is not in the individual, but in the collection of
individuals who make up the social system; and it is, in reality, the
resultant of, or the compromise between, the various elementary forces
which make up human society. Yes, compromise is a purely mechanical
affair, based on the principle of the parallelogram of forces; and as
public opinion is the result of a compromise, we may calculate its
force. For example: 'It is required to know the state of public opinion
in the matter of politics, when the results of a General Election show
that the Conservatives are to the Liberals as 10 : 9.'

Let OC be the direction of the Conservative force.

Let OL be that of the Liberal.

Then by _data_ OC : OL :: 10 : 9.

[Illustration]

Complete the parallelogram, and join OP.

Then OP represents the force of public opinion in magnitude and
direction.

N.B.--The direction of OL is determined by the amount of deviation of
the policy of the Liberals from that of the Conservatives.

As in physical, so in social science, impulsive forces sometimes act,
and effectually disturb our system and our calculations. Public opinion
is very liable to the action of disturbing forces. Panic is an impulsive
force, which defies the power of the most learned professors of social
science to determine its magnitude and direction. Some strange
unforeseen catastrophe--the fascination caused by a brilliant and
unscrupulous orator, a cruel wrong, a blind revenge for real or
imaginary injustice--will sometimes rouse one element of passion latent
in the vast body of public opinion; so that it breaks with all that
hitherto restrained and balanced it, and precipitates society into a
course of conduct inconsistent with its former behaviour, and bloodshed,
revolution, the breaking-up of laws, are the terrible results of panic
or revengeful passion.

Society is, as it were, split up by the terrible action of such
impulsive forces, just as wood is split up by the repeated blows of the
hatchet. It is, therefore, the duty of statesmen to increase the power
or force of cohesion, to strengthen the fibres of the State, so that the
force of such impulsive blows may not be felt, nor disturb the
continuity of the framework of the State. If such measures had been
adopted in the neighbouring country of France, much misery might have
been avoided, and the terrible revolutions which have so frequently
convulsed her social system entirely prevented.

_Friction_ is another disturbing element in our calculations, and
although it may be made a useful servant, it is a bad master in
mathematics, as in polemics. Without the aid of friction, progress would
be impossible. For example: Take the case of a man with perfectly smooth
skates on perfectly hard, smooth ice; he would be unable to reach the
land unless he had provided himself with some stones, by throwing which
he would just be able to get to his destination by a backward motion.
The engine would be unable to proceed on its iron road if it were not
for friction. The same is true in polemical science: the government of
the country would not be able to be carried on under our present
conditions if it were not for _party friction_. But suppose it increased
indefinitely, party friction becomes party _obstruction_; and the engine
of the State would no longer proceed smoothly and evenly along its
appointed course at the rate of sixty miles an hour, but would resemble
an old-fashioned coach, up to its axle-trees in mud, its motion
altogether stopped by the action of party friction.

We have seen that forces have two ways of acting: that of compelling
rest and that of producing motion. In statics forces act so as to
prevent any change of motion, or disturb the body's original position.
In kinetics, on the contrary, the power is recognised as acting so as to
produce or change a body's motion. Now, in polemical science we have
these two ways of considering the action of forces. There is the
_statical_ or _conservative_ force, which compels rest, which seeks
security, stability, and peace, and is not ardently devoted to change.
It reduces the system to equilibrium. There are, of course, two kinds of
equilibrium--_stable_ and _unstable_--according as the social and
political system is in a healthy or unhealthy state. If a body is in
stable equilibrium, and any slight motion takes place, the body will
return immediately to its former position; but if in unstable, it will
decline further and further away from its original position, and be
entirely upset. So a healthy and sound conservative equilibrium is not
disturbed by outside forces, and the State will resume its former
position of stability and rest when the opposing force is withdrawn. But
an unhealthy and insecure conservatism is as easily disturbed as an egg
balanced on its narrow end.

The kinetics of society, that is to say the Radical way of estimating
force, is the party of motion, generally supposed to be the 'party of
progress.' It has therefore many attractions in the eyes of those who
delight in motion, speed, and rushing about. To run at full speed, to
feel the keen air upon one's face, to experience the delightful
sensation of freedom of will, and limb, are joys which cannot be denied.
Such exercise is beneficial to the system, bodily or political. Motion
is the life of all things; it is characteristic of nature; it adores
nature; because it is an emblem and characteristic of life. The
ceaseless rolling of the ocean waves, the swaying of the trees, the
bending of the flowers, the waving of the corn, all these fill us with
pleasure; whereas a flat uninteresting plain, unrelieved by the motion
of terrestrial objects, is depressing to the spirit. So there is much to
be said in favour of motion, and Carlyle has defined progress as 'living
movement.' And men love this 'living movement,' and take up the
Laureate's cry:

               'Forward, forward, let us range,
    Let the great world spin for ever down the ringing
                Grooves of change.'

But, after all, there is a danger in this everlasting motion. We cannot
tell whither this progress may lead. It may be along a safe sure road;
but perchance a precipice may open out before us; and rejoicing in the
acceleration of our velocity, with eyes intent upon some distant heights
of glory and ambition, we may not discover our danger until it is too
late to stop, and a terrible plunge into an unknown abyss of turmoil and
tumultuous waves is the alarming result of an unguarded policy of
unrestrained 'progress.' I recall to my mind the quaint words of Holmes
which aptly illustrate my contention.

   'If the wild filly, "Progress", thou would'st ride,
    Have young companions ever at thy side;
    But wouldst thou stride the staunch old mare, "Success,"
    Go with thine elders, though they please thee less.'

Progress and success do not always go together hand in hand; and while
motion is essential to life, it is not always safe to urge a country
forward at too great a speed; and security and stability are quite as
important to the nation's life as actual progress.

There are other impulsive forces which act occasionally in the sphere
of politics, and which baffle all our calculations, and exclude
scientific considerations of the polemical problems which arise.
_Ambition_ is such an impulsive force, and when the rulers of the people
are actuated by it, and struggle for money, place, and power, politics
is degraded from its position as a science, and it becomes impossible to
estimate the result of forces so generated.

In my next lecture I propose to treat the important subject of the Laws
which govern States and Governments, and which regulate, generate, and
control the social forces which we have seen at work in the body
politic.




PAPER VII.

LAWS OF POLITICAL MOTION.


Since the last time I had the honour of addressing you on polemical
matters, I have met with a passage in the writings of M. Auguste Comte
which afforded me much pleasure. It seemed to be the one word for which
I had been waiting, and confirmed many of my own impressions and
speculations. He lays down two propositions: first, that the
constructive politics of the future must be based on the history of the
past; and second, that political science is a composite study, and
presupposes the complete apprehension of every branch of science,
beginning with the physical, such as astronomy, and ending with the
moral, such as ethics and sociology. M. Comte evidently does not regard
as a vain dream and imaginative speculation the theory that it will be
possible for statesmen to calculate a policy, and to determine a course
of action by purely scientific considerations. May I entertain the hope
that in this university, where all branches of physical science have
found a home, and are studied by most able and learned professors, the
science of politics may be pursued under most favourable circumstances?
I trust that each professor will bring before me the results of their
deliberations, and contribute to the growth of this particular science
for which our university has already become deservedly famous.

My present lecture is devoted to the important consideration of _Law_.
At first sight it may appear to you that the wills and passions of
mankind are so diverse and unknowable, that it would be absurd to
suppose that they can be calculated, or rendered amenable to any law.
But Professor Amos has pointed out that in proportion as we examine
history, and compare the actions present and past of different nations
and states, the more uniform does human nature appear; the more
calculable the actions, sentiments, and emotions of large masses of
people. As we have already stated, the difficulties of the study are not
likely to deter the professors of Girtham College from the pursuit of
any particular branch of science.

_A priori_ we might suppose from analogy that these polemical laws
existed, as there is no department of nature which is not governed by
law. It is an essential feature in nature, and also in government. What
is political economy but the study of certain laws of nature? These were
first discovered by Adam Smith, and have since been traced and estimated
by such men as Ricardo, the two Mills, Professor Cairnes, Jevons, and
many others. Moreover, our physical constitutions are governed by laws,
which physicians have determined, and which it is perilous to resist.
Our moral constitution is also governed by laws, which evidently exist,
although it is difficult to find them out. But the nation is only an
assemblage of individuals; and since individuals are so governed, it is
only natural to suppose that the nation, composed of individuals, is so
constituted and controlled. And not only is that true, but we shall see
that polemical laws are as permanent and universal, as invariable and
irreversible, as the laws of nature which regulate the courses of the
heavenly bodies, and raise the tides, or depress the sandstone hills.

We may notice first the preponderant impulse observable in a nation's
life in favour of supporting existing facts and institutions; and every
reformer has discovered the difficulty and danger of changing or
opposing the customs and habits of the people. As a wheel will travel
most smoothly along a well-worn groove, whereby friction is diminished,
so there is a natural national tendency always to run along those paths
with which the habits and customs of the people have made them familiar.
This law is nothing else than Newton's first law of motion, which is
quite as applicable to human masses as to lifeless matter. The tendency
of matter to remain at rest, if unmoved by any external agency, and of
persisting to move after it has once been set in motion, is a
conservative tendency; and is as true in political science as in any
other.

The special branch of our science, which we may call the _Biology of
Politics_, shows how absolute is the domain of law in polemical matters.
The law of human life is that men are born, grow, become strong and
vigorous, and then decay and die. This is the law of life, to which we
must all yield an enforced obedience. This same law is observed to be at
work in the heavenly bodies; and astronomy shows us that planets are
born, flourish, and at length die, just as our human bodies do. The moon
is, as you may have observed, a dead planet, such as our earth may be
some day. The same growth and decay are also manifest in national life.
First, there is the birth of the nation, which sometimes lies a long
time in a dormant state, and then wakes up to life and energy. China and
Russia are examples of dormant States, just waking from a long sleep of
childishness and ignorance. The next stage is the strong an healthy
period of its existence, which England is at present enjoying; and then,
after various stages of gradual decline, we come to the senile period of
national life, when every energy and faculty, every national feeling and
power of invention, are completely exhausted. As an example of this
depressing condition, we may mention Turkey and several of the effete
States of South America. Sometimes, when life is nearly extinct in the
human body, physicians have made use of the power of galvanism, in order
to revive the dying energies. This process of galvanizing a State into
life was tried by Lord Palmerston and others on the worn-out frame of
Turkey. But such attempts can only meet with partial and transitory
success; and where the loss of national power and faculty betokens the
senile period of the nation's existence, it is vain to attempt to
restore its former life and energy. The study of the biology of
politics presents many interesting and important details in this special
branch of knowledge; and I commend this part of our subject to the
special attention of the professor of physiology. The law of development
is observable in nations as in nature. Recent scientific discoveries
have tended to take away all ideas of _chance_ in the workings of
nature, and have substituted _law_ instead of it. It would be
unscientific and incorrect to speak of the world being formed by the
'fortuitous concourse of atoms.' So we cannot speak of a State being
generated in this manner. Laws--economical, geographical,
natural--preside over the formation of States and nations, and produce
their further development.

The laws of political motion occupy the same prominent place in our new
science as Newton's laws do in ordinary dynamics. These are very
important in calculating the positions which various States will occupy
in the future. First, we have the _doctrine of nationality_, which
prevented the progress of Austria into Italy, and of the Bourbons in
Naples, and produced the amalgamation of the small German States in the
great empire of Germany. The second law of political motion is the
doctrine of the _independence_ of all true States, and the equality of
all States to each other. This had its growth in feudalism; and all the
chief wars of modern times have been the result of the efforts of nature
to establish this law of independence. The doctrine of intervention is a
modification of the preceding law, and is applicable when the law of
necessity demands its use, such as the restoration of order after
protracted anarchy, the abolition of slave trade, etc. The third law is
the _law of morality_. Just as for each man there exists a _right_ and a
_wrong_; just as _duty_ and _conscience_ are certain elements in his
daily motion, which dictate his course of action, although he may chose
to neglect them; so a nation is bound by the same moral laws which
govern the individual; and a nation errs if it transgresses them.
Christianity is the agent which has produced so powerful an influence
in making men obey the dictates of conscience and walk in the path of
duty; and I read with thankfulness the conclusion of Mr. Amos, that
Christianity has triumphed quite as much in moralizing secular politics
as it has in the sphere of individual life.

       *       *       *       *       *

These are some of the principal laws of motion which I have observed at
work in various States and nations. Inasmuch as political science
embraces, in addition to the physical sciences, all those branches which
are contained in ethics, economics, jurisprudence, sociology and others,
the laws of each are generally applicable to the whole grand subject of
which my lectures treat. Other general laws may be deduced, and have
been enumerated in my previous lectures, from the social properties of
curves and conics; and when our researches are complete we may hope to
produce a code of laws for the guidance of our statesmen which maybe of
immense use in determining the policies of the future. Already there is
strong evidence that the affairs of this country are being conducted on
sound scientific principles, rather than by any species of guess-work or
haphazard contrivances. The use of history is recognised as extremely
important in determining a future line of conduct; and statesmen are in
the habit of endeavouring to find from their study of the past what is
the logical sequence of events. Just as mathematicians endeavour to
determine the law of a series of figures, and having found the law, can
write down the next, and the next, _ad infinitum_; so scientific
politicians may be able soon to establish the various laws of a series
of events, and calculate their course of actions. That there is
considerable progress in this direction is manifest by the value which
they place upon statistics, and their continued use of this important
information.

There are a few great evils in our present system which are strongly
opposed to any scientific methods in politics; and in the interests of
the country as well as those of science they ought to be removed. One
great evil is the want of political and scientific knowledge on the part
of the electors, who are in the habit of choosing their representatives
on personal grounds, or party considerations, rather than on sound
principles of political science. All this is opposed to any idea of law.
Owing to the ignorance of the electors they fall an easy prey to
adventurers and unprincipled politicians, who make all kinds of specious
promises, tempt them with all manner of baits, and make self-interest
instead of the welfare of the State the principle of voting. Selfishness
is the ruin of social life and intercourse, the destroyer of all
happiness, peace, and mutual trust in family life or in society. It is
the root of most of the faults, vices, and crimes in the individual; and
who can tell the endless disasters which will befall the State, where
selfishness is the chief motive-power of the electors and the elected? A
selfish statesman, one who goes into Parliament to gain his own ends and
forward his own personal interests, is a disgrace to society--

   'Feeling himself, his own low self, the whole,
    When he by sacred sympathy might make
    The whole one self. Self, that no alien knows!
    Self, far diffused as fancy's wing can travel!
    Self, spreading still, oblivious of its own,
    Yet all of all possessing!'

I have said that the ignorance of the electorate makes them an easy prey
to such men; and until they have learnt to detect the false from the
true, until they become acquainted with the elements of political
science, and have been taught that their own selfish interests are not
the highest aims of social government, it is vain to hope for a
reasonable method of regulating the affairs of the nation, based upon
logical laws and scientific principles.

And how is this work of educating the electors to be accomplished? Not,
I maintain, by furious speeches and rhetorical displays; not by bribery,
baits and banter; but by patient, never-ceasing labour, by lectures on
history and science, by individual instruction, is the great work to be
accomplished upon which the security and stability of the country
depend.

Then we may hope that the 'Reign of Law' in polemical science may be
ushered in with the joyful acclamations of an enlightened and united
people, and its benign influence extend from the throne of the monarch
and the council-chamber of his ministers to the hearth of the cottager.
Politicians will rule by law; policies be calculated by laws; people
vote by law; and then methinks I see in my mind (to use the words of the
blind old poet) a noble and puissant nation rousing herself like a
strong man after sleep, and shaking her invincible locks; methinks I see
her as an eagle, renewing her mighty youth, and kindling her undazzled
eyes at the full mid-day beam; purging and unsealing her long-abused
sight at the fountain itself of heavenly radiance; while the whole noise
of timorous and flocking birds flutter about amazed at what she means.
Such is the glorious vision of the 'Reign of Law.' Let it be the
business of every Englishman and Englishwoman to arrange the framework
of our social and political system, that law may have an uninterrupted
sway; then shall we be a united, prosperous, and contented people, and
the reign of lawless agitators, bribery-mongers, and counterfeit
statesmen will have passed away into the oblivion and obscurity of a
more suitable but less favoured region.




PAPER VIII.

ON THE PRINCIPLE OF POLEMICAL COHESION.


In my previous lectures I have had occasion to mention the principle of
cohesion; but it plays so vital a part in the constitution of States and
their relations to each other that I consider it advisable to devote
this lecture entirely to it.

This is a large and comprehensive subject, and embraces such principles
as the Centralization of States; the Co-operation of States; Monogamic
Marriage; Unions; Free Trade, and many others equally important. We have
already noticed that cohesion is a well-known property of matter; that
its influence is not confined to the regions of physical sciences; and
that it is the manifest duty of all governments to increase the force
of cohesion.

Various methods have been tried to accomplish this purpose. The
principle of Feudalism was one of the earliest attempts to produce the
cohesion of the nation; and, in an elementary condition of society, it
was partly successful. The theories of 'Divine Right' and 'Social
Contract' were other methods which have been adopted; and the unity of
the Christian Church has been the great means of producing the cohesion
of the State in olden times; and its aid may be again required for the
same beneficent object in future complications and social disruptions.

But it is always advantageous in scientific pursuits to go back to first
principles; and we will adopt that method in our present investigations.
The social unit is the family; the multiplication of families makes the
tribe; the multiplication of tribes makes the State; and, therefore, we
shall not be far wrong if we consider the family tie as the first
principle of political cohesion. I am in agreement with several learned
thinkers upon this subject when I say that marriage is a most important
political factor; and as marriage cannot take place without women, it is
evident that women play a very important part in promoting the cohesion
of the State.

This prominent position was duly assigned to women by one of our
greatest political philosophers, M. Auguste Comte, who strongly opposed
the fatal fallacy of ancient political systems, which greatly
overestimated the powers of men, and depreciated those of women. If the
superiority of bodily strength be the sole cause of greatness in
political and intellectual pursuits, then, most noble lords of creation,
we yield to you the palm--you are our masters in this respect. But if,
on the other hand, it can be shown that physical strength is not a
requisite for great achievements in these occupations; if the powers of
endurance, elasticity, adaptability, nervous energy, and patience are
quite as needful as mere animal strength; then we women are quite as
capable, and indeed more capable than men, for achieving political
greatness. In the 'good old days,' when the law of might was right, and
the strongest arm was the most powerful machinery in the government of
the country, women were compelled naturally to occupy a less prominent
position in the conduct of the affairs of the nation; and for centuries
they have been degraded by a dominating tradition, and supposed
incapable of performing duties for which they were mentally well suited.
But those militant days are past. Animal strength and brute force are no
longer needed in the councils of the nation; and the time has arrived
when women should cease to be oppressed by the disparaging, illogical
deductions of former generations, and when their assistance ought to be
invoked in the great work of promoting the nation's welfare.

I have stated that marriage is an important political factor; and,
therefore, women have always occupied a primary, though obscure, part in
political affairs. The cohesion of the State has been produced by the
secret influence of family life. But it may be asked, What kind of
marriage is most conducive to national cohesion? This question has been
carefully and conclusively answered by a learned scientific writer, who
shows that polygamic marriage never exists in an advanced state, as
instanced by the history of Judaism and Mohammedanism; that a strict
form of monogamic marriage is essential to political greatness and true
progress in civilization. The cohesion of the State is destroyed by
polygamy, and by any system which relaxes the binding nature of the
marriage tie. 'Domestic disorganization is a sure augury of political
disruption.'

Cohesion, the essential property of all rightly constituted nations, is
often in danger of being lost when the State is geographically very
large, or when local interests have greater power than the attractive
force of the central government. To obviate this evil, the method of
centralization has been adopted with satisfactory results, as in the
case of the United States of America, and Germany.

By this means the local authorities are brought into close relationship
with the central head, and the centrifugal influences of independent
interests and customs are counteracted by the force of central
attraction. Centralization increases the importance of the whole body,
and, like the pendulum of a clock, regulates the movements of the whole
State. In some cases it tends to make the government despotic, when the
local governments are entirely under the control of the central; and
every enactment, and scheme, and plan checked and supervised by the
chief officers of the State. Such was the system adopted in France by
Napoleon III. But cohesion without the enforcement of a hard and rigid
connection, a general supervision without severe tyrannical
jurisdiction, are the best methods of securing the unity of composite
States.

But the force of cohesion is evidently at work in the nation apart from
centralization. Men who have a community of interests unite together
for the purposes of strength and mutual assistance. They combine for the
sake of securing means of support in sickness, and form benefit
societies, such as the Order of Oddfellows or Foresters. This force of
cohesion has produced trade unions, and similar institutions which exist
for the purpose of protecting a common interest, and giving expression
to the concurrent opinions of the members. These have their legitimate
use in every civilized State, in spite of some of the disadvantages
which follow in their train. There are, of course, opposed interests in
every community: _attractive_ forces, which produce trade unions,
guilds, corporations, companies, and the like; and _repulsive_ forces,
which result from the opposed interests of employers and employed,
landlords and tenants, and similar pairs of different classes in the
community. As time goes on, and the State advances with it, these forces
will gain in strength; the cohesion of classes will become greater;
association will grow as naturally as the bubbles form on the surface
of our evening beverage. It is a law of nature, and therefore cannot be
resisted. But the repulsive forces will be no less strong, and to
calculate the resultant of these contending interests will be the
problem for practical statesmen to solve.

The force of cohesion is also evidently at work, not only in individual
States, but also amongst the nations of Europe, and of the world. That
is to say, there is an evident desire for co-operation on the part of
those nations who have attained to the highest degree of civilization
and internal cohesion. International law is based on the principle of
cohesion, and every day it is gaining power and favour in the eyes of
our leading statesmen. The doctrine of Free Trade, which, if universally
adopted, would be of the greatest service to mankind, results from a
desire for co-operation; and whatever evils may result from one-sided
Free Trade in this country at the present time, there can be no doubt
that ultimately the complete system will be adopted.

Sad is the fate of a nation when the force of cohesion is weakened. The
first revolution in France is a proof of this assertion; there was no
cohesion, no common faith, or loyalty to the throne and Government; and
indeed the Government, which was rotten to the core, was hardly likely
to awake any feelings of loyalty and respect; and therefore the social
disruption which followed was only a natural sequence of events, and was
prophesied with the accuracy with which an astronomer can foretell an
eclipse. But that is not all; when the cohesion of the State is
destroyed, it takes a long time to restore the action of the force; and,
as in the case of France, further disruption is sure to take place.

In this lecture I have already enumerated some of the ways in which this
force acts; there are doubtless others which will suggest themselves to
you. But I contend that the prosperity of the State, and the peace of
the world, depend upon cohesion. Let this be your work, most noble
professors, to promote the action of this helpful and life-giving
force. Promote, as far as in you lies, the sacred union of family life.
Encourage the generous feelings of true loyalty and patriotism amongst
the people of this realm of England; counsel our statesmen with regard
to the primary necessity of national cohesion, and the advantages of
international co-operation; and your work will be blessed; your names
will rank with those heroes of the sword and of the pen who have raised
our beloved country to her present pinnacle of greatness and prosperity;
and your memory will live in the hearts of your grateful countrymen.


[Editorial Note.]--We regret to state that the various MSS. in the
sealed desk are nearly exhausted, and are therefore compelled to present
the series of lectures on polemical studies in an incomplete form. But
we had the good fortune to light upon a brief diary which discloses some
interesting information with regard to the Author's life and
occupations. We append a few extracts:




Extracts from the Author's Diary.


_June 3rd_.--Arnold called again to-day--the fifth time during the last
fortnight! His attention is rather overpowering, and wastes much of my
valuable time. He says he hates science--the heathen!--and wants me to
lecture in classics. He affirms that mathematics are dry and hard--too
hard for women, and tend to make them unsympathetic and critically
severe. I am afraid I was rather severe with him. But really he is very
trying, and always seems to talk like a Greek chorus in the most
profound platitudes. Arnold is a classical tutor at Clare College. My
old pupil is getting on famously. Poor fellow! he seems quite oppressed
with his work. But he is making great progress, and sticks to his books
like--a student of Girtham College!

_June 4th_.--Lectured on the Scientific Basis of Blackstone's
Commentaries; afterwards received pupils until 1 p.m. Really Blanch
S---- is more tiresome than ever. It appears that she has taken up with
a young undergraduate of King's, and there is no prospect of any
improvement in her work unless this nonsense is terminated. How foolish
some of my sex are, in spite of their improved opportunities! I blush
for them! Arnold has sent me a copy of Robert Browning's 'Belaustion,'
in order to make me like classics, and give up science. Misguided young
man! He has written some tolerable verses on the fly-leaf; but I have no
intention of playing Belaustion to his 'entranced youth.' These are his
verses:

   'My lady dear, if I may call you so,
    For you are dearer than all else beside,
    I know the love you bear to golden verse,
    To golden thoughts enshrined in classic lore,
    To all that's beautiful; so here I send
    Some echoes of the songs of ancient days,
    Attuned and chanted by an English bard,
    Who fires one's old love for the rolling lines
    Of youthful Hellas; may your cultured ear
    Receive, and gladly welcome his sweet song.
    And while we revel in the poet's dream,
    And hear his actors speak, we'll play our parts.
    You, sweet Belaustion on the temple-steps,
    Taking your captors captive by your voice;
    And I, the youth who, more entranced than all,
    Was bound by fetters that he would not loose;
    And so we'll play our part. What say you, dear?'

_June 6th_.--Have just seen our new Professor of Physics, Amelia
Cordial, who is an excellent woman, and well suited for the high office
which she holds. She has told me of the foolish conduct of Lady Mary,
who is evidently of opinion that the professorial mantle ought to have
fallen on her shoulders. Really, this jealousy in the ranks of the
learned is most disgraceful; and the bickerings which arise from
disappointed ambition, the envyings and silly quarrels, are the weak
places in our female collegiate system.

Such good news! The wrangler list is just out, and my hard-working pupil
is _bracketed twelfth!_ This is really delightful, and abundantly repays
us for all our hard toil. But really I have not found working with him
distasteful; he is such an excellent pupil, so painstaking and eager,
that I have quite looked forward to his coming, and found him much more
interesting than some of these foolish maidens. But I almost dread
seeing him. He will be so elated and overpoweringly grateful, whereas I
ought to be grateful to him for all his work for me; for I am sure he
would never have gone in for the Tripos if I had not persuaded him.
Well, I wonder why he does not come to tell me of his triumph.

_June 7th_.--_It_ has come! and I half expected it. My eager pupil
writes with all the energy and love of his noble nature to ask me to be
his wife! He says _that_ is all he cares for, and only values his
Honours as a step to a higher honour and dignity, that of gaining my
love and being my husband. All this is very nice to read; but a terribly
difficult problem is placed before me for solution. I do indeed love
this dear, good fellow--no one could help doing so, I am sure; but do I
not love science more? There is a stringent regulation in this
University that no one shall occupy the position of professor who is
bound by any domestic ties or cares. All married women are excluded. If
I say 'Yes,' I must resign my high position, leave this beloved college,
give no more lectures to entranced audiences. In the interests of
science, ought I to refuse, and sacrifice my heart's affections for the
cause of mathematics? But if I say 'No,' I must give up--_him_;
sacrifice his happiness too, and blight his life. Was ever anyone so
perplexed? Science, aid thine obedient servant! May I not determine this
vital question by thine all-pervading light?...

       *       *       *       *       *

[Editorial Note.]--We had just arrived at this exciting moment in the
life of the learned and accomplished lady whose writings form the
subject of these pages--a moment when love and science were trembling in
the balance--when a footstep was heard upon the stairs leading to our
study, and ere we could secrete our MS. the door was opened, and a
well-known voice exclaimed:

'I do not know why you should have become so studious lately, Ernest,
and why you should refuse to take me into your confidence. You spend
hours and hours in this room all by yourself, writing away, and never
say a word to me about the subject of your literary work. There was a
time when things were different, and you were not so slow in availing
yourself of my help, and asking my advice.'

We murmured something about taking up the pen which had been laid aside
by a far abler hand, and our deep gratitude for past assistance in our
work, which could never be forgotten.

'And do you think that I cannot help you now?' our visitor replied, in a
very injured tone of voice. 'Is the old power dead, because it has not
recently been used? Ernest, I think you very ungrateful not to confide
in me. Come, tell me what you are writing.'

A suggestion about the proverbial curiosity of women rose to our lips,
but died away without utterance. In the meantime, her eyes wandered over
our study-table strewed with papers, and lighted upon the well-worn
desk.

'Why, Ernest, where did you find this? My dear old desk, which has been
lost ever so long! I do believe you have been ransacking its contents!
Why did you not tell me that you had found it? What are you doing with
my papers, sir?'

The mischief was out! We tried to explain that the world ought not to be
deprived of that which would benefit mankind; that the peace and
prosperity of the country might be sacrificed if it were deprived of
these discoveries of science, which were calculated to secure such
beneficial results.

At length we gained our point, and obtained the full sanction of the
late Lady Professor of Girtham College to publish her papers. Thus her
obedient pupil is enabled to repay his late instructress for all her
kindness to him, and in some measure to compensate the scientific and
political world for the loss of one of its most original investigators
in the regions of polemical studies, which, not without a struggle, she
resigned when she deigned to become his wife.


THE END.




_Elliot Stock, Paternoster Row, London._





End of Project Gutenberg's The Romance of Mathematics, by P. Hampson