George Atherton Aitken.

The life and works of John Arbuthnot, M.D., fellow of the Royal College of Physicians online

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besides, your lands being generally in the worst repair, that
is, in the most improveable condition, and your security, by
the use of a register, the best in the island, no doubt, after
the restraint of laws is taken off, strangers will be encouraged
to purchase among you. Why then will you choose to live in
a miserable moiling condition, paying high interest for money,
which land rents cannot discharge, having no way to dispose
of your younger children, but by sending them abroad into
the wide world to seek their fortunes ; whereas, after the



4o6 WORKS OF DR. ARBUTHNOT.

conclusion of this great affair, you will have opportunities to
employ them in trade and business, and access (according to
merit) to the best posts of Great Britain ? As for your tenants,
the necessity of their masters is the occasion of their poverty ;
trade will enable them to let longer leases, and you to take
them ; and conform you in time to English customs, where
masters govern a free people, and are duly paid their rents ;
and tenants enjoy what remains with equal security. As for
your tradesmen, the value of your manufacture will be raised,
you will have the opportunity to dispose of it, not only over
all the island, but over all the world : you are ingenious, in-
dustrious, and live cheap, what then can hinder you to be
m.ore rich than those who have less of all these qualities?
Where there are hands to work, and simples to work upon,
and vent for the manufactvu^e, it is impossible but there mvist
be trade : if our own stock is not sufficient, you will be assisted
by that of England : the very novelty of the thing will in
some measure contribute to this ; for all the branches of
traffic in England, being traded bare, where there are new
subjects of trade, merchants will try new projects ; their
interest will never suffer them to be partial to this or that
country, but they will spend their money where they can have
the best bargain. And your poor labourers may expect to
raise their wages considerably.

You see, the objections used by the opposers of an union
are either frivolous, founded upon gross falsehoods, or do
plainly prove the contrary of what they are adduced for. And
I have that opinion of the understanding of several of the
anti-uniters, that they do not so much as convince them-
selves : they are only a veil drawn over your eyes, to hide
from you your present poverty and slavery, and the glorious
prospect which an union with England presents you with.
You are used only as tools and machines, to bring about their
factious and ambitious designs. However, I shall beseech all
such gentlemen and persons of quality to consider, that it is
not a slight matter to sacrifice the present and future pros-
perity of their country to an unreasonable humour ; to make
a numerous people and their posterity'", beggars and slaves for
ages to come ; and perhaps their country a field of blood, by
endeavouring to entail this upon their neighbours as well as
themselves : or if they are swayed with some reason of less



A SERMON AT THE MERC AT CROSS. 407

importance, as the treaty not being of their own framing,
I desire them to consider, that this is so very chiklish, that a
senator shouhl be ashamed to own it. If the pretty little
masters, their children, should take their fathers' places in
Parliament, such a reason would hardly be allowed to pass
current among them : an union is a matter of great weight
and importance, and very good or bad in itself. If it is a
bad thing, our most intimate friends the treaters can never
recommend it ; if it is a good thing, it is so great a good, that
we ought not to refuse it from those against whom our personal
resentments run highest. Among the opposers of the union,
I know a great many persons of honour, who have as true a
sense of liberty, and as great a concern for the welfare of their
country as any ; such need only lay aside some few prejudices,
and reflect ; their judgments will quickly inform them of the
true value of the proposal. To such as are afraid of the
Cluirch and religion, I shall only say, that the religion of the
Church of England is imposed upon no man within the do-
minions of England. As for the squeamishness of sitting in
Parliament with prelates, and the fear of being disarmed of
all other weapons, but what are allowed by the Gospel ; these
are such unchi'istian dissuasives from an union, that to
mention them only is to refute them. The putting an end
to uncharitable and unreasonable divisions about our trifling
difi^erences in religion, is one of the great benefits Scotland
will reap by this union. I am not so much terrified at the
vision of a noble lord ', as he is himself, but heartily wish to
see a plantation of as rich Jews as any in Amsterdam, as rich
Independents, Quakers, and Anabaptists as any in England,
settled in all the trading towns of the kingdom. Not but that
I think all motives that are not penal ought to be used for
their conversion, but I would not have churchmen afraid of
the increase of their manufacture too ; for heretics are properly
the subject which they are to work upon : to be afraid to live
among heretics, is to refuse the task their Master has imposed
upon them. Their predecessors, the Apostles, used to go, at
the hazard of their persons, to preach the Gospel to the Jews ;
they are afraid the Jews should come to them, where they run
no risk at all in attempting their conversion. In a word, if

1 ' The Lord Belhaven's Speech the 2nd of November, on the subject
in the Scotch Parliament, Saturday, matter of an Union,' 1706.



40 8 WORKS OF DR. ARBUTHNOT.

any unjust tyranny over the persons, estates, or consciences
of men be the motive which prevails with some to oppose
this union, I would have such consider, that to govern a free
people, is a more noble and honourable character, than to
insult over slaves and beggars ; and if any such there be, who
hug their chains, and are fond of their rags, and, as a wretched
people once did by the Romans, refuse their liberty when
offered, they are unworthy of so generous and beneficial a
proposal. Lastly, if this is only a scuffle raised by the united
force of the Skillin and Louis d'Or, let such consider, that
both of them are not to be put in the balance with the Guinea,
which they may get by their industry.

Consider then, in this your day, the happy condition of
your neighbouring nation : survey their verdant fields, their
beautiful plantations and sumptuous gardens, where cultvire,
art, and expenses reign ; their i)opulous and flourishing cities.
View the magnificence of their public structures ; the neatness,
cleanliness, conveniency, and costly furniture of their private
houses : consider the liberty and plenty of their meanest
commoners ; the comfortable estates which even the lowest
of their tradesmen leave to their families ; the immense riches
of their merchants ; the grandeur and magnificence of the
learned societies ; the prodigious stocks of their trading com-
panies ; the unconquerable force of their fleets and armies ;
the justice and exact execution of their laws ; and the wise
administration of their government : ponder all these things,
and then sure you will not reckon them your enemies, who
offer you a partnership in so great blessings ; but will conclude
with the wise man in my text, ' Better is he that laboureth,
and abound eth in all things, than he that boast eth himself,
and wanteth bread.'



AN" ESSAY



ON THE



USEFULNESS OF MATHEMATICAL LEARNING,

In a Letter from a Gentleman in the City to his Friend

IN Oxford\

I AM glad to hear from you that the study of the mathe-
matics is promoted and encouraged among the youth of your
University. The great mfluence which these sciences have on
philosophy and all useful learning, as well as the concerns of
the puljlic, may sufficiently recommend them to your choice
and consideration ; and the particular advantages which you
of that place enjoy, give us just reason to expect from you a
suitable improvement in them. I have here sent you some
short reflections upon the usefulness of mathematical learning,
which may serve as an argument to incite you to a closer and
more vigorous pursuit of it.

In all ages and countries where learning hath prevailed,
the mathematical sciences have been looked upon as the most
considerable branch of it. The very name MiWrjais implies no
less ; by which they were called either for their excellency, or
because of all the sciences they were first taught, or because
they were judged to comprehend ti^Vto ra Madrjfiara. And
amongst those that are commonly reckoned to be the seven
liberal arts, four are mathematical, to wit, arithmetic,
music, geometry, and astronomy.

But notwithstanding their excellency and reputation, they
have not been taught nor studied so universally as some of the
rest ; which I take to have proceeded from the following causes :
the aversion of the greatest part of mankind to serious attention
and close arguing ; theii' not comprehending sufficiently the
necessity or great usefulness of these in other parts of learning ;

* See pages, 24-26.



4IO WORKS OF DR. ARBUTHNOT.

an opinion that this study requires a particular genius and turn
of head, which few are so happy as to be born with ; and the
Avant of public encouragement, and able masters. For these,
and perhaps some other reasons, this study hath been generally
neglected, and regarded only by some few persons whose happy
genius and curiosity have prompted them to it, or who have
been forced upon it by its immediate subsei-viency to some
particular ai"t or office.

Therefore I think I cannot do better service to learning,
youth, and the nation in general, than by shewing that the
mathematics of all parts of human knowledge, for the improve-
ment of the mind, for their subsei-viency to other arts, and their
usefulness to the commonwealth, deserve most to be encouraged.
I know a discourse of this nature will be offensive to some,
who, while they are ignorant of mathematics, yet think them-
selves masters of all valuable learning ; but their disjileasure
must not deter me from delivering an useful truth.

The advantages which accrue to the mind by mathematical
studies consist chiefly in these things : first, in accustoming it
to attention ; secondly, in giving it a habit of close and de-
monstrative reasoning ; thirdly, in freeing it from prejudice,
credulity, and superstition. First, the mathematics make the
mind attentive to the objects which it considers. This they
do by entertaining it with a great variety of tmths which are
delightful and evident, but not obvious. Truth is the same
thmg to the understanding, as music to the ear, and beauty to
the eye. The pursuit of it does really as much gratify a natural
faculty implanted in us by our wise Creator, as the pleasing of
our senses ; only in the former case, as the object and faculty
are more spiritual, the delight is the more pure, free from the
regret, turpitude, lassitude and intemperance that commonly
attend sensual pleasures. The most part of other sciences
consisting only of probable reasonings, the mind has not where
to fix ; and wanting sufficient principles to pursue its searches
upon, gives them over as impossible. Again, as in mathe-
matical investigations truth may be found, so it is not always
obvious : tliis sjjurs the mind, and makes it diligent and
attentive. In Geometrla (says Quintilian, 1. i. c. lo) partem
fatentur esse utilem tcncris acfatibus : agitari namque animos,
Clique acui ingenia, et celeritafetn pcrcipiendi venire inde concedunf.
And Plato (in Itepuh. lib. vii.) obsen^es, that the youth who



USEFULNESS OF MATHEMATICAL LEARNIXG. 41 1
are furnished with mathematical knowledge are prompt and

quick at all other sciences, tU ndiTa ra MaO^inira o^i'is (JHiiiovrai.

Therefore he calls it, Kara nmbdav oSoV. And indeed youth is
generally so much more delighted with mathematical studies
than with the unpleasant tasks that are sometimes imposed
upon them, that I have known some reclaimed by them from
idleness and neglect of learning, and acquire in time a habit of
thinking, diligence, and attention ; qualities which we ought
to study by all means to beget in their desultoiy and roving
minds.

The second advantage which the mind reaps fiom mathe-
matical knowledge, is a habit of clear, demonstrative, and
methodical reasonmg. We are contrived by nature to learn by
imitation more than by precept ; and I believe in that respect
reasoning is much like other inferior avis (as dancing, singing,
&c.) acquired by practice. By accustoming ourselves to reason
closely about quantity, we acquire a habit of doing so in other
things. It is suiinismg to see what superficial mconsequential
reasonings satisfy the most part of mankmd. A piece of vnt,
a jest, a simile, or a quotation of an author, passes for a mighty
argument : with such things as these are the most pai't of
authors stuffed, and from these weighty premises they infer
their conclusions. Tills weakness and effeminacy of mankind
in being persuaded where they are delighted, have made them
the sport of orators, poets, and men of wit. Those himina
orationis are indeed veiy good diversion for the fancy, but are
not the proper business of the understanding ; and where a
man pretends to write on abstract subjects in a scieutifical
method, he ought not to debauch in them. Logical precepts
are more useful, nay, they are absolutely necessary for a rule of
formal arguing in public disputations, and confounding an
obstinate and perverse adversary, and exposing him to the
audience, or readers. But in the search of truth, an imitation
of the method of the geometers will cany a man further than
all the dialectical rules. Then- analysis is the proper model we
ought to fonn ourselves upon, and imitate in the regular
disposition and progress of our enquii'ies ; and even he who is
ignorant of the nature of mathematical analysis uses a method
somewhat analogous to it. The composition of the geometers,
or theii- method of demonstrating truths alreadj^ found out, -s-iz.
by definitions of w^ ords agreed upon, by self-evident truths, and



4T2 WORKS OF DR. ARBUTHNOT.

propositions that have been already demonstrated, is practicable
in other subjects, though not to the same perfection, the natural
want of evidence in the things themselves not allowing it ; but
it is imitable to a considerable degree. I dare appeal to some
writings of our own age and nation, the authors of which have
been mathematically inclined. I shall add no more on this
head, but that one who is accustomed to the methodical
systems of truths, which the geometers have reared up in the
several branches of those sciences which they have cultivated,
will hardly bear with the confusion and disorder of other
sciences, but endeavour as far as he can to reform them.

Thirdly, mathematical knowledge adds a manly vigour to the
mind, frees it from pi'ejudice, credulity, and superstition. This
it does two ways : first, by accustoming us to examine, and not
to take things upon trust ; secondly, by giving us a clear and
extensive knowledge of the system of the world ; which, as it
creates in us the most profound reverence of the almighty and
wise Creator, so it frees us from the mean and narrow thoughts
which ignorance and superstition are apt to beget. How great
an enemy mathematics are to superstition appears from this,
that in those countries, where Romish priests exercise their
barbarous tyranny over the minds of men, astronomers, who
are fully persuaded of the motion of the earth, dare not speak
out ; but though the Inquisition may extort a recantation, the
Pope and a General Council too will not find themselves able to
persuade to the contraiy opinion. Perhaps this may have given
occasion to a calumnious suggestion, as if mathematics were an
enemy to religion, which is a scandal thrown both on the one
and the other ; for truth can never be an enemy to true religion,
which appears always to the best advantage when it is most
examined : —

Si propius stes
Te capiet magis.

On the contraiy, the mathematics are friends to religion ;
inasmuch as they charm the passions, restrain the impetuosity
of imagination, and purge the mind from error and prejudice.
Vice is error, confusion and false reasoning ; and all truth is
more or less opposite to it. Besides, mathematical studies may
serve for a pleasant entertainment for those hours which young
men are apt to throw away upon their vices ; the delightfulness



USEFULNESS OF MATHEMATICAL LEARNING. 413

of them being such, as to make solitude not only easy, hut
desii'able.

What I have said may sen-e to recommend mathematics for
acquiring a vigorous constitution of mind ; for which puqjose
they are as useful, as exercise is for procuring health and
strength to the body. I proceed now to shew theii- vast extent
and usefulness in other parts of knowledge. And here it might
suffice to tell you, that mathematics is the science of quantity,
or the art of reasoning about things that are capable of more
and less, and that the most part of the objects of our know-
ledge are such : as matter, space, number, time, motion,
gravity, &c. We have but imperfect ideas of things without
quantity, and as mipei-fect a one of quantity itself without the
help of mathematics. All the visible works of God Almighty
are made in number, weight, and measure ; therefore to consider
them we ought to understand arithmetic, geometiy, and statics ;
and the greater advances we make in those aiis, the more
capable we are of considermg such things as are the oi'dinaiy
objects of our conceptions. But this will farther appear from
parficulars.

And first, if we consider to what perfection we now know
the courses, periods, order, distances, and proporfions of the
several great bodies of the universe, at least such as fall within
our view, we shall have cavise to admire the sagacity and
industry of the mathematicians, and the power of numbers and
geometiy well applied. Let us cast our eyes backward, and
consider astronomy in its infancy ; or rather let us suppose it
still to begm : for instance, a colony of rude countiy people,
transplanted into an island remote from the commerce of all
mankind, without so much as the knowledge of the calendar,
and the periods of the seasons, without instruments to make
observations, or any the least notion of obsen'ations or instru-
ments. When is it we could expect any of then- posterity
should an-ive at the art of predicting an eclipse ? Not only so,
but the art of reckoning all eclipses that are past or to come,
for any number of years ? When is it we could suppose that
one of those islanders transported to any other place of the
earfh, should be able by the inspection of the heavens to find
how much he were south or north, east or west of his oAvn
island, and to conduct his ship back thither? For mj- part,
though I know this may be, and is daily done, by what is



414 WORKS OF DR. ARBUTHNOT.

known in astronomy ; yet when I consider the vast industry,
sagacity, multitude of observations, and other extrinsic things
necessaiy for such a sublime piece of knowledge, I should be
apt to pronounce it impossible, and never to be hoped for.
Now we are let so much into the knowledge of the machine of
the universe and motion of its parts by the rules of this
science, perhaps the invention may seem easy. But when we
reflect what penetration and contrivance were necessaiy to lay
the foundations of so great and extensive an art, we cannot but
admire its first inventors ; as Thales Milesius, who, as Diogenes
Laei-tius and Pliny say, first predicted eclipses ; and his scholar
Anaximander Milesius, who found out the globous figure of the
earth, the equinoctial points, the obliquity of the ecliptic, the
principles of gnomonics, and made the first sphere or image of
the heavens ; and Pjrthagoras, to whom we owe the discovery
of the true system of the world, and order of the planets,
though it may be they were assisted by the Egj^jtians and
Chaldeans. But whoever they were that first made these bold
steps in this noble art, they desei-ve the praise and admiration
of all future ages.

Felices animos, quibiis haec cognoscere primis,

Inque domos superas scandere cura fuit !
Credibile est illos pariter vitiisque jocisque

Altius humanis exeruisse caput.
Non Venus et vinuni sublimia pectora fregit ;

Officiumque fori, militiaeque labor.
Non levis ambitio, perfusaque gloria fuco,

Magnarumve fames sollicitavit opum.
Admovere oculis distantia sidera nostris ;

Aetheraque ingenio supposuere suo. — Omd, Fast. I.

But though the industry of former ages had discovered the
periods of the great bodies of the universe, and the true system
and order of them, and their orbits pretty near ; yet was there
one tiling still reserved for the glory of tliis age, and the
honour of the English nation, the grand secret of the whole
machine ; which, now it is discovered, proves to be (like the
other contrivances of infinite wisdom) simple and natural, de-
pending upon the most known and most common property of
matter, viz. gravity. From this the incomparable Mr. Newton '
has demonstrated the theories of all the bodies of the solar

' Sir Isaac Newton (1642-1727). Prlncipla Mathematica, appeared in
His great work, Philosophiae Naturalis 1687.



USEFULNESS OF MATHEMATICAL LEARNING. 415

system, of all the primary planets and their secondaries, and
among others, the moon, which seemed most averse to numbers ;
and not only of the planets, the slowest of which completes its
period in less than half the age of a man, but likewise of the
comets, some of which it is probable spend more than 2000 years
in one revolution about the sun ; for whose theory he has laid
such a foundation, that after ages, assisted with more observa-
tions, may l)e able to calculate their returns. In a word, the
precession of the eqxiinoctial points, the tides, the unequal
vibration of pendulous bodies in different latitudes, &c., are no
more a question to those that have geometry enough to under-
stand what he has delivered on those subjects : a perfection in
philosophy that the boldest thinker durst hardly have hoped
for ; and, unless mankind turn barbarous, will continue the
reputation of this nation, as long as the fabric of nature shall
endure. After this, what is it we may not expect from '
geometiy joined to observations and experiments ?

The next considerable object of natural knowledge I take to
be light. How unsuccessful enquuies are about this glorious
body without the help of geometry, may appear from the empty
and frivolous discourses and disputations of a sort of men that
call themselves philosophers ; whom nothing will serve perhaps,
but the knowledge of the very nature and intimate causes of
every thing : while on the other hand, the geometers not
troubling themselves with those fruitless enquiries about the
nature of light, have discovered two remarkable properties of it,
in the reflexion and refraction of its beams ; and from those,
and their straightness in other cases, have invented the noble
arts of optics, catoptrics, and dioptrics ; teaching us to manage
this subtile body for the improvement of our knowledge, and
useful purposes of life. They have likewise demonstrated the
causes of several celestial appearances, that arise from the
inflection of its beams, both in the heavenly bodies themselves
and other phenomena, as Parhelia, the Iris, &c., and by a late
experiment they have discovered the celerity of its motion.
And we shall know yet more surprising properties of light,
when Mr. Newton shall be pleased to gratify the world with
his book of light and colours \

* Newton's Optics, or a Treatise of in 1704. His theory of Light and
the Beflexions, Refractions, Inflections Colours had been printed in the
<md Colours of Light, was published Transactions of the Royal Society



4t6 works of dr. arbuthnot.

The fluids which involve our earth, viz. air and water, are
the next great and conspicuous bodies that nature presents to
our view ; and I think we know little of either, but what is
owing to mechanics and geometry. The two chief properties
of air, its gravity and elastic force, have been discovered by
mechanical experiments. From thence the decrease of the air's
density according to the increase of the distance of the earth has
been demonstrated by geometers, and confirmed by experiments
of the subsidence of the mercuiy in the Torricellian experiment.
From this likewise, by assistance of geometry, they have deter-



Online LibraryGeorge Atherton AitkenThe life and works of John Arbuthnot, M.D., fellow of the Royal College of Physicians → online text (page 37 of 47)