The labyrinth and abyss of infinity is also a new course Sir Isaac Newton
has gone through, and we are obliged to him for the clue, by whose
assistance we are enabled to trace its various windings.
Descartes got the start of him also in this astonishing invention. He
advanced with mighty steps in his geometry, and was arrived at the very
borders of infinity, but went no farther. Dr. Wallis, about the middle
of the last century, was the first who reduced a fraction by a perpetual
division to an infinite series.
The Lord Brouncker employed this series to square the hyperbola.
Mercator published a demonstration of this quadrature; much about which
time Sir Isaac Newton, being then twenty-three years of age, had invented
a general method, to perform on all geometrical curves what had just
before been tried on the hyperbola.
It is to this method of subjecting everywhere infinity to algebraical
calculations, that the name is given of differential calculations or of
fluxions and integral calculation. It is the art of numbering and
measuring exactly a thing whose existence cannot be conceived.
And, indeed, would you not imagine that a man laughed at you who should
declare that there are lines infinitely great which form an angle
infinitely little?
That a right line, which is a right line so long as it is finite, by
changing infinitely little its direction, becomes an infinite curve; and
that a curve may become infinitely less than another curve?
That there are infinite squares, infinite cubes, and infinites of
infinites, all greater than one another, and the last but one of which is
nothing in comparison of the last?
All these things, which at first appear to be the utmost excess of
frenzy, are in reality an effort of the subtlety and extent of the human
mind, and the art of finding truths which till then had been unknown.
This so bold edifice is even founded on simple ideas. The business is to
measure the diagonal of a square, to give the area of a curve, to find
the square root of a number, which has none in common arithmetic. After
all, the imagination ought not to be startled any more at so many orders
of infinites than at the so well-known proposition, viz., that curve
lines may always be made to pass between a circle and a tangent; or at
that other, namely, that matter is divisible in _infinitum_. These two
truths have been demonstrated many years, and are no less
incomprehensible than the things we have been speaking of.
For many years the invention of this famous calculation was denied to Sir
Isaac Newton. In Germany Mr. Leibnitz was considered as the inventor of
the differences or moments, called fluxions, and Mr. Bernouilli claimed
the integral calculus. However, Sir Isaac is now thought to have first
made the discovery, and the other two have the glory of having once made
the world doubt whether it was to be ascribed to him or them. Thus some
contested with Dr. Harvey the invention of the circulation of the blood,
as others disputed with Mr. Perrault that of the circulation of the sap.
Hartsocher and Leuwenhoek disputed with each other the honour of having
first seen the _vermiculi_ of which mankind are formed. This Hartsocher
also contested with Huygens the invention of a new method of calculating
the distance of a fixed star. It is not yet known to what philosopher we
owe the invention of the cycloid.
Be this as it will, it is by the help of this geometry of infinites that
Sir Isaac Newton attained to the most sublime discoveries. I am now to
speak of another work, which, though more adapted to the capacity of the
human mind, does nevertheless display some marks of that creative genius
with which Sir Isaac Newton was informed in all his researches. The work
I mean is a chronology of a new kind, for what province soever he
undertook he was sure to change the ideas and opinions received by the
rest of men.
Accustomed to unravel and disentangle chaos, he was resolved to convey at
least some light into that of the fables of antiquity which are blended
and confounded with history, and fix an uncertain chronology. It is true
that there is no family, city, or nation, but endeavours to remove its
original as far backward as possible. Besides, the first historians were
the most negligent in setting down the eras: books were infinitely less
common than they are at this time, and, consequently, authors being not
so obnoxious to censure, they therefore imposed upon the world with
greater impunity; and, as it is evident that these have related a great
number of fictitious particulars, it is probable enough that they also
gave us several false eras.
It appeared in general to Sir Isaac that the world was five hundred years
younger than chronologers declare it to be. He grounds his opinion on
the ordinary course of Nature, and on the observations which astronomers
have made.
By the course of Nature we here understand the time that every generation
of men lives upon the earth. The Egyptians first employed this vague and
uncertain method of calculating when they began to write the beginning of
their history. These computed three hundred and forty-one generations
from Menes to Sethon; and, having no fixed era, they supposed three
generations to consist of a hundred years. In this manner they computed
eleven thousand three hundred and forty years from Menes's reign to that
of Sethon.
The Greeks before they counted by Olympiads followed the method of the
Egyptians, and even gave a little more extent to generations, making each
to consist of forty years.
Now, here, both the Egyptians and the Greeks made an erroneous
computation. It is true, indeed, that, according to the usual course of
Nature, three generations last about a hundred and twenty years; but
three reigns are far from taking up so many. It is very evident that
mankind in general live longer than kings are found to reign, so that an
author who should write a history in which there were no dates fixed, and
should know that nine kings had reigned over a nation; such an historian
would commit a great error should he allow three hundred years to these
nine monarchs. Every generation takes about thirty-six years; every
reign is, one with the other, about twenty. Thirty kings of England have
swayed the sceptre from William the Conqueror to George I., the years of
whose reigns added together amount to six hundred and forty-eight years;
which, being divided equally among the thirty kings, give to every one a
reign of twenty-one years and a half very near. Sixty-three kings of
France have sat upon the throne; these have, one with another, reigned
about twenty years each. This is the usual course of Nature. The
ancients, therefore, were mistaken when they supposed the durations in
general of reigns to equal that of generations. They, therefore, allowed
too great a number of years, and consequently some years must be
subtracted from their computation.
Astronomical observations seem to have lent a still greater assistance to
our philosopher. He appears to us stronger when he fights upon his own
ground.
You know that the earth, besides its annual motion which carries it round
the sun from west to east in the space of a year, has also a singular
revolution which was quite unknown till within these late years. Its
poles have a very slow retrograde motion from east to west, whence it
happens that their position every day does not correspond exactly with
the same point of the heavens. This difference, which is so insensible
in a year, becomes pretty considerable in time; and in threescore and
twelve years the difference is found to be of one degree, that is to say,
the three hundred and sixtieth part of the circumference of the whole
heaven. Thus after seventy-two years the colure of the vernal equinox
which passed through a fixed star, corresponds with another fixed star.
Hence it is that the sun, instead of being in that part of the heavens in
which the Ram was situated in the time of Hipparchus, is found to
correspond with that part of the heavens in which the Bull was situated;
and the Twins are placed where the Bull then stood. All the signs have
changed their situation, and yet we still retain the same manner of
speaking as the ancients did. In this age we say that the sun is in the
Ram in the spring, from the same principle of condescension that we say
that the sun turns round.
Hipparchus was the first among the Greeks who observed some change in the
constellations with regard to the equinoxes, or rather who learnt it from
the Egyptians. Philosophers ascribed this motion to the stars; for in
those ages people were far from imagining such a revolution in the earth,
which was supposed to be immovable in every respect. They therefore
created a heaven in which they fixed the several stars, and gave this
heaven a particular motion by which it was carried towards the east,
whilst that all the stars seemed to perform their diurnal revolution from
east to west. To this error they added a second of much greater
consequence, by imagining that the pretended heaven of the fixed stars
advanced one degree eastward every hundred years. In this manner they
were no less mistaken in their astronomical calculation than in their
system of natural philosophy. As for instance, an astronomer in that age
would have said that the vernal equinox was in the time of such and such
an observation, in such a sign, and in such a star. It has advanced two
degrees of each since the time that observation was made to the present.
Now two degrees are equivalent to two hundred years; consequently the
astronomer who made that observation lived just so many years before me.
It is certain that an astronomer who had argued in this manner would have
mistook just fifty-four years; hence it is that the ancients, who were
doubly deceived, made their great year of the world, that is, the
revolution of the whole heavens, to consist of thirty-six thousand years.
But the moderns are sensible that this imaginary revolution of the heaven
of the stars is nothing else than the revolution of the poles of the
earth, which is performed in twenty-five thousand nine hundred years. It
may be proper to observe transiently in this place, that Sir Isaac, by
determining the figure of the earth, has very happily explained the cause
of this revolution.
All this being laid down, the only thing remaining to settle chronology
is to see through what star the colure of the equinoxes passes, and where
it intersects at this time the ecliptic in the spring; and to discover
whether some ancient writer does not tell us in what point the ecliptic
was intersected in his time, by the same colure of the equinoxes.
Clemens Alexandrinus informs us, that Chiron, who went with the
Argonauts, observed the constellations at the time of that famous
expedition, and fixed the vernal equinox to the middle of the Ram; the
autumnal equinox to the middle of Libra; our summer solstice to the
middle of Cancer, and our winter solstice to the middle of Capricorn.
A long time after the expedition of the Argonauts, and a year before the
Peloponnesian war, Methon observed that the point of the summer solstice
passed through the eighth degree of Cancer.
Now every sign of the zodiac contains thirty degrees. In Chiron's time,
the solstice was arrived at the middle of the sign, that is to say to the
fifteenth degree. A year before the Peloponnesian war it was at the
eighth, and therefore it had retarded seven degrees. A degree is
equivalent to seventy-two years; consequently, from the beginning of the
Peloponnesian war to the expedition of the Argonauts, there is no more
than an interval of seven times seventy-two years, which make five
hundred and four years, and not seven hundred years as the Greeks
computed. Thus in comparing the position of the heavens at this time
with their position in that age, we find that the expedition of the
Argonauts ought to be placed about nine hundred years before Christ, and
not about fourteen hundred; and consequently that the world is not so old
by five hundred years as it was generally supposed to be. By this
calculation all the eras are drawn nearer, and the several events are
found to have happened later than is computed. I do not know whether
this ingenious system will be favourably received; and whether these
notions will prevail so far with the learned, as to prompt them to reform
the chronology of the world. Perhaps these gentlemen would think it too
great a condescension to allow one and the same man the glory of having
improved natural philosophy, geometry, and history. This would be a kind
of universal monarchy, with which the principle of self-love that is in
man will scarce suffer him to indulge his fellow-creature; and, indeed,
at the same time that some very great philosophers attacked Sir Isaac
Newton's attractive principle, others fell upon his chronological system.
Time that should discover to which of these the victory is due, may
perhaps only leave the dispute still more undetermined.