_An Analytical Resolution of certain Equations of the 3d, 5th, 7th, 9th
Powers, and so on _ad Infinitum_, in finite Terms, after the manner
of _Cardan's_ Rules for Cubicks. By Mr. _A. Moivre_, F. R. S._ 365
_A Discourse concerning the Action of the Sun and Moon on Animal
Bodies; and the Influence which this may have in many Diseases. By
_Richard Mead_, M. D. F. R. S._ 371
_A Translation of Part of Monsieur _Fontenelle's_ Preface to the
Memoirs of the Royal Academy at _Paris_, in the Year 1699. treating
of the Usefulness of Mathematical Learning._
But to what purpose should People become fond of the Mathematicks and
Natural Philosophy. Of what use are the Transactions of the Academy?
These are common Questions, which most do not barely propose as
Questions; and it will not be improper to clear them.
People very readily call useless, what they do not understand. It is a
sort of Revenge; and as the Mathematicks and Natural Philosophy are
known but by few, they are generally look'd upon as useless. The reason
of this is; because they are crabbed and not easily learnt.
We have a Moon to light us in the Night; What is it to us, say they,
whether _Jupiter_ hath four? Why so many laborious Observations, so many
tedious Calculations to know exactly their Course? They'll not afford us
the more Light for it; and Nature, which hath plac'd these little
Planets without the reach of our Eyes, doth not seem to have made them
for us. According to this plausible Argument they ought not to have been
observ'd with a Telescope, nor study'd. But it is certain, that we had
been considerable Loosers by it: For those who have some insight into
the Principles of Geography and Navigation know, that since these four
Moons about _Jupiter_ have been discover'd, they have been more useful
to those Sciences than our own Moon; and that they serve, and shall more
and more serve to make new Sea-Charts, infinitely more exact than the
Old; and are likely to save the Lives of a vast many Seamen. Did we reap
no other advantage from Astronomy than this from these Satellites of
_Jupiter_, that wou'd be sufficient to justifie those prodigious
Calculations, those assiduous and nice Observations, this great number
of elaborate Instruments, and this Noble Edifice built only for this
Science. However the greatest part of Mankind know nothing of these
Satellites of _Jupiter_, unless perhaps by hear-say, and that too
confusedly; or else they are ignorant of what Affinity they have with
Navigation, or of the great Improvements which have been lately made in
it.
This is the Fate of Sciences, which are study'd and improv'd by few.
Most People are not sensible of their Progress, and especially when made
in some mean Callings. But what doth it signifie, that we can now more
easily direct the Course of Rivers, cut out Canals, and settle new
Navigations; because our Method of taking the Level and making Sluces is
infinitely better than heretofore? Some Masons and Seamen have thereby
found their Business easier, but they themselves were not sensible of
the Skill of the Geometrician who directed them. They were mov'd, as the
Body by a Soul, it doth not know. Others are yet less sensible of the
Genius that presided over the Undertaking; and the World is the better
for its succeeding well, but not altogether free from Ingratitude.
Anatomy, which is some time since so carefully study'd, can't become
more exact, but Chyrurgical Operations must also be more sure. Surgeons
know this; but those who receive the Benefit of their Art know nothing
of it. And indeed how should they? They would be oblig'd to compare Old
with Modern Surgery; and this wou'd take too much Time, and go against
the Grain: So that since the Operation hath succeeded well, they do not
think it material to know whether it had succeeded as well in another
Century.
It is strange that so many things are before our Eyes, and that we do
not see them. Your Handycraft Shops are full of ingenious Works; but yet
we hardly mind them: And very useful and well contriv'd Instruments and
Experiments want Spectators, who wou'd be wonderfully pleas'd, wou'd
they take the pains to admire them.
If a Learned Society have made some Improvements in Geometry, Anatomy,
Mechanicks, or any other useful Science, it must not be expected, that
the World will go back to so remote a Spring to thank and applaud them
for the Usefulness of their Productions: For it will be more easie to
enjoy the Benefit of their Discoveries and Improvements than to know
them. The Determination of Longitude by the Satellites, the Discovery of
the _Ductus Thoracicus_, a more convenient, and more exact Level, are
not Novelties so fit to make a noise as a pleasant Poem, or a handsome
Piece of Oratory.
Altho' the Usefulness of Mathematicks and Natural Philosophy is obscure,
yet it is real. To consider Mankind in their Natural State, nothing is
more useful to them, than what may preserve their Lives, and produce
those Arts, which are both great Helps and Ornaments to Publick
Societies.
As for what concerns the Preservation of Life, it peculiarly belongs to
Physick; which for that reason is divided in the Academy into three
Branches, which make three different sorts of Members of this Society,
Anatomy, Chymistry, and Botanicks. Every Body knows of what Importance
it is to have an exact Knowledge of Human Body, and of what Medicines
may be extracted from Minerals and Plants.
As for Arts, too tedious to be reckon'd, they depend some upon Natural
Philosophy, others upon Mathematicks.
One wou'd think at first, that if the Mathematicks were to be confin'd
to what is useful in them, they ought only to be improv'd in those
things, which have an immediate and sensible affinity with Arts, and the
rest ought to be neglected as a Vain Theory. But this wou'd be a very
wrong Notion. As for Instance, the Art of Navigation hath a necessary
Connexion with Astronomy, and Astronomy can never be too much improv'd
for the Benefit of Navigation. Astronomy cannot be without Opticks by
reason of Perspective Glasses; and both, as all other Parts of
Mathematicks, are grounded upon Geometry, and to go as far as you can,
even upon Algebra.
Geometry, and especially Algebra, are the Keys of all the Inquiries,
that can be made concerning Magnitude. These Sciences which are only
conversant about abstruse Relations, and simple Ideas, may seem dry and
barren, whilst they keep within the Verge of the Intellectual World; but
mixt Mathematicks, which stoop to Matter, and consider the Motion of the
Stars, the Augmentation of moving Forces, the different Passages of the
Rays of Light through different Mediums; the different Effects of Sound
by the Vibration of Things; to conclude all those Sciences, which
discover the particular Relations of Sensible Magnitudes go on farther
and more securely, when the Art of discovering Relations in General is
more perfect. The Universal Instrument cannot be too extensive, too
handy, or too easily apply'd: It is useful to all the Sciences, and they
cannot be without it: And therefore among the Mathematicians of the
Academy, who are design'd to be useful to the Publick, the Geometricians
and Algebrists make a Class, as well as the Astronomers and Mechanicks.
However, it is certain, that Speculations purely of Geometry, or of
Algebra, are not about useful things: But it is certain too, that those
that are not, either lead or belong to those that are. It is in it self
a very barren thing to know, that in a Parabola a Subtangant is double
the corresponding Abscissæ; but yet it is a Degree of Knowledge
necessary to the Art of throwing Bombs, so exactly as they can do now.
There are not by far so many evident Uses as Propositions or Truths in
the Mathematicks: Yet it is enough if the Concourse of several Truths is
generally of some use.
Farther, a Geometrical Speculation, which was not at first applicable to
any use, becomes so afterwards. When the greatest Geometricians in the
Seventeenth Century set about to study a new Curve, which they call'd a
Cycloide, they only engag'd themselves in a meer Speculation out of
Vanity, striving to outdo one another by the Discovery of difficult
Theorems. They did not even pretend that this was for the Publick Good;
however by diving into the Nature of the Cycloide it was found, that it
was destin'd to make Pendulums as perfect as may be, and carry the
Measure of Time as far as it can go.
It is the same thing with Natural Philosophy as with Geometry. The
Anatomy of Animals seems insignificant; and it only concerns us to know
that of Human Body. But yet some Parts of it, which are of so nice, or
so confus'd a Make, that they are invisible, are sensible and manifest
in the Body of an Animal. Hence it is, that Monsters themselves are not
to be neglected. The Mechanism conceal'd in a particular Kind or in a
common Make, is unfolded in another kind, or in an extraordinary Make;
and one wou'd be almost apt to say, that Nature by multiplying and
varying so much her Works, can't sometimes forbear betraying her
Secrets. All that the Antients knew of the Load-stone, was, that it
attracts Iron. But whether they did not value a Curiosity, which
promis'd them nothing; or that their Genius did not lead them to make
Experiments, they have not examin'd this Stone as carefully as they
might. One Experiment taught them, that it turns of its self towards the
Poles of the World, and did put into their Hands the inestimable
Treasure of the Mariners Compass. They might easily have made this
Discovery important, and yet they did not do it; and if they had spent a
little more time upon a Curiosity which seem'd useless to them, the
Latent use of it had soon appear'd.
Let us always make a Collection of Mathematical and Physical Truths;
happen what it will we can't hazard much by it. It is certain, that they
shall be drawn from Springs, whence a great many useful ones have
already been drawn. We have reason to presume, that we shall draw from
thence, some that shall shine as soon as they are discover'd, and
convince us of their Usefulness. Other Truths shall stay some time till
a piercing Meditation, or some happy Accident discovers their Use. Some
Truths being consider'd by themselves shall be barren, till they are
consider'd with reference to one another. Lastly, let the worse come to
the worse, some shall be eternally useless.
I mean useless with reference to sensible and gross Uses; for otherwise
they shall not be so. An Object upon which alone you cast your Eyes is
the clearer and brighter, when the neighbouring Objects, which however
you do not look upon, are also enlighten'd; because it hath the Benefit
of the Rays, which are reflected from them. Thus those Discoveries,
which are palpably useful, and deserve our chiefest Attention, are in
some measure enlighten'd by those, which may be call'd useless. For all
Truths make one another more lucid.
It is always useful to have right Notions, even of useless Subjects. And
tho' we cou'd reap no benefit by the Knowledge of Numbers and Sines, yet
it wou'd still be the only certain Knowledge granted to our Natural
Light, and they wou'd serve to give our Reason the first Habit of and
Inclination to Truth. They wou'd teach us to operate upon Truths; to
take the Thread of them, which is generally very fine and almost
imperceptible; and to follow it as far as it reaches: In a word, they
wou'd make Truth so familiar, that we might on other Occasions know it
at first sight, and almost by Instinct.
A Geometrical Genius is not so confin'd to Geometry, but that it may be
capable of learning other Sciences. A Tract of Morality, Politicks, or
Criticism, and even a Piece of Oratory, supposing the Author qualify'd
otherwise for those Performances, shall be the better for being compos'd
by a Geometrician. That Order, Perspicuity, _Precision_ and Exactness,
which some time since are found in good Books, may originally proceed
from that Geometrical Genius, which is now more common than ever, and in
some manner is communicated by one Relation to another, nay even to
those that do not understand Geometry. Sometimes a Great Man draws all
his Cotemporaries after him; and he who hath the justest Claim to the
Glory of having settled a new Art of Arguing, was an Excellent
Geometrician.
Lastly, whatever raises us to Great and Noble Reflexions, tho' they be
purely Speculative, afford a Spiritual and Philosophical _Utility_. The
Wants of the Mind are perhaps as many as those of the Body. She desires
to extend her Knowledge: All that can be known, is necessary to her, and
there can be no better Proof than this, that she is design'd for Truth.
Nothing perhaps can redound more to her Glory, than the Pleasure that is
felt sometimes, in spight of ones self, in the dry and crabbed Questions
of Algebra.
But without running counter to the common Notions, and recurring to
Advantages which may seem too far fetch'd and refin'd, it may fairly be
own'd, that the Mathematicks and Natural Philosophy have some things
which are only subservient to Curiosity; and so have those Sciences
which are most generally acknowledg'd to be useful, as History, _&c._
History doth not in every Part of it supply us with Examples of Vertue
and Rules for our Behaviour. For besides these, therein you have a View
of the perpetual Revolutions of Human Affairs, of the Beginning and Fall
of Empires, of Manners, Customs, and Opinions which continually succeed
one another; and in a word, of all that rapid, tho' insensible, Motion
that carries all before it, and incessantly alters the Face of the Earth.
Had we a mind to oppose Curiosity to Curiosity, we shou'd find that
instead of the Motion, which agitates Nations, and gives birth to, and
destroys States; Natural Philosophy considers that Great and Universal
Motion, which hath put the whole Frame of Nature in Order, and suspended
the Cœlestial Bodies in several Spheres, and which illuminates and
extinguishes some Stars; and by following always unalterable Laws,
diversifies its effects _ad infinitum_. If the surprising difference of
Manners and Opinions of Mankind is so entertaining; there is too a great
deal of Pleasure to study the prodigious diversity of the Structure of
the different Species of Animals, with reference to their different
Functions, to the Elements they live in, to the Climates they inhabit,
and the Aliments they are to take, _&c._ The most curious strokes of
History shall hardly be more curious than the _Phosphorus_, the cold
Liquors which being mixt together, break out into a flame; Silver Trees,
the almost Magical Operations of the Load-Stone, and a vast number of
Secrets, which Art hath discover'd by a near and diligent Scrutiny of
Nature.
Lastly, Natural Philosophy doth as much as it is possible unravel the
Footsteps of that Infinite Intellect and Wisdom, who hath made all
things: Whereas the Object of History are the disorderly Effects of the
Passion, and of Humane Caprices; and so odd a Series of Events, that
some formerly fancy'd that a Blind and Senseless Deity had the Direction
of them.
We must not look upon the Sublime Reflexions which Natural Philosophy
leads us to make concerning the Author of the Universe, as meer
Curiosities. For this stupendous Work, which appears always more
wonderful the more we know it, gives us such exalted Notions of its
Maker, that they fill our Minds with Admiration and Respect. But above
all, Astronomy and Anatomy are the two Sciences which more palpably lay
before us two grand Attributes of our Creator; one his Immensity by the
distance, Magnitude and Number of Cœlestial Bodies; the other his
Infinite Knowledge by the Mechanism of Animals. True Natural Philosophy
is a kind of Theology.
The different views of Humane Understanding are almost infinite; and
Nature is really so. So that we may every day expect some Discoveries,
either in Mathematicks or Natural Philosophy, which shall be of a new
sort of Utility or Curiosity. Make a Collection of all the different
Advantages which the Mathematicks afforded a Hundred Years ago, and
you'll find nothing to be compar'd to the Perspective Glasses they have
furnish'd since that time, and which are a new Organ to the Sight, and
cou'd not be expected from Art. How surpriz'd had the Ancients been, if
they had been told that their Posterity, by the help of some
Instruments, shou'd one day see a vast number of Objects which they did
not see; a Heaven that was unknown to them; and Plants and Animals they
did not even suspect it was possible to exist. Naturalists had already a
great many curious Experiments; but within about half a Century, the
Air-Pump hath produced a prodigious quantity of them wholly new, and
which by shewing Bodies in a Space void of Air, shews them as
transported in a World different from ours, where they undergo
Alterations whereof we had no Notion. The Excellency of Geometrical
Methods, which are every day invented and improv'd, may perhaps at last
exhaust Geometry; that is, The Art of making Geometrical Discoveries,
and that is all: Whereas Natural Philosophy, which contemplates an
Object of an unlimited Variety, and _Fæcundity_, shall always find room
for new Observations, and opportunities to increase its vast Stock, and
shall have the Advantage of never being a compleat Science.
There are so many things to be discover'd, whereof a great part, in all
likelyhood shall never be known; that they give an opportunity to those
who will not encounter with the Thorns and Difficulties of Natural
Philosophy, to affect a sort of Discouragement. A great many to vilify
this Natural Science, pretend a mighty veneration for the works of
Nature, and that they are absolutely incomprehensible. However, Nature
is never so admirable, nor so admir'd as when known. True it is, that
what is known is inconsiderable in comparison of what is not yet known.
Nay, Sometimes what is not known, is exactly what seems shou'd be the
soonest known. As for instance, it is not at least certainly known, why
a Stone thrown up into the Air falls down again; but we certainly know
the cause of the Rainbow, why it doth not exceed a certain height; why
its breadth is always the same; why when there are two Rainbows at the
same time, the Colours of the one are overset with reference to the
Colours of the other; and yet the fall of a Stone in the Air appears a
more simple Phænomenon, than the Rainbow. But in a word, altho' we do
not know every thing, we are not neither ignorant of every thing. And
altho' we are ignorant of the most simple Events, yet we have a
knowledge of what seems the most Complex. So that if we have on the one
hand reason to fear, lest our Vanity shou'd flatter us with the hopes of
attaining to the knowledge of things above our reach; on the other we
ought to dread, lest our Slothfulness should also flatter us that we are
condemn'd to a greater degree of Ignorance than really we are.
People may think that the Sciences do not begin to exert themselves,
either because they cou'd be but imperfect among the Ancients; or
because we have almost lost the Footsteps of them during the gloomy
Darkness of Barbarity; or because a better method hath been taken about
100 Years ago. Was the Progress Historically examin'd, they have already
made in so short a time, notwithstanding the strong, but false
Prejudices they had long to encounter with, even sometimes the foreign
Obstacles they have met with from Authority and Power; the want of Zeal
for Sciences so remote from common use, those few who apply'd themselves
to this Work, and the weak Motives which engag'd them in it; a Man would
wonder at the Greatness and Rapidity of the Progress of the Sciences,
and even we might observe some new ones to start out of nothing, and
perhaps be tempted to have too great hopes of future Improvements.
The greater reason we have of future Success, the greater we have to
look upon the Sciences as in their Cradles, at least Natural Philosophy.
And therefore the Academy is only now employ'd to make an ample
Provision of Observations, and Facts well attested, which may one day be
the foundation of a System. For before the Systematical Natural
Philosophy can raise solid Edifices; Experimental Natural Philosophy
must be in a condition to supply it with good Materials.
None but Societies, of those too countenanc'd and encourag'd by the
Prince, can successfully make and prepare this Collection of Materials.
All the Learning, Care, Life and Wealth of one Private Man can never
answer this Design. There are too many different Experiments to be made,
which are to be too much vary'd, and a long time prosecuted with the
same Temper and Mind. The Cause of the least Effect is so wrap'd up,
that unless you very carefully open all the various Foldings, you cannot
come at it.
Hitherto the Academy of Sciences hath consider'd Nature but by parcels:
They have fix'd upon no general System, for fear of falling into the
inconveniency of hasty Systems, which are very grateful to the
impatience of Humane Understanding; and being once settled, are
Obstacles to what Truths are afterwards discover'd. This day we are sure
of a Fact, to morrow we shall be sure of another that hath no relation
with the former. However some Conjectures are ventur'd at upon Causes;
but they are only Conjectures. So that this Collection, which the
Academy gives to the Publick, is compos'd of separate Fragments,
independant of one another; whereof every one who is the Author,
warrants the Facts and Experiments; and whose Arguments are approv'd by
the Academy, but with Restrictions becoming Wise and Wary Scepticks.
Time perhaps will come, when these scatter'd Fragments shall be united
into one regular Body; and if they be such as they are wish'd, they may
of themselves Unite. A great many Truths, when their Numbers is
considerable, shew so near a Relation to, and so mutual a Dependance
upon one another, that it seems, that notwithstanding their violent
Separation, they have a natural Tendency to be re-united.