In those published afterwards (1618), he changed this for 1.0000000,
making of course that of 100, 2.0000000, and so forth. This
construction has been followed since; but those of the first method
are not wholly neglected; they are called hyperbolical logarithms,
from expressing a property of that curve. Napier found a coadjutor
well worthy of him in Henry Briggs, professor of geometry at Gresham
college. It is uncertain from which of them the change in the form of
logarithms proceeded. Briggs, in 1618, published a table of logarithms
up to 1,000, calculated by himself. This was followed in 1624 by his
greater work, Arithmetica Logarithmica, containing the logarithms of
all natural numbers as high as 20,000, and again from 90,000 to
100,000. These are calculated to fourteen places of decimals, thus
reducing the error, which strictly speaking, must always exist from
the principle of logarithmical construction, to an almost
infinitesimal fraction. He had designed to publish a second table,
with the logarithms of sines and tangents to the 100th part of a
degree. This he left in a considerably advanced state; and it was
published by Gellibrand in 1633. Gunter had as early as 1620 given the
logarithms of sines and tangents on the sexagesimal scale, as far as
seven decimals. Vlacq, a Dutch bookseller, printed in 1628 a
translation of Brigg’s Arithmetica Logarithmica, filling up the
interval from 20,000 to 90,000 with logarithms calculated to eleven
decimals. He published also in 1633 his Trigonometrica Artificialis,
the most useful work, perhaps, that had appeared, as it incorporated
the labours of Briggs and Gellibrand, but with no great regard to the
latter’s fair advantage. Kepler came like a master to the subject; and
observing that some foreign mathematicians disliked the theory upon
which Napier had explained the nature of logarithms, as not rigidly
geometrical, gave one of his own to which they could not object. But
it may probably be said that the very novelty to which the disciples
of the ancient geometry were averse, the introduction of the notion of
velocity into mathematical reasoning, was that which linked the
abstract science of quantity with nature, and prepared the way for
that expansive theory of infinites which bears at once upon the
subtlest truths that can exercise the understanding, and the most
evident that can fall under the senses.
|Kepler’s new geometry.|
9. It was, indeed, at this time that the modern geometry, which, if it
deviates something from the clearness and precision of the ancient,
has incomparably the advantage over it in its reach of application,
took its rise. Kepler was the man that led the way. He published, in
1615, his Nova Stereometria Doliorum, a treatise on the capacity of
casks. In this he considers the various solids which may be formed by
the revolution of a segment of a conic section round a line which is
not its axis, a condition not unfrequent in the form of a cask. Many
of the problems which he starts he is unable to solve. But what is
most remarkable in this treatise is that he here suggests the bold
idea, that a circle may be deemed to be composed of an infinite number
of triangles, having their bases in the circumference, and their
common apex in the centre; a cone, in like manner, of infinite
pyramids, and a cylinder of infinite prisms.[603] The ancients had
shown, as is well known, that a polygon inscribed in a circle, and
another described about it, may, by continual bisection of their
sides, be made to approach nearer to each other than any assignable
differences. The circle itself lay, of course, between them. Euclid
contents himself with saying that the circle is greater than any
polygon that can be inscribed in it, and less than any polygon that
can be described about it. The method by which they approximated to
the curve space by continual increase or diminution of the rectilineal
figure was called exhaustion, and the space itself is properly called
by later geometers the limit. As curvilineal and rectilineal spaces
cannot possibly be compared by means of superposition, or by showing
that their several constituent portions could be made to coincide, it
had long been acknowledged impossible by the best geometers to
quadrate by a direct process any curve surface. But Archimedes had
found, as to the parabola, that there was a rectilineal space, of
which he could indirectly demonstrate that it was equal, that is,
could not be unequal, to the curve itself.
[603] Fabroni, Vitæ Italorum, i., 272.
|Its difference from the ancient.|
10. In this state of the general problem, the ancient methods of
indefinite approximation having prepared the way, Kepler came to his
solution of questions which regarded the capacity of vessels.
According to Fabroni, he supposed solids to consist of an infinite
number of surfaces, surfaces of an infinity of lines, lines of
infinite points.[604] If this be strictly true, he must have left
little, in point of invention, for Cavalieri. So long as geometry is
employed as a method of logic, an exercise of the understanding on
those modifications of quantity which the imagination cannot
grasp, such as points, lines, infinites, it must appear almost an
offensive absurdity to speak of a circle as a polygon with an infinite
number of sides. But when it becomes the handmaid of practical art, or
even of physical science, there can be no other objection, than always
arises from incongruity and incorrectness of language. It has been
found possible to avoid the expressions attributed to Kepler; but they
seem to denote in fact nothing more than those of Euclid or
Archimedes; that the difference between a magnitude and its limit may
be regularly diminished, till, without strictly vanishing, it becomes
less than any assignable quantity, and may consequently be disregarded
in reasoning upon actual bodies.
[604] Idem quoque solida cogitavit ex infinito numero
superflcierum existere, superficies autem ex lineis infinitis, ac
lineis ex infinitis punctis. Ostendit ipse quantum ea ratione
brevior fieri via possit ad vera quædam captu difficiliora, cum
antiquarum demonstrationum circuitus ac methodus inter se
comparandi figuras circumscriptas et inscriptas iis planis aut
solidis, quæ mensuranda essent, ita declinarentur. Ibid.
|Adopted by Galileo.|
11. Galileo, says Fabroni, trod in the steps of Kepler, and in his
first dialogue on mechanics, when treating on a cylinder cut out of a
hemisphere, became conversant with indivisibles (familiarem habere
cœpit cum indivisibilibus usum). But in that dialogue he confused the
metaphysical notions of divisible quantity, supposing it to be
composed of unextended indivisibles; and not venturing to affirm that
infinites could be equal or unequal to one another, he preferred to
say, that words denoting equality or excess could only be used as to
finite quantities. In his fourth dialogue on the centre of gravity, he
comes back to the exhaustive method of Archimedes.[605]
[605] Fabroni, Vitæ Italorum, i., 272.
|Extended by Cavalieri.|
12. Cavalieri, professor of mathematics at Bologna, the generally
reputed father of the new geometry, though Kepler seems to have so
greatly anticipated him, had completed his method of indivisibles in
1626. The book was not published till 1635. His leading principle is
that solids are composed of an infinite number of surfaces placed one
above another as their indivisible elements. Surfaces are formed in
like manner by lines, and lines by points. This, however, he asserts
with some excuse and explanation; declaring that he does not use the
words so strictly, as to have it supposed that divisible quantities
truly and literally consist of indivisibles, but that the ratio of
solids is the same as that of an infinite number of surfaces, and that
of surfaces the same as of an infinite number of lines; and to put an
end to cavil, he demonstrated that the same consequences would follow
if a method should be adopted, borrowing nothing from the
consideration of indivisibles.[606] This explanation seems to have
been given after his method had been attacked by Guldin in 1640.
[606] Non eo rigore a se voces adhiberi, ac si dividuæ
quantitates verè ac propriè ex indivisibilibus existerent;
verumtamen id sibi duntaxat velle, ut proportio solidorum eadem
esset ac ratio superficierum omnium numero inflnitarum, et
proportio superficierum eadem ac illa infinitarum linearum:
denique ut omnia, quæ contra dici poterant, in radice præcideret,
demonstravit, easdem omnino consecutiones erui, si methodi aut
rationes adhiberentur omnino diversæ, quæ nihil ab indivisibilium
consideratione penderent. Fabroni.
Il n’est aucun cas dans la géometrie des indivisibles, qu’on ne
puisse facilement reduire à la forme ancienne de démonstration.
Ainsi, c’est s’arrêter à l’écorce que de chicaner sur le mot
d’indivisibles. Il est impropre si l’on veut, mais il n’en
résulte aucun danger pour la géometrie; et loin de conduire à
l’erreur, cette méthode, au contraire, a été utile pour atteindre
à des vérités qui avoient échappé jusqu’alors aux efforts des
géométres. Montucla, vol. ii., p. 39.
|Applied to the ratios of solids.|
13. It was a main object of Cavalieri’s geometry to demonstrate the
proportions of different solids. This is partly done by Euclid, but
generally in an indirect manner. A cone, according to Cavalieri, is
composed of an infinite number of circles decreasing from the base to
the summit, a cylinder of an infinite number of equal circles. He
seeks, therefore, the ratio of the sum of all the former to that of
all the latter. The method of summing an infinite series of terms in
arithmetical progression was already known. The diameters of the
circles in the cone decreasing uniformly were in arithmetical
progression, and the circles would be as their squares. He found that
when the number of terms is infinitely great, the sum of all the
squares described on lines in arithmetical progression is exactly one
third of the greatest square multiplied by the number of terms. Hence,
the cone is one third of a cylinder of the same base and altitude, and
the same may be shown of other solids.
|Problem of the cycloid.|
14. This bolder geometry was now very generally applied in difficult
investigations. A proof was given in the celebrated problems relative
to the cycloid, which served as a test of skill to the mathematicians
of that age. The cycloid is the curve described by a point in a
circle, while it makes one revolution along a horizontal base, as in
the case of a carriage wheel. It was far more difficult to determine
its area. It was at first taken for the segment of a circle. Galileo
considered it, but with no success. Mersenne, who was also unequal to
the problem, suggested it to a very good geometer, Roberval, who,
after some years, in 1634, demonstrated that the area of the cycloid
is equal to thrice the area of the generating circle. Mersenne
communicated this discovery to Descartes, who, treating the matter as
easy, sent a short demonstration of his own. On Roberval’s intimating
that he had been aided by a knowledge of the solution, Descartes found
out the tangents of the curve, and challenged Roberval and Fermat to
do the same. Fermat succeeded in this, but Roberval could not achieve
the problem, in which Galileo also and Cavalieri failed; though it
seems to have been solved afterwards by Viviani. “Such,” says
Montucla, “was the superiority of Descartes over all the geometers of
his age, that questions which most perplexed them cost him but an
ordinary degree of attention.” In this problem of the tangents (and it
might not, perhaps, have been worth while to mention it otherwise in
so brief a sketch), Descartes made use of the principle introduced by
Kepler, considering the curve as a polygon of an infinite number of
sides, so that an infinitely small arc is equal to its chord. The
cycloid has been called by Montucla, the Helen of geometers. This
beauty was, at least, the cause of war, and produced a long
controversy. The Italians claim the original invention as their own;
but Montucla seems to have vindicated the right of France to every
solution important in geometry. Nor were the friends of Roberval and
Fermat disposed to acknowledge so much of the exclusive right of
Descartes as was challenged by his disciples. Pascal, in his history
of the cycloid, enters the lists on the side of Roberval. This was not
published till 1658.
|Progress of algebra.|
15. Without dwelling more minutely on geometrical treatises of less
importance, though in themselves valuable, such as that of Gregory St.
Vincent, in 1647, or the Cyclometricus of Willebrod Snell, in 1621, we
come to the progress of analysis during this period. The works of
Vieta, it may be observed, were chiefly published after the year 1600.
They left, as must be admitted, not much in principle for the more
splendid generalisations of Harriott and Descartes. It is not
unlikely, that the mere employment of a more perfect notation would
have led the acute mind of Vieta to truths which seem to us, who are
acquainted with them, but a little beyond what he discovered.
|Briggs. Girard.|
16. Briggs, in his Arithmetica Logarithmica, was the first who clearly
showed what is called the Binomial Theorem, or a compendious method of
involution, by means of the necessary order of co-efficients in the
successive powers of a binomial quantity. Cardan had partially, and
Vieta much more clearly, seen this, nor was it likely to escape one so
observant of algebraic relations as the latter. Albert Girard, a
Dutchman, in his Invention Nouvelle en Algebre, 1629, conceived a
better notion of negative roots than his predecessors. Even Vieta had
not paid attention to them in any solution. Girard, however, not only
assigns their form, and shows, that in a certain class of cubic
equations there must always be one or two of this description, but
uses this remarkable expression: “A negative solution means in
geometry that the _minus_ recedes as the _plus_ advances.”[607] It
seems manifest that till some such idea suggested itself to the minds
of analysts, the consideration of negative roots, though they could
not possibly avoid perceiving their existence, would merely have
confused their solutions. It cannot, therefore, be surprising that not
only Cardan and Vieta, but Harriott himself, should have disregarded
them.
[607] La solution par moins s’explique en géometrie en
retrogradant, et le moins recule ou le plus avance. Montucla,
p. 112.
|Harriott.|
17. Harriott, the companion of Sir Walter Raleigh in Virginia, and the
friend of the Earl of Northumberland, in whose house he spent the
latter part of his life, was destined to make the last great discovery
in the pure science of algebra. Though he is mentioned here after
Girard, since the Artis Analyticæ Praxis was not published till 1631,
this was ten years after the author’s death. Harriott arrived at a
complete theory of the genesis of equations, which Cardan and Vieta
had but partially conceived. By bringing all the terms on one side, so
as to make them equal to zero, he found out that every unknown
quantity in an equation has as many values as the index of its powers
in the first term denotes; and that these values, in a necessary
sequence of combinations, from the co-efficients of the succeeding
terms into which the decreasing powers of the unknown quantity enter,
as they do also, by their united product, the last or known term of
the equation. This discovery facilitated the solution of equations, by
the necessary composition of their terms which it displayed.
It was evident, for example, that each root of an equation must be a
factor, and consequently a divisor, of the last term.[608]
[608] Harriott’s book is a thin folio of 180 pages, with very
little besides examples; for his principles are shortly and
obscurely laid down. Whoever is the author of the preface to this
work cannot be said to have suppressed or extenuated the merits
of Vieta, or to have claimed anything for Harriott but what he is
allowed to have deserved. Montucla justly observes, that Harriott
_very rarely_ makes an equation equal to zero, by bringing all
the quantities to one side of the equation.
18. Harriott introduced the use of small letters instead of capitals
in algebra; he employed vowels for unknown, consonants for known
quantities, and joined them to express their product.[609] There is
certainly not much in this; but its evident convenience renders it
wonderful that it should have been reserved for so late an era.
Wallis, in his History of Algebra, ascribes to Harriott a long list of
discoveries, which have been reclaimed for Cardan and Vieta, the great
founders of the higher algebra, by Cossali and Montucla.[610] The
latter of these writers has been charged, even by foreigners, with
similar injustice towards our countryman; and that he has been
provoked by what he thought the unfairness of Wallis to something like
a depreciation of Harriott, seems as clear as that he has himself
robbed Cardan of part of his due credit in swelling the account of
Vieta’s discoveries. From the general integrity, however, of
Montucla’s writings, I am much inclined to acquit him of any wilful
partiality.
[609] Oughtred, in his Clavis Mathematica, published in 1631,
abbreviated the rules of Vieta, though he still used capital
letters. He also gives succinctly the praxis of algebra, or the
elementary rules we find in our common books, which, though what
are now first learned, were, from the singular course of
algebraical history, discovered late. They are, however, given
also by Harriott. Wallisii Algebra.
[610] These may be found in the article Harriott of the
Biographia Britannica. Wallis, however, does not suppress the
honour due to Vieta quite as much as is intimated by Montucla.
|Descartes.|
19. Harriott had shown what were the hidden laws of algebra, as the
science of symbolical notation. But one man, the pride of France and
wonder of his contemporaries, was destined to flash light upon the
labours of the analyst, and to point out what those symbols, so darkly
and painfully traced, and resulting commonly in irrational or even
impossible forms, might represent and explain. The use of numbers, or
of letters denoting numbers, for lines and rectangles capable of
division into aliquot parts, had long been too obvious to be
overlooked, and is only a compendious abbreviation of geometrical
proof. The next step made was the perceiving that irrational numbers,
as they are called, represent incommensurable quantities; that is, if
unity be taken for the side of a square, the square-root of two will
represent its diagonal. Gradually the application of numerical and
algebraical calculation to the solution of problems respecting
magnitude became more frequent and refined.[611] It is certain,
however, that no one before Descartes had employed algebraic formulæ
in the construction of curves; that is, had taught the inverse
process, not only how to express diagrams by algebra, but how to turn
algebra into diagrams. The ancient geometers, he observes, were
scrupulous about using the language of arithmetic in geometry, which
could only proceed from their not perceiving the relation between the
two; and this has produced a great deal of obscurity and embarrassment
in some of their demonstrations.[612]
[611] See note in Vol. II., p. 445.
[612] Œuvres de Descartes, v. 323.
|His application of algebra to curves.|
20. The principle which Descartes establishes is that every curve, of
those which are called geometrical, has its fundamental equation
expressing the constant relation between the absciss and the ordinate.
Thus, the rectangle under the abscisses of a diameter of the circle is
equal to the square of the ordinate, and the other conic sections, as
well as higher curves, have each their leading property, which
determines their nature, and shows how they may be generated. A simple
equation can only express the relation of straight lines; the solution
of a quadratic must be found in one of the four conic sections; and
the higher powers of an unknown quantity lead to curves of a superior
order. The beautiful and extensive theory developed by Descartes in
this short treatise displays a most consummate felicity of genius.
That such a man, endowed with faculties so original, should have
encroached on the just rights of others, is what we can only believe
with reluctance.
|Suspected plagiarism from Harriott.|
21. It must, however, be owned that independently of the suspicions of
an unacknowledged appropriation of what others had thought before him,
which unfortunately hang over all the writings of Descartes, he has
taken to himself the whole theory of Harriott on the nature of
equations in a manner which, if it is not a remarkable case of
simultaneous invention, can only be reckoned a very unwarrantable
plagiarism. For not only he does not name Harriott, but he evidently
introduces the subject as an important discovery of his own, and in
one of his letters asserts his originality in the most positive
language.[613] Still it is quite possible that, prepared as the way
had been by Vieta, and gifted as Descartes was with a wonderfully
intuitive acuteness in all mathematical reasoning, he may in this, as
in other instances, have struck out the whole theory by himself.
Montucla extols the algebra of Descartes, that is, so much of it as
can be fairly claimed for him without any precursor, very highly; and
some of his inventions in the treatment of equations have long been
current in books on that science. He was the first who showed what
were called impossible or imaginary roots, though he never assigns
them, deeming them no quantities at all. He was also perhaps the first
who fully understood negative roots, though he still retains the
appellation, false roots, which is not so good as Harriott’s epithet,
privative. According to his panegyrist, he first pointed out that in
every equation (the terms being all on one side) which has no
imaginary roots, there are as many changes of signs as positive roots,
as many continuations of them as negative.
[613] Tant s’en faut que les choses que j’ai écrites puissent
être aisément tirées de Viéte, qu’au contraire ce qui est cause
que mon traité est difficile à entendre, c’est que j’ai tâché à
n’y rien mettre que ce que j’ai crû n’avoir point été su ni par
lui ni par aucun autre; comme on peut voir si on confére ce que
j’ai écrit du nombre des racines qui sont en chaque équation,
dans la page 372, qui est l’endroit où je commence à donner les
règles de mon algèbre, avec ce que Viéte en a écrit tout à la fin
de son livre, De Emendatione Æquationum; car on verra que je le
determine généralement en toutes équations, au lieu que lui n’en
aiant donné que quelques exemples particuliers, dont il fait
toutefois si grand état qu’il a voulu conclure son livre par là,
il a montre qu’il ne le pouvoit déterminer en général. Et ainsi
j’ai commencé où il avoit achevé, ce que j’ai fait toutefois sans
y penser; car j’ai plus feuilleté Viéte depuis que j’ai reçu
votre dernière que je n’avois jamais fait auparavant, l’ayant
trouvé ici par hasard entre les mains d’un de mes amis; et entre
nous, je ne trouve pas qu’il en ait tant su que je pensois, non
obstant qu’il fût fort habile. This is in a letter to Mersenne in
1637. Œuvres de Descartes, vol. vi., p. 300.
The charge of plagiarism from Harriott was brought against
Descartes in his lifetime: Roberval, when an English gentleman
showed him the Artis Analyticæ Praxis, exclaimed eagerly, Il l’a
vu! il l’a vu! It is also a very suspicious circumstance, if
true, as it appears to be, that Descartes was in England the year
(1631) that Harriott’s work appeared. Carcavi, a friend of
Roberval, in a letter to Descartes in 1649, plainly intimates to
him that he has only copied Harriott as to the nature of
equations Œvres des Descartes, vol. x., p. 373. To this
accusation Descartes made no reply. See Biographia Britannica,
art. Harriott. The Biographie Universelle unfairly suppresses all
mention of this, and labours to depreciate Harriott.
See Leibnitz’s catalogue of the supposed thefts of Descartes in
Vol. III., p. 267, of this work.
|Fermat.|
22. The geometer next in genius to Descartes, and perhaps nearer to
him than to any third, was Fermat, a man of various acquirements, of
high rank in the parliament of Toulouse, and of a mind incapable of
envy, forgiving of detraction, and delighting in truth, with almost
too much indifference to praise. The works of Fermat were not
published till long after his death in 1665; but his frequent
discussions with Descartes, by the intervention of their common
correspondent Mersenne, render this place more appropriate for the
introduction of his name. In these controversies Descartes never
behaved to Fermat with the respect due to his talents; in fact, no one
was ever more jealous of his own pre-eminence, or more unwilling to
acknowledge the claims of those who scrupled to follow him implicitly,
and who might in any manner be thought rivals of his fame. Yet it is
this unhappy temper of Descartes which ought to render us more
unwilling to credit the suspicions of his designed plagiarism from the
discoveries of others; since this, combined with his unwillingness to
acknowledge their merits, and affected ignorance of their writings,
would form a character we should not readily ascribe to a man of great
genius, and whose own writings give many apparent indications of
sincerity and virtue. But in fact there was in this age a great
probability of simultaneous invention in science, from developing
principles that had been partially brought to light. Thus Roberval
discovered the same method of indivisibles as Cavalieri, and Descartes
must equally have been led to this theory of tangents by that of
Kepler. Fermat also, who was in possession of his principal
discoveries before the geometry of Descartes saw the light, derived
from Kepler his own celebrated method, de maximis et minimis;
a method of discovering the greatest or least value of a variable
quantity, such as the ordinate of a curve. It depends on the same
principle as that of Kepler. From this he deduced a rule for drawing
tangents to curves different from that of Descartes. This led to a
controversy between the two geometers, carried on by Descartes, who
yet is deemed to have been in the wrong, with his usual quickness of
resentment. Several other discoveries, both in pure algebra and
geometry, illustrate the name of Fermat.[614]
[614] A good article on Fermat, by M. Maurice, will be found in
the Biographie Universelle.
|Algebraic geometry not successful at first.|
23. The new geometry of Descartes was not received with the universal
admiration it deserved. Besides its conciseness and the inroad it made
on old prejudices as to geometrical methods, the general boldness of
the author’s speculations in physical and metaphysical philosophy, as
well as his indiscreet temper, disinclined many who ought to have
appreciated it; and it was in his own country, where he had ceased to
reside, that Descartes had the fewest admirers. Roberval made some
objections to his rival’s algebra, but with little success. A
commentary on the treatise of Descartes by Schooten, professor of
Geometry at Leyden, first appeared in 1649.
|Astronomy.--Kepler.|
24. Among those who devoted themselves ardently and successfully to
astronomical observations at the end of the sixteenth century, was
John Kepler, a native of Wirtemburg, who had already shown that he was
likely to inherit the mantle of Tycho Brahe. He published some
astronomical treatises of comparatively small importance in the first
years of the present period. But in 1609 he made an epoch in that
science by his Astronomia Nova αιτιολογτος, [aitiologêtos], or
Commentaries on the Planet Mars. It had been always assumed that the
heavenly bodies revolve in circular orbits round their centre, whether
this were taken to be the sun or the earth. There was, however, an
apparent eccentricity or deviation from this circular motion, which it
had been very difficult to explain, and for this Ptolemy had devised
his complex system of epicycles. No planet showed more of this
eccentricity than Mars; and it was to Mars that Kepler turned his
attention. After many laborious researches he was brought by degrees
to the great discovery, that the motion of the planets, among which,
having adopted the Copernican system, he reckoned the earth, is not
performed in circular but in elliptical orbits, the sun not occupying
the centre but one of the foci of the curve; and, secondly, that it is
performed with such a varying velocity, that the areas described by
the radius vector, or line which joins this focus to the revolving
planet, are always proportional to the times. A planet, therefore,
moves less rapidly as it becomes more distant from the sun. These are
the first and second of the three great laws of Kepler. The third was
not discovered by him till some years afterwards. He tells us himself
that on the 8th May, 1618, after long toil in investigating the
proportion of the periodic times of the planetary movements to their
orbits, an idea struck his mind, which, chancing to make a mistake in
the calculation, he soon rejected. But a week after, returning to the
subject, he entirely established his grand discovery, that the squares
of the times of revolution are as the cubes of the mean distances of
the planets. This was first made known to the world in his Mysterium
Cosmo graphicum, published in 1619; a work mingled up with many
strange effusions of a mind far more eccentric than any of the planets
with which it was engaged. In the Epitome Astronomiæ Copernicanæ,
printed the same year, he endeavours to deduce this law from his
theory of centrifugal forces. He had a very good insight into the
principles of universal gravitation, as an attribute of matter; but
several of his assumptions as to the laws of motion are not consonant
to truth. There seems indeed to have been a considerable degree of
good fortune in the discoveries of Kepler; yet, this may be deemed the
reward of his indefatigable laboriousness, and of the ingenuousness
with which he renounced any hypothesis that he could not reconcile
with his advancing knowledge of the phenomena.
|Conjectures as to comets.|
25. The appearance of three comets in 1619 called once more the
astronomers of Europe to speculate on the nature of those anomalous
bodies. They still passed for harbingers of worldly catastrophies; and
those who feared them least could not interpret their apparent
irregularity. Galileo, though Tycho Brahe had formed a juster notion,
unfortunately took them for atmospheric meteors. Kepler, though he
brought them from the far regions of space, did not suspect the nature
of their orbits, and thought that, moving in straight lines,
they were finally dispersed and came to nothing. But a Jesuit, Grassi,
in a treatise, De Tribus Cometis, Rome, 1618, had the honour of
explaining what had baffled Galileo, and first held them to be planets
moving in vast ellipses round the sun.[615]
[615] The Biographie Universelle, art. Grassi, ascribes this
opinion to Tycho.
|Galileo’s discovery of Jupiter’s satellites.|
26. But long before this time the name of Galileo had become immortal
by discoveries which, though they would certainly have soon been made
by some other, perhaps far inferior, observer, were happily reserved
for the most philosophical genius of the age. Galileo assures us that,
having heard of the invention of an instrument in Holland which
enlarged the size of distant objects, but knowing nothing of its
construction, he began to study the theory of refractions till he
found by experiment, that by means of a convex and concave glass in a
tube, he could magnify an object threefold. He was thus encouraged to
make another which magnified thirty times; and this he exhibited in
the autumn of 1609 to the inhabitants of Venice. Having made a present
of his first telescope to the senate, who rewarded him with a pension,
he soon constructed another; and in one of the first nights of
January, 1610, directing it towards the moon, was astonished to see
her surface and edges covered with inequalities. These he considered
to be mountains, and judged by a sort of measurement that some of them
must exceed those of the earth. His next observation was of the milky
way; and this he found to derive its nebulous lustre from myriads of
stars not distinguishable through their remoteness, by the unassisted
sight of man. The nebulæ in the constellation Orion he perceived to be
of the same character. Before his delight at these discoveries could
have subsided, he turned his telescope to Jupiter, and was surprised
to remark three small stars, which, in a second night’s observation,
had changed there places. In the course of a few weeks, he was able to
determine by their revolutions, which are very rapid, that these are
secondary planets, the moons or satellites of Jupiter; and he had
added a fourth to their number. These marvellous revelations of nature
he hastened to announce in a work, aptly entitled Sidereus Nuncius,
published in March, 1610. In an age when the fascinating science of
astronomy had already so much excited the minds of philosophers, it
may be guessed with what eagerness this intelligence from the heavens
was circulated. A few, as usual, through envy or prejudice, affected
to contemn it. But wisdom was justified of her children. Kepler, in
his Narratio de observatis a se Quatuor Jovis Satellitibus, 1610,
confirmed the discoveries of Galileo. Peiresc, an inferior name, no
doubt, but deserving of every praise for his zeal in the cause of
knowledge, having with difficulty procured a good telescope, saw the
four satellites in November, 1610, and is said by Gassendi to have
conceived at that time the ingenious idea that their occultations
might be used to ascertain the longitude.[616]
[616] Gassendi Vita Peirescii, p. 77.
|Other discoveries by him.|
27. This is the greatest and most important of the discoveries of
Galileo. But several others were of the deepest interest. He found
that the planet Venus had phases, that is, periodical differences of
apparent form like the moon; and that these are exactly such as would
be produced by the variable reflection of the sun’s light on the
Copernican hypothesis; ascribing also the faint light on that part of
the moon which does not receive the rays of the sun, to the reflection
from the earth, called by some late writers earth-shine; which, though
it had been suggested by Mæstlin, and before him by Leonardo da Vinci,
was not generally received among astronomers. Another striking
phenomenon, though he did not see the means of explaining it, was the
triple appearance of Saturn, as if smaller stars were conjoined as it
were like wings to the planet. This, of course, was the ring.
|Spots of the sun discovered.|
28. Meantime the new auxiliary of vision which had revealed so many
wonders could not lie unemployed in the hands of others. A
publication, by John Fabricius, at Wittenberg, in July, 1611, De
Maculis in Sole visis, announced a phenomenon in contradiction of
common prejudice. The sun had passed for a body of liquid flame, or,
if thought solid, still in a state of perfect ignition. Kepler had,
some years before, observed a spot, which he unluckily mistook for the
orb of Mercury in its passage over the solar orb. Fabricius was not
permitted to claim this discovery as his own. Scheiner, a Jesuit,
professor of mathematics at Ingolstadt, asserts in a letter, dated
12th of November, 1611, that he first saw the spots in the month of
March in that year, but he seems to have paid little attention to them
before that of October. Both Fabricius, however, and Scheiner
may be put out of the question. We have evidence, that Harriott
observed the spots on the sun as early as December 8th, 1610. The
motion of the spots suggested the revolution of the sun round its
axis, completed in twenty-four days, as it is now determined; and
their frequent alterations of form, as well as occasional
disappearance, could only be explained by the hypothesis of a luminous
atmosphere in commotion, a sea of flame, revealing at intervals the
dark central mass of the sun’s body which it envelopes.
|Copernican system held by Galileo.|
29. Though it cannot be said, perhaps, that the discoveries of Galileo
would fully prove the Copernican system of the world to those who were
already insensible to reasoning from its sufficiency to explain the
phenomena, and from the analogies of nature, they served to
familiarise the mind to it, and to break down the strong rampart of
prejudice which stood in its way. For eighty years, it has been said,
this theory of the earth’s motion had been maintained without censure;
and it could only be the greater boldness of Galileo in its assertion
which drew down upon him the notice of the church. But, in these
eighty years since the publication of the treatise of Copernicus, his
proselytes had been surprisingly few. They were now becoming more
numerous: several had written on that side; and Galileo had begun to
form a school of Copernicans who were spreading over Italy. The
Lincean society, one of the most useful and renowned of Italian
academies, founded at Rome by Frederic Cesi, a young man of noble
birth, in 1603, had, as a fundamental law, to apply themselves to
natural philosophy; and it was impossible that so attractive and
rational a system as that of Copernicus could fail of pleasing an
acute and ingenious nation strongly bent upon science. The church,
however, had taken alarm; the motion of the earth was conceived to be
as repugnant to Scripture as the existence of antipodes had once been
reckoned; and in 1616, Galileo, though respected and in favour with
the court of Rome, was compelled to promise that he would not maintain
that doctrine in any manner. Some letters that he had published on the
subject were put, with the treatise of Copernicus and other works,
into the Index Expurgatorius, where, I believe, they still
remain.[617]
[617] Drinkwater’s Life of Galileo. Fabroni, Vitæ Italorum,
vol. i. The former seems to be mistaken in supposing that Galileo
did not endeavour to prove his system compatible with Scripture.
In a letter to Christina, the Grand Duchess of Tuscany, the
author (Brenna) of the Life in Fabroni’s work, tells us, he
argued very elaborately for that purpose. In ea videlicet
epistolâ philosophus noster ita disserit, ut nihil etiam ab
hominibus, qui omnem in sacrarum literarum studio consumpsissent
ætatem, aut subtilius aut verius aut etiam accuratius explicatum
expectari potuerit, p. 118. It seems, in fact, to have been this
over-desire to prove his theory orthodox, which incensed the
church against it. See an extraordinary article on this subject
in the eighth number of the Dublin Review (1838). Many will
tolerate propositions inconsistent with orthodoxy, when they are
not brought into immediate juxtaposition with it.
|His dialogues, and persecution.|
30. He seems, notwithstanding this, to have flattered himself that,
after several years had elapsed, he might elude the letter of this
prohibition by throwing the arguments in favour of the Ptolemaic and
Copernican systems into the form of a dialogue. This was published in
1632; and he might, from various circumstances, not unreasonably hope
for impunity. But his expectations were deceived. It is well known
that he was compelled by the Inquisition at Rome, into whose hands he
fell, to retract, in the most solemn and explicit manner, the
propositions he had so well proved, and which he must have still
believed. It is unnecessary to give a circumstantial account,
especially as it has been so well done in a recent work, the Life of
Galileo, by Mr. Drinkwater Bethune. The papal court meant to humiliate
Galileo, and through him to strike an increasing class of philosophers
with shame and terror; but not otherwise to punish one, of whom even
the inquisitors must, as Italians, have been proud; his confinement,
though Montucla says it lasted for a year, was very short. He
continued, nevertheless, under some restraint for the rest of his
life, and though he lived at his own villa near Florence, was not
permitted to enter the city.[618]
[618] Fabroni. His Life is written in good Latin, with knowledge
and spirit, more than Tiraboschi has ventured to display.
It appears from some of Grotius’s Epistles, that Galileo had
thought, about 1635, of seeking the protection of the United
Provinces. But on account of his advanced age he gave this up:
fessus senio constituit manere in quibus est locis, et potius quæ
ibi sunt incommoda perpeti, quam malæ ætati migrandi onus, et
novas parandi amicitias imponere. The very idea shows that he
must have deeply felt the restraint imposed upon him in his
country. Epist. Grot. 407, 446.
|Descartes alarmed by this.|
31. The church was not mistaken in supposing that she should
intimidate the Copernicans, but very much so in expecting to suppress
the theory. Descartes was so astonished at hearing of the sentence on
Galileo, that he was almost disposed to burn his papers, or at least
to let no one see them. “I cannot collect,” he says, “that he who is
an Italian, and a friend of the pope, as I understand, has been
criminated on any other account than for having attempted to establish
the motion of the earth. I know that this opinion was formerly
censured by some cardinals; but I thought I had since heard that no
objection was now made to its being publicly taught even at
Rome.”[619] It seems not at all unlikely that Descartes was induced,
on this account, to pretend a greater degree of difference from
Copernicus than he really felt, and even to deny, in a certain sense
of his own, the obnoxious tenet of the earth’s motion.[620] He was not
without danger of a sentence against truth nearer at hand; Cardinal
Richelieu having had the intention of procuring a decree of the
Sorbonne to the same effect, which, by the good sense of some of that
society, fell to the ground.[621]
[619] Vol. vi., p. 239. He says here, of the motion of the earth,
Je confesse que s’il est faux, tous les fondemens de ma
philosophie le sont aussi.
[620] Vol. vi., p. 50.
[621] Montucla, ii., p. 297.
|Progress of Copernican system.|
32. The progress, however, of the Copernican theory in Europe, if it
may not actually be dated from its condemnation at Rome, was certainly
not at all slower after that time. Gassendi rather cautiously took
that side; the Cartesians brought a powerful reinforcement; Bouillaud
and several other astronomers of note avowed themselves favourable to
a doctrine which, though in Italy it lay under the ban of the papal
power, was readily saved on this side of the Alps by some of the
salutary distinctions long in use to evade that authority.[622] But in
the middle of the seventeenth century, and long afterwards, there were
mathematicians of no small reputation, who struggled staunchly for the
immobility of the earth; and except so far as Cartesian theories might
have come in vogue, we have no reason to believe that any persons
unacquainted with astronomy, either in this country or on the
continent, had embraced the system of Copernicus. Hume has censured
Bacon for rejecting it; but if Bacon had not done so, he would have
anticipated the rest of his countrymen by a full quarter of a century.
[622] Id., p. 50.
|Descartes denies general gravitation.|
33. Descartes, in his new theory of the solar system, aspired to
explain the secret springs of nature, while Kepler and Galileo had
merely showed their effects. By what force the heavenly bodies were
impelled, by what law they were guided, was certainly a very different
question from that of the orbit they described or the period of their
revolution. Kepler had evidently some notion of that universally
mutual gravitation which Hooke saw more clearly, and Newton
established on the basis of his geometry.[623] But Descartes rejected
this with contempt. “For,” he says “to conceive this we must not only
suppose that every portion of matter in the universe is animated, and
animated by several different souls which do not obstruct one another,
but that those souls are intelligent and even divine; that they may
know what is going on in the most remote places, without any messenger
to give them notice, and that they may exert their powers there.”[624]
Kepler, who took the world for a single animal, a leviathan that
roared in caverns and breathed in the ocean tides, might have found it
difficult to answer this, which would have seemed no objection at all
to Campanella. If Descartes himself had been more patient towards
opinions which he had not formed in his own mind, that constant divine
agency, to which he was, on other occasions, apt to resort, could not
but have suggested a sufficient explanation of the gravity of matter,
without endowing it with self-agency. He had, however, fallen upon a
complicated and original scheme; the most celebrated, perhaps, though
not the most admirable, of the novelties which Descartes brought into
philosophy.
[623] “If the earth and moon,” he says, “were not retained in
their orbits, they would fall one on another, the moon moving
about 33/34 of the way, the earth the rest, supposing them
equally dense.” By this attraction of the moon he accounts for
tides. He compares the attraction of the planets towards the sun
to that of heavy bodies towards the earth.
[624] Vol. x., p. 560.
|Cartesian theory of the world.|
34. In a letter to Mersenne, January 9th, 1639, he shortly states that
notion of the material universe, which he afterwards published in the
Principia Philosophiæ. “I will tell you,” he says, “that I conceive,
or rather I can demonstrate, that besides the matter which composes
terrestrial bodies, there are two other kinds; one very subtle, of
which the parts are round or nearly round like grains of sand, and
this not only occupies the pores of terrestrial bodies, but
constitutes the substance of all the heavens; the other incomparably
more subtle, the parts of which are so small and move with such
velocity, that they have no determinate figure, but readily take at
every instant that which is required to fill all the little intervals
which the other does not occupy.”[625] To this hypothesis of a double
æther he was driven by his aversion to admit any vacuum in nature; the
rotundity of the former corpuscles having been produced, as he
fancied, by their continual circular motions, which had rubbed off
their angles. This seems at present rather a clumsy hypothesis, but it
is literally that which Descartes presented to the world.
[625] Vol. viii., p. 73.
35. After having thus filled the universe with different sorts of
matter, he supposes that the subtler particles, formed by the
perpetual rubbing off of the angles of the larger in their progress
towards sphericity, increased by degrees till there was a superfluity
that was not required to fill up the intervals; and this, flowing
towards the centre of the system, became the sun, a very subtle and
liquid body, while in like manner, the fixed stars were formed in
other systems. Round these centres the whole mass is whirled in a
number of distinct vortices, each of which carries along with it a
planet. The centrifugal motion impels every particle in these vortices
of each instant to fly off from the sun in a straight line; but it is
retained by the pressure of those which have already escaped and form
a denser sphere beyond it. Light is no more than the effect of
particles seeking to escape from the centre, and pressing one on
another, though perhaps without actual motion.[626] The planetary
vortices contain sometimes smaller vortices, in which the satellites
are whirled round their principal.
[626] J’ai souvent averti que par la lumière je n’entendois pas
tant le mouvement que cette inclination ou propension que ces
petits corps ont à se mouvoir, et que ce que je dirois du
mouvement, pour être plus aisément entendu, se devoit rapporter à
cette propension; d’où il est manifeste qua selon moi l’on ne
doit entendre autre chose par les couleurs que les différentes
variétés qui arrivent en ces propensions. Vol. vii., p. 193.
36. Such, in a few words, is the famous Cartesian theory, which,
fallen in esteem as it now is, stood its ground on the continent of
Europe, for nearly a century, till the simplicity of the Newtonian
system, and, above all, its conformity to the reality of things,
gained an undisputed predominance. Besides the arbitrary suppositions
of Descartes, and the various objections that were raised against the
absolute plenum of space and other parts of his theory, it has been
urged that his vortices are not reconcilable, according to the laws of
motion in fluids, with the relation, ascertained by Kepler, between
the periods and distances of the planets; nor does it appear why the
sun should be in the focus, rather than in the centre of their orbits.
Yet, within a few years it has seemed not impossible, that a part of
his bold conjectures will enter once more with soberer steps into the
schools of philosophy. His doctrine as to the nature of light,
improved as it was by Huygens, is daily gaining ground over that of
Newton; that of a subtle æther pervading space, which in fact is
nearly the same thing, is becoming a favourite speculation, if we are
not yet to call it an established truth; and the affirmative of a
problem, which an eminent writer has started, whether this æther has a
vorticose motion round the sun, would not leave us very far from the
philosophy it has been so long our custom to turn into ridicule.
|Transits of Mercury and Venus.|
37. The passage of Mercury over the sun was witnessed by Gassendi in
1631. This phenomenon, though it excited great interest in that age,
from its having been previously announced, so as to furnish a test of
astronomical accuracy, recurs too frequently to be now considered as
of high importance. The transit of Venus is much more rare. It
occurred on December 4, 1639, and was then only seen by Horrox, a
young Englishman of extraordinary mathematical genius. There is reason
to ascribe an invention of great importance, though not perhaps of
extreme difficulty, that of the micrometer, to Horrox.
|Laws of Mechanics.|
|Statics of Galileo.|
38. The satellites of Jupiter and the phases of Venus are not so
glorious in the scutcheon of Galileo as his discovery of the true
principles of mechanics. These, as we have seen in the former volume,
were very imperfectly known till he appeared; nor had the additions to
that science since the time of Archimedes been important. The treatise
of Galileo, Della Scienza Mecanica, has been said, I know not on what
authority, to have been written in 1592. It was not published,
however, till 1634, and then only in a French translation by Mersenne,
the original not appearing till 1649. This is chiefly confined to
statics, or the doctrine of equilibrium; it was in his dialogues on
motion, Della Nuova Scienza, published in 1638, that he developed his
great principles of the science of dynamics, the moving forces of
bodies. Galileo was induced to write his treatise on mechanics, as he
tells us, in consequence of the fruitless attempts he witnessed in
engineers to raise weights by a small force, “as if with their
machines they could cheat nature, whose instinct as it were by
fundamental law is that no resistance can be overcome except by a
superior force.” But as one man may raise a weight to the height of a
foot by dividing it into equal portions, commensurate to his power,
which many men could not raise at once, so a weight, which raises
another greater than itself, may be considered as doing so by
successive instalments of force, during each of which it traverses as
much space as a corresponding portion of the larger weight. Hence the
velocity, of which space uniformly traversed in a given time is the
measure, is inversely as the masses of the weights; and thus the
equilibrium of the straight lever is maintained, when the weights are
inversely as their distance from the fulcrum. As this equilibrium of
unequal weights depends on the velocities they would have if set in
motion, its law has been called the principle of virtual velocities.
No theorem has been of more important utility to mankind. It is one of
those great truths of science, which combating and conquering enemies
from opposite quarters, prejudice and empiricism, justify the name of
philosophy against both classes. The waste of labour and expense in
machinery would have been incalculably greater in modern times, could
we imagine this law of nature not to have been discovered; and as
their misapplication prevents their employment in a proper direction,
we owe in fact to Galileo the immense effect which a right application
of it has produced. It is possible, that Galileo was ignorant of the
demonstration given by Stevinus of the law of equilibrium in the
inclined plane. His own is different; but he seems only to consider
the case when the direction of the force is parallel to that of the
plane.
|His Dynamics.|
39. Still less was known of the principles of dynamics than of those
of statics, till Galileo came to investigate them. The acceleration of
falling bodies, whether perpendicularly or on inclined planes, was
evident; but in what ratio this took place, no one had succeeded in
determining, though many had offered conjectures. He showed that the
velocity acquired was proportional to the time from the commencement
of falling. This might now be demonstrated from the laws of motion;
but Galileo, who did not perhaps distinctly know them, made use of
experiment. He then proved by reasoning that the spaces traversed in
falling were as the squares of the times or velocities; that their
increments in equal times were as the uneven numbers, 1, 3, 5, 7, and
so forth; and that the whole space was half what would have been
traversed uniformly from the beginning with the final velocity. These
are the great laws of accelerated and retarded motion, from which
Galileo deduced most important theorems. He showed that the time in
which bodies roll down the length of inclined planes is equal to that
in which they would fall down the height, and in different planes is
proportionate to the height; and that their acquired velocity is in
the same ratios. In some propositions he was deceived; but the science
of dynamics owes more to Galileo than to any one philosopher. The
motion of projectiles had never been understood; he showed it to be
parabolic; and in this he not only necessarily made use of a principle
of vast extent, that of compound motion, which, though it is clearly
mentioned in one passage by Aristotle[627] and may probably be implied
in the mechanical reasonings of others, does not seem to have been
explicitly laid down by modern writers, but must have seen the
principle of curvilinear deflection by forces acting in infinitely
small portions of time. The ratio between the times of vibration in
pendulums of unequal length, had early attracted Galileo’s attention.
But he did not reach the geometrical exactness of which this subject
is capable.[628] He developed a new principle as to the resistance of
solids to the fracture of their parts, which, though Descartes as
usual treated it with scorn, is now established in philosophy. “One
forms, however,” says Playfair, “a very imperfect idea of this
philosopher from considering the discoveries and inventions, numerous
and splendid as they are, of which he was the undisputed author. It is
by following his reasonings, and by pursuing the train of his
thoughts, in his own elegant, though somewhat diffuse exposition
of them, that we become acquainted with the fertility of his
genius, with the sagacity, penetration, and comprehensiveness of his
mind. The service which he rendered to real knowledge is to be
estimated not only from the truths which he discovered, but from the
errors which he detected; not merely from the sound principles which
he established, but from the pernicious idols which he overthrew. Of
all the writers who have lived in an age which was yet only emerging
from ignorance and barbarism, Galileo has most entirely the tone of
true philosophy, and is most free from any contamination of the times,
in taste, sentiment, and opinion.”[629]
[627] Drinkwater’s Life of Galileo, p. 80.
[628] Fabroni.
[629] Preliminary Dissertation to Encyclop. Britain.
|Mechanics of Descartes.|
40. Descartes, who left nothing in philosophy untouched, turned his
acute mind to the science of mechanics, sometimes with signal credit,
sometimes very unsuccessfully. He reduced all statics to one
principle, that it requires as much force to raise a body to a given
height, as to raise a body of double weight to half the height. This
is the theorem of virtual velocities in another form. In many respects
he displays a jealousy of Galileo, and an unwillingness to acknowledge
his discoveries, which puts himself often in the wrong. “I believe,”
he says, “that the velocity of very heavy bodies which do not move
very quickly in descending increases nearly in a duplicate ratio; but
I deny that this is exact, and I believe that the contrary is the case
when the movement is very rapid.”[630] This recourse to the air’s
resistance, a circumstance of which Galileo was well aware, in order
to diminish the credit of a mathematical theorem, is unworthy of
Descartes; but it occurs more than once in his letters. He maintained
also, against the theory of Galileo, that bodies do not begin to move
with an infinitely small velocity, but have a certain degree of motion
at the first instance, which is afterwards accelerated.[631] In this
too, as he meant to extend his theory to falling bodies, the consent
of philosophers has decided the question against him. It was a
corollary from these notions that he denies the increments of spaces
to be according to the progression of uneven numbers.[632] Nor would
he allow that the velocity of a body augments its force, though it is
a concomitant.[633]
[630] Œuvres de Descartes, vol. viii., p. 24.
[631] Il faut savoir, quoique Galilée et quelques autres disent
au contraire, que les corps qui commencent à descendre, ou à se
mouvoir en quelque façon que ce soit, ne passent point par tous
les degrés de tardiveté; mais que des le premier moment ils ont
certaine vitesse qui s’augmente après de beaucoup, et c’est de
cette augmentation que vient la force de la percussion. viii.,
181.
[632] Cette proportion d’augmentation selon les nombres impairs,
1, 3, 5, 7, &c., qui est dans Galilée et que je crois vous avoir
aussi écrite autrefois, ne peut être vraie, qu’en supposant deux
ou trois choses qui sont très fausses, dont l’une est que le
mouvement croisse par degrés depuis le plus lent, ainsi que le
songe Galilée, et l’autre que la résistance de l’air n’empêche
point. Vol. ix., p. 349.
[633] Je pense que la vitesse n’est pas la cause de
l’augmentation de la force, encore qu’elle l’accompagne toujours.
Id. p. 356, See also vol. viii., p. 14. He was probably perplexed
by the metaphysical notion of causation, which he knew not how to
ascribe to mere velocity. The fact that increased velocity is a
condition or antecedent of augmented force could not be doubted.
|Law of motion laid down by Descartes.|
41. Descartes, however, is the first who laid down the laws of motion;
especially that all bodies persist in their present state of rest or
uniform rectilineal motion till affected by some force. Many had
thought, as the vulgar always do, that a continuance of rest was
natural to bodies, but did not perceive that the same principle of
inertia or inactivity was applicable to them in rectilineal motion.
Whether this is deducible from theory, or depends wholly on
experience, by which we ought to mean experiment, is a question we
need not discuss. The fact, however, is equally certain; and hence
Descartes inferred that every curvilinear deflection is produced by
some controlling force, from which the body strives to escape in the
direction of a tangent to the curve. The most erroneous part of his
mechanical philosophy is contained in some propositions as to the
collision of bodies, so palpably incompatible with obvious experience
that it seems truly wonderful he could ever have adopted them. But he
was led into these paradoxes by one of the arbitrary hypotheses which
always governed him. He fancied it a necessary consequence from the
immutability of the divine nature that there should always be the same
quantity of motion in the universe; and rather than abandon this
singular assumption he did not hesitate to assert, that two hard
bodies striking each other in opposite directions would be reflected
with no loss of velocity; and, what is still more outrageously
paradoxical, that a smaller body is incapable of communicating motion
to a greater; for example, that the red billiard-ball cannot
put the white into motion. This manifest absurdity he endeavoured to
remove by the arbitrary supposition, that when we see, as we
constantly do, the reverse of his theorem take place, it is owing to
the air, which, according to him, renders bodies more susceptible of
motion, than they would naturally be.
|Also those of compound forces.|
42. Though Galileo, as well as others, must have been acquainted with
the laws of the composition of moving forces, it does not appear that
they had ever been so distinctly enumerated as by Descartes, in a
passage of his Dioptrics.[634] That the doctrine was in some measure
new may be inferred from the objections of Fermat; and Clerselier,
some years afterwards, speaks of persons “not much versed in
mathematics, who cannot understand an argument taken from the nature
of compound motion.”[635]
[634] Vol. v., p. 18.
[635] Vol. vi., p. 508.
|Other discoveries in mechanics.|
43. Roberval demonstrated what seems to have been assumed by Galileo,
that the forces on an oblique or crooked lever balance each other,
when they are inversely as the perpendiculars drawn from the centre of
motion to their direction. Fermat, more versed in geometry than
physics, disputed this theorem which is now quite elementary.
Descartes, in a letter to Mersenne, ungraciously testifies his
agreement with it.[636] Torricelli, the most illustrious disciple of
Galileo, established that when weights balance each other in all
positions, their common centre of gravity does not ascend or descend,
and conversely.
[636] Je suis de l’opinion, says Descartes, de ceux qui disent
que _pondera sunt in æquilibrio quando sunt in ratione reciproca
linearum perpendicularium_, &c., vol. xi., p. 357. He would not
name Roberval; one of those littlenesses which appear too
frequently in his letters and in all his writings. Descartes in
fact could not bear to think that another, even though not an
enemy, had discovered anything. In the preceding page he says:
C’est une chose ridicule que de vouloir employer la raison du
levier dans la poulie, ce qui est, si j’ai bonne mémoire, une
imagination de Guide Ubalde. Yet this imagination is demonstrated
in all our elementary books on mechanics.
|In Hydrostatics and pneumatics.|
44. Galileo, in a treatise entitled, Delle Cose che stanno nell’Acqua,
lays down the principles of hydrostatics already established by
Stevin, and among others what is called the hydrostatical paradox.
Whether he was acquainted with Stevin’s writings, may be perhaps
doubted; it does not appear that he mentions them. The more difficult
science of hydraulics was entirely created by two disciples of
Galileo, Castellio and Torricelli. It is one everywhere of high
importance, and especially in Italy. The work of Castellio, Della
Misura dell’Acque Correnti, and a continuation, were published at
Rome, in 1628. His practical skill in hydraulics, displayed in
carrying off the stagnant waters of the Arno, and in many other public
works, seems to have exceeded his theoretical science. An error, into
which he fell, supposing the velocity of fluids to be as the height
down which they had descended, led to false results. Torricelli proved
that it was as the square root of the altitude. The latter of these
two was still more distinguished by his discovery of the barometer.
The principle of the syphon or sucking-pump, and the impossibility of
raising water in it more than about thirty-three feet, were both well
known; but even Galileo had recourse to the clumsy explanation that
nature limited her supposed horror of a vacuum to this altitude. It
occurred to the sagacity of Torricelli that the weight of the
atmospheric column pressing upon the fluid which supplied the pump was
the cause of this rise above its level; and that the degree of rise
was consequently the measure of that weight. That the air had weight
was known, indeed, to Galileo and Descartes; and the latter not only
had some notion of determining it by means of a tube filled with
mercury, but in a passage which seems to have been much overlooked,
distinctly suggests as one reason why water will not rise above
eighteen _brasses_ in a pump, “the weight of the water which
counterbalances that of the air.”[637] Torricelli happily thought of
using mercury, a fluid thirteen times heavier, instead of water, and
thus invented a portable instrument by which the variations of the
mercurial column might be readily observed. These he found to
fluctuate between certain well known limits, and in circumstances
which might justly be ascribed to the variations of atmospheric
gravity. This discovery he made in 1643; and in 1648, Pascal, by his
celebrated experiment on the Puy de Dome, established the theory of
atmospheric pressure beyond dispute. He found a considerable
difference in the height of the mercury at the bottom and the top of
that mountain; and a smaller yet perceptible variation was proved on
taking the barometer to the top of one of the loftiest churches in
Paris.
[637] Vol. vii., p. 437.
|Optics.--Discoveries of Kepler.|
|Invention of the telescope.|
45. The science of optics was so far from falling behind other
branches of physics in this period, that, including the two great
practical discoveries which illustrate it, no former or later
generation has witnessed such an advance. Kepler began, in the year
1604, by one of his first works, Paralipomena ad Vitellionem, a title
somewhat more modest than he was apt to assume. In this supplement to
the great Polish philosopher of the middle ages, he first explained
the structure of the human eye, and its adaptation to the purposes of
vision. Porta and Maurolycus had made important discoveries, but left
the great problem untouched. Kepler had the sagacity to perceive the
use of the retina as the canvas on which images were painted. In his
treatise, says Montucla, we are not to expect the precision of our own
age; but it is full of ideas novel and worthy of a man of genius. He
traced the causes of imperfect vision in its two principal cases,
where the rays of light converge to a point before or behind the
retina. Several other optical phenomena are well explained by Kepler;
but he was unable to master the great enigma of the science, the law
of refraction. To this he turned his attention again in 1611, when he
published a treatise on Dioptrics. He here first laid the foundation
of that science. The angle of refraction, which Maurolycus had
supposed equal to that of incidence, he here assumed to be one third
of it; which, though very erroneous as a general theorem, was
sufficiently accurate for the sort of glasses he employed. It was his
object to explain the principle of the telescope; and in this he well
succeeded. That admirable invention was then quite recent. Whatever
endeavours have been made to carry up the art of assisting vision by
means of a tube to much more ancient times, it seems to be fully
proved that no one had made use of combined lenses for that purpose.
The slight benefit which a hollow tube affords by obstructing the
lateral ray, must have been early familiar, and will account for
passages which have been construed to imply what the writers never
dreamed of.[638] The real inventor of the telescope is not certainly
known. Metius of Alkmaer long enjoyed that honour; but the best claim
seems to be that of Zachary Jens, a dealer in spectacles at
Middleburg. The date of the invention, or at least of its publicity,
is referred, beyond dispute, to 1609. The news of so wonderful a
novelty spread rapidly through Europe; and in the same year, Galileo,
as has been mentioned, having heard of the discovery, constructed, by
his own sagacity, the instrument which he exhibited at Venice. It is,
however, unreasonable to regard himself as the inventor; and in this
respect his Italian panegyrists have gone too far. The original sort
of telescope, and the only one employed in Europe for above thirty
years, was formed of a convex object-glass with a concave eye-glass.
This, however, has the disadvantage of diminishing too much the space
which can be taken in at one point of view; “so that,” says Montucla,
“one can hardly believe that it could render astronomy such service as
it did in the hands of a Galileo or a Scheiner.” Kepler saw the
principle upon which another kind might be framed with both glasses
convex. This is now called the astronomical telescope, and was first
employed a little before the middle of the century. The former, called
the Dutch telescope, is chiefly used for short spying-glasses.
[638] Even Dutens, whose sole aim is to depreciate those whom
modern science has most revered, cannot pretend to show that the
ancients made use of glasses to assist vision. Origine des
Découvertes, i., 218.
|Of the microscope.|
46. The microscope has also been ascribed to Galileo; and so far with
better cause, that we have no proof of his having known the previous
invention. It appears, however, to have originated, like the
telescope, in Holland, and perhaps at an earlier time. Cornelius
Drebbel, who exhibited the microscope in London about 1620, has often
passed for the inventor. It is suspected by Montucla that the first
microscopes had concave eye-glasses; and that the present form with
two convex glasses is not older than the invention of the astronomical
telescope.
|Antonio de Dominis.|
47. Antonio de Dominis, the celebrated archbishop of Spalatro, in a
book published in 1611, though written several years before, De Radiis
Lucis in Vitris Perspectivis et Iride, explained more of the phenomena
of the rainbow than was then understood. The varieties of colour had
baffled all inquirers, though the bow itself was well known to be the
reflection of solar light from drops of rain. Antonio de Dominis, to
account for these, had recourse to refraction, the known means of
giving colour to the solar ray; and guiding himself by the experiment
of placing between the eye and the sun a glass bottle of water, from
the lower side of which light issued in the same order of colours as
in the rainbow, he inferred that after two refractions and one
intermediate reflection within the drop, the ray came to the eye
tinged with different colours, according to the angle at which it had
entered. Kepler, doubtless ignorant of De Dominis’s book, had
suggested nearly the same. “This, though not a complete theory of the
rainbow, and though it left a great deal to occupy the attention,
first of Descartes, and afterwards of Newton, was probably just, and
carried the explanation as far as the principles then understood
allowed it to go. The discovery itself may be considered as an anomaly
in science, as it is one of a very refined and subtle nature, made by
a man who has given no other indication of much scientific sagacity or
acuteness. In many things, his writings show great ignorance of
principles of optics well known in his time, so that Boscovich, an
excellent judge in such matters, has said of him, ‘Homo opticarum
rerum supra quod patiatur ea ætas imperitissimus.’”[639] Montucla is
hardly less severe on De Dominis, who, in fact, was a man of more
ingenious than solid understanding.
[639] Playfair, Dissertation on Physical Philosophy, p. 119.
|Dioptrics of Descartes.--Law of refraction.|
48. Descartes announced to the world in his Dioptrics, 1637, that he
had at length solved the mystery which had concealed the law of
refraction. He showed that the sine of the angle of incidence at which
the ray enters, has, in the same medium, a constant ratio to that of
the angle at which it is refracted, or bent in passing through. But
this ratio varies according to the medium; some having a much more
refractive power than others. This was a law of beautiful simplicity
as well as extensive usefulness; but such was the fatality, as we
would desire to call it, which attended Descartes, that this discovery
had been indisputably made twenty years before by a Dutch geometer of
great reputation, Willibrod Snell. The treatise of Snell had never
been published; but we have the evidence both of Vossius and Huygens,
that Hortensius, a Dutch professor, had publicly taught the discovery
of his countryman. Descartes had long lived in Holland; privately, it
is true, and by his own account reading few books; so that in this, as
in other instances, we may be charitable in our suspicions; yet it is
unfortunate that he should perpetually stand in need of such
indulgence.
|Disputed by Fermat.|
49. Fermat did not inquire whether Descartes was the original
discoverer of the law of refraction but disputed its truth. Descartes,
indeed, had not contented himself with experimentally ascertaining it,
but, in his usual manner, endeavoured to show the path of the ray by
direct reasoning. The hypothesis he brought forward seemed not very
probable to Fermat, nor would it be permitted at present. His rival,
however, fell into the same error; and starting from an equally
dubious supposition of his own, endeavoured to establish the true law
of refraction. He was surprised to find that, after a calculation
founded upon his own principle, the real truth of a constant ratio
between the sines of the angles came out according to the theorem of
Descartes. Though he did not the more admit the validity of the
latter’s hypothetical reasoning, he finally retired from the
controversy with an elegant compliment to his adversary.
|Curves of Descartes.|
50. In the Dioptrics of Descartes, several other curious theorems are
contained. He demonstrated that there are peculiar curves, of which
lenses may be constructed, by the refraction from whose superficies
all the incident rays will converge to a focal point, instead of being
spread, as in ordinary lenses, over a certain extent of surface,
commonly called its spherical aberration. The effect of employing such
curves of glass would be an increase of illumination, and a more
perfect distinctness of image. These curves were called the ovals of
Descartes; but the elliptic or hyperbolic speculum would answer nearly
the same purpose. The latter kind has been frequently attempted; but,
on account of the difficulties in working them, if there were no other
objection, none but spherical lenses are in use. In Descartes’s
theory, he explained the equality of the angles of incidence and
reflection in the case of light, correctly as to the result, though
with the assumption of a false principle of his own, that no motion is
lost in the collision of hard bodies such as he conceived light to be.
Its perfect elasticity makes his demonstration true.
|Theory of the rainbow.|
51. Descartes carried the theory of the rainbow beyond the point where
Antonio de Dominis had left it. He gave the true explanation of the
outer bow, by a second intermediate reflection of the solar
ray within the drop: and he seems to have answered the question most
naturally asked, though far from being of obvious solution, why all
this refracted light should only strike the eye in two arches with
certain angles and diameters, instead of pouring its prismatic lustre
over all the rain-drops of the cloud. He found that no pencil of light
continued, after undergoing the processes of refraction and reflection
in the drop, to be composed of parallel rays, and consequently to
possess that degree of density which fits it to excite sensation in
our eyes, except the two which make those angles with the axis drawn
from the sun to an opposite point at which the two bows are perceived.
CHAPTER XXVI.
HISTORY OF SOME OTHER PROVINCES OF LITERATURE FROM 1600 TO 1650.
SECT. I.
ON NATURAL HISTORY.
_Zoology--Fabricius on Language of Brutes--Botany._
|Aldrovandus.|
1. The vast collections of Aldrovandus on zoology, though they may be
considered as representing to us the knowledge of the sixteenth
century, were, as has been seen before, only published in a small part
before its close. The fourth and concluding part of his Ornithology
appeared in 1603; the History of Insects in 1604. Aldrovandus himself
died in 1605. The posthumous volumes appeared in considerable
intervals: that on molluscous animals and zoophytes in 1606; on fishes
and cetacea in 1613; on whole-hoofed quadrupeds in 1616; on digitate
quadrupeds, both viviparous and oviparous, in 1637; on serpents in
1640; and on cloven-hoofed quadrupeds in 1642. There are also volumes
on plants and minerals. These were all printed at Bologna, and most of
them afterwards at Frankfort; but a complete collection is very rare.
|Clusius.|
2. In the Exotica of Clusius, 1605, a miscellaneous volume on natural
history, chiefly, but not wholly, consisting of translations or
extracts from older works, we find several new species of simiæ, the
manis, or scaly ant-eater of the old world, the three-toed sloth, and
one or two armadillos. We may add also the since extinguished race,
that phœnix of ornithologists, the much-lamented dodo. This portly
bird is delineated by Clusius, such as it then existed in the
Mauritius.
|Rio and Marcgraf.|
3. In 1648, Piso on the Materia Medica of Brazil, together with
Marcgraf’s Natural History of the same country, was published at
Leyden, with notes by De Laet. The descriptions of Marcgraf are good,
and enable us to identify the animals. They correct the imperfect
notions of Gesner, and add several species which do not appear in his
work, or perhaps in that of Aldrovandus: such as the tamandua, or
Brasilian ant-eater; several of the family of cavies; the coati-mondi,
which Gesner had perhaps meant in a defective description; the lama,
the pacos, the jaguar, and some smaller feline animals; the prehensile
porcupine, and several ruminants. But some, at least, of these had
been already described in the histories of the West Indies, by
Hernandez d’Oviedo, Acosta, and Herrera.
|Jonston.|
4. Jonston, a Pole of Scots origin, collected the information of his
predecessors in a Natural History of Animals, published in successive
parts from 1648 to 1652. The History of Quadrupeds appeared in the
latter year. “The text,” says Cuvier, “is extracted, with some taste,
from Gesner, Aldrovandus, Marcgraf, and Mouffet; and it answered its
purpose as an elementary work in natural history, till Linnæus taught
a more accurate method of classifying, naming, and describing animals.
Even Linnæus cites him continually.”[640] I find in Jonston a pretty
good account of the chimpanzee (Orang-otang Indorum, ab Angola
delatus), taken perhaps from the Observationes Medicæ of Tulpius.[641]
The delineations in Jonston being from copper-plates, are superior to
the coarse wood-cuts of Gesner, but fails sometimes very greatly in
exactness. In his notions of classification, being little else than a
compiler, it may be supposed that he did not advance a step beyond his
predecessors. The Theatrum Insectorum by Mouffet, an English physician
of the preceding century, was published in 1634; it seems to be
compiled in a considerable degree from the unpublished papers of
Gesner and foreign naturalists, whom the author has rather too
servilely copied. Haller, however, is said to have placed Mouffet
above all entomologists before the age of Swammerdam.[642]
[640] Biogr. Univ.
[641] Grotius; Epist. ad Gallos, p. 21., gives an account of a
chimpanzee, monstrum hominis dicam an bestiæ? and refers to
Tulpius. The doubt of Grotius as to the possible humanity of this
quam similis turpissima bestia nobis, is not so strange as the
much graver language of Linnæus.
[642] Biogr. Univ. Chalmers. I am no judge of the merits of the
book; but if the following sentence of the English translation
does it no injustice, Mouffet must have taken little pains to do
more than transcribe. “In Germany and England I do not hear that
there are any _grasshoppers_ at all; but if there be, they are
_in both countries_ called Bow-krickets, or Baulm-krickets,” p.
989. This translation is subjoined to Topsell’s History of
Four-footed Beasts, collected out of Gesner and others, in an
edition of 1658. The first edition of Topsell’s very ordinary
composition was in 1608.
|Fabricius on the language of brutes.|
5. We may place under the head of zoology a short essay by Fabricius
de Aquapendente on the language of brutes; a subject very curious in
itself, and which has by no means sufficiently attracted notice even
in this experimental age. It cannot be said that Fabricius enters
thoroughly into the problem, much less exhausts it. He divides the
subject into six questions:--1. Whether brutes have a language, and of
what kind: 2. How far it differs from that of man, and whether the
languages of different species differ from one another: 3. What is its
use: 4. In what modes animals express their affections: 5. What means
we have of understanding their language: 6. What is their organ of
speech. The affirmative of the first question he proves by authority
of several writers, confirmed by experience, especially of hunters,
shepherds, and cowherds, who know by the difference of sounds what
animals mean to express. It may be objected that brutes utter sounds,
but do not speak. But this is merely as we define speech; and he
attempts to show that brutes by varying their utterance do all that we
do by _literal_ sounds. This leads to the solution of the second
question. Men agree with brutes in having speech, and in forming
elementary sounds of determinate time; but ours is more complex; these
elementary sounds, which he calls _articulos_, or joints of the
voice, being quicker and more numerous. Man, again, forms his sounds
more by means of the lips and tongue, which are softer in him than
they are in brutes. Hence, his speech runs into great variety and
complication, which we call language, while that of animals within the
same species is much more uniform.
6. The question as to the use of speech to brutes is not difficult.
But he seems to confine this utility to the expression of particular
emotions, and does not meddle with the more curious inquiry, whether
they have a capacity of communicating specific facts to one another;
and if they have, whether this is done through the organs of the
voice. The fourth question is, in how many modes animals express their
feelings. These are by look, by gesture, by sound, by voice, by
language. Fabricius tells us that he had seen a dog, meaning to expel
another dog from the place he wished himself to occupy, begin by
looking fierce, then use meaning gestures, then growl, and finally
bark. Inferior animals, such as worms, have only the two former sorts
of communication. Fishes, at least some kinds, have a power of
emitting a sound, though not properly a voice; this may be by the fins
or gills. To insects also he seems to deny voice, much more language,
though they declare their feelings by sound. Even of oxen, stags, and
some other quadrupeds, he would rather say that they have no voice
than language. But cats, dogs, and birds, have a proper language. All,
however, are excelled by man, who is truly called μεροψ [meropsi],
from his more clear and distinct articulations.
7. In the fifth place, however difficult it may appear to understand
the language of brutes, we know that they understand what is said to
them; how much more, therefore, ought we, superior in reason, to
understand them. He proceeds from hence to an analysis of the
passions, which he reduces to four: joy, desire, grief, and fear.
Having thus drawn our map of the passions, we must ascertain by
observation what are the articulations of which any species of animals
is capable, which cannot be done by description. His own experiments
were made on the dog and the hen. Their articulations are sometimes
complex; as, when a dog wants to come into his master’s chamber, he
begins by a shrill small yelp, expressive of desire, which becomes
deeper, so as to denote a mingled desire and annoyance, and ends in a
lamentable howl of the latter feeling alone. Fabricius gives several
other rules deduced from observation of dogs, but ends by confessing
that he has not fully attained his object, which was to furnish
everyone with a compendious method of understanding the language of
animals: the inquirer must therefore proceed upon these rudiments, and
make out more by observation and good canine society. He shows
finally, from the different structure of the organs of speech, that no
brute can ever rival man; their chief instrument being the throat,
which we use only for vowel sounds. Two important questions are hardly
touched in this little treatise: first, as has been said, whether
brutes can communicate specific facts to each other; and secondly, to
what extent they can associate ideas with the language of man. These
ought to occupy our excellent naturalists.
|Botany--Columna.|
8. Columna, belonging to the Colonna family, and one of the greatest
botanists of the sixteenth century, maintained the honour of that
science during the present period, which his long life embraced. In
the academy of the Lincei, founded by Prince Fredric Cesi about 1606,
and to which the revival of natural philosophy is greatly due Columna
took a conspicuous share. His Ecphrasis, a history of rare plants, was
published in two parts at Rome, in 1606 and 1616. In this he laid down
the true basis of the science, by establishing the distinction of
genera, which Gesner, Cæsalpin, and Camerarius had already conceived,
but which it was left for Columna to confirm and employ. He alone, of
all the contemporary botanists, seems to have appreciated the luminous
ideas which Cæsalpin had bequeathed to posterity.[643] In his
posthumous observations on the natural history of Mexico by Hernandez,
he still farther developed the philosophy of botanical arrangements.
Columna is the first who used copper instead of wood to delineate
plants; an improvement which soon became general. This was in the
Φυτοβασανος, [Phytobasanos], sive Plantarum aliquot Historia, 1594.
There are errors in this work; but it is remarkable for the accuracy
of the descriptions, and for the correctness and beauty of the
figures.[644]
[643] Biogr. Univ.
[644] Id. Sprengel.
|John and Gaspar Bauhin.|
9. Two brothers, John and Gaspar Bauhin, inferior in philosophy to
Columna, made more copious additions to the nomenclature and
description of plants. The elder, who was born in 1541, and had
acquired some celebrity as a botanist in the last century, lived to
complete, but not to publish, an Historia Plantarum Universalis, which
did not appear till 1650. It contains the descriptions of 5,000
species, and the figures of 3,577, but small and ill executed. His
brother, though much younger, had preceded him, not only by the
Phytopinax in 1596, but by his chief work, the Pinax Theatri Botanici,
in 1623. “Gaspar Bauhin,” says a modern botanist, “is inferior to his
brother in his descriptions and in sagacity; but his delineations are
better, and his synonyms more complete. They are both below Clusius in
description, and below several older botanists in their figures. In
their arrangement they follow Lobel, and have neglected the lights
which Cæsalpin and Columna had held out. Their chief praise is to have
brought together a great deal of knowledge acquired by their
predecessors, but the merit of both has been exaggerated.”[645]
[645] Biog. Univ. Pulteney speaks more highly of John Bauhin.
“That which Gesner performed for zoology, John Bauhin effected in
botany. It is, in reality, a repository of all that was valuable
in the ancients, in his immediate predecessors, and in the
discoveries of his own time, relating to the history of
vegetables, and is executed with that accuracy and critical
judgment which can only be exhibited by superior talents.” Hist.
of Botany in England, i. 190.
|Parkinson.|
10. Johnson, in 1636, published an edition of Gerard’s Herbal. But the
Theatrum Botanicum of Parkinson, in 1640, is a work, says Pulteney, of
much more originality than Gerard’s and it contains abundantly more
matter. We find in it near 3,800 plants; but many descriptions recur
more than once. The arrangement is in seventeen classes, partly
according to the known or supposed qualities of the plant, and partly
according to their external character.[646] “This heterogeneous
classification, which seems to be founded on that of Dodoens, shows
the small advances that had been made towards any truly scientific
distribution; on the contrary, Gerard, Johnson, and Parkinson, had
rather gone back, by not sufficiently pursuing the example of Lobel.”
[646] P. 146.
SECT. II.
ON ANATOMY AND MEDICINE.
_Claims of early Writers to the Discovery of the Circulation of the
Blood--Harvey--Lacteal Vessels discovered by Asellius--Medicine._
|Valves of the veins discovered.|
11. The first important discovery that was made public in this century
was that of the valves of the veins; which is justly ascribed to
Fabricius de Aquapendente, a professor at Padua; because, though some
of these valves are described even by Berenger, and further
observations were made on the subject by Sylvius, Vesalius, and other
anatomists, yet Fallopius himself had in this instance thrown back the
science by denying their existence, and no one before Fabricius had
generalised the discovery. This he did in his public lectures as early
as 1524; but his tract De Venarum Ostiolis appeared in 1603. This
discovery, as well as that of Harvey, has been attributed to Father
Paul Sarpi, whose immense reputation in the north of Italy accredited
every tale favourable to his glory. But there seems to be no sort of
ground for either supposition.
|Theory of the blood’s circulation.|
12. The discovery of a general circulation in the blood has done such
honour to Harvey’s name, and has been claimed for so many others, that
it deserves more consideration than we can usually give to anatomical
science. According to Galen, and the general theory of anatomists
formed by his writings, the arterial blood flows from the heart to the
extremities, and returns again by the same channels, the venous blood
being propelled, in like manner, to and from the liver. The discovery
attributed to Harvey was, that the arteries communicate with the
veins, and that all the blood returns to the heart by the latter
vessels. Besides this general or systemic circulation, there is one
called the pulmonary, in which the blood is carried by certain
arteries through the lungs, and returned again by corresponding veins,
preparatory to its being sent into the general sanguineous system; so
that its course is through a double series of ramified vessels, each
beginning and terminating at the heart, but not at the same side of
the heart; the left side, which from a cavity called its ventricle
throws out the arterial blood by the aorta, and by another called its
auricle receives that which has passed through the lungs by the
pulmonary vein, being separated by a solid septum from the right side,
which, by means of similar cavities, receives the blood of all the
veins, excepting those of the lungs, and throws it out into the
pulmonary artery. It is thus evident, that the word pulmonary
circulation is not strictly proper, there being only one for the whole
body.
|Sometimes ascribed to Servetus.|
13. The famous work of Servetus, Christianismi Restitutio, has excited
the attention of the literary part of the world, only by the unhappy
fate it brought upon the author, and its extreme scarcity, but by a
remarkable passage wherein he has been supposed to describe the
circulation of the blood. That Servetus had a just idea of the
pulmonary circulation and the aeration of the blood in the lungs, is
manifest by this passage, and is denied by no one; but it has been the
opinion of anatomists that he did not apprehend the return of the mass
of the blood through the veins to the right auricle of the heart.[647]
[647] In the first volume of this work, p. 643, I have observed
that Levasseur had come much nearer to the theory of a general
circulation than Servetus. But the passage in Levasseur, which I
knew only from the quotation in Portal, Hist. de l’Anatomie, i.,
373, does not, on consulting the book itself, bear out the
inference which Portal seems to deduce; and he has, not quite
rightly, omitted all expressions which he thought erroneous. Thus
Levasseur precedes the first sentence of Portal’s quotation by
the following: Intus (in corde) sunt sinus seu ventriculi duo
tantum, septo quodam medio discreti, _per cujus foramina_ sanguis
et spiritus communicatur. In utroque duo vasa habentur. For this
he quotes Galen; and the perforation of the septum of the heart
is known to be one of Galen’s errors. Upon the whole, there seems
no ground for believing that Levasseur was acquainted with the
general circulation; and though his language may at first lead us
to believe that he speaks of that through the lungs, even this is
not distinctly made out. Sprengel, in his History of Medicine,
does not mention the name of Levasseur (or Vassæus, as he was
called in Latin) among those who anticipated, in any degree, the
discovery of circulation. The book quoted by Portal is Vassæus in
Anatomen Corporis Humani Tabulæ Quatuor, several times printed
between 1540 and 1560.
Andrès (Origine e Progressio d’Ogni Litteratura, vol. xiv., p.
37) has put in a claim for a Spanish farrier, by name Reina, who,
in a book printed in 1552, but of which there seems to have been
an earlier edition (Libro di Maniscalcheria hecho y ordenado por
Francisco de la Reyna), asserts, in few and plain words, as
Andrès quotes them in Italian, that the blood goes in a circle
through all the limbs. I do not know that the book has been seen
by anyone else; and it would be desirable to examine the context,
since other writers have seemed to know the truth without really
apprehending it.
That Servetus was only acquainted with the pulmonary circulation,
has been the general opinion. Portal, though in one place he
speaks with less precision, repeatedly limits the discovery to
this; and Sprengel does not entertain the least suspicion that it
went farther. Andrès (xiv. 38), not certainly a medical
authority, but conversant with such, and very partial to Spanish
claimants, asserts the same. If a more general language may be
found in some writers, it may be ascribed to their want of
distinguishing the two circulations. A medical friend who, at my
request, perused and considered the passage in Servetus, as it is
quoted in Allwoerden’s life, says in a letter, “All that this
passage implies which has any reference to the greater
circulation, may be comprised in the following points:--1. That
the heart transmits a vivifying principle along the arteries and
the blood which they contain to the anastomosing veins; 2. That
this living principle vivifies the liver and the venous system
generally; 3. That the liver produces the blood itself, and
transmits it through the vena cava to the heart, in order to
obtain the vital principle, by performing the lesser circulation,
which Servetus seems perfectly to comprehend.
“Now, according to this view of the passage, all the movement of
the blood _implied_ is that which takes place from the
liver, through the vena cava to the heart, and that of the lesser
circulation. It would appear to me that Servetus is on the brink
of the discovery of the circulation; but that his notions
respecting the transmission of his ‘vitalis spiritus,’ diverted
his attention from that great _movement_ of the blood
itself, which Harvey discovered.... It is clear, that the
quantity of blood sent to the heart for the elaboration of the
vital spiritus, is, according to Servetus, only that furnished by
the liver to the vena cava inferior. But the blood thus
introduced is represented by him as performing the circulation
through the lungs very regularly.”
It appears singular that, while Servetus distinctly knew that the
septum of the heart, paries ille medius, as he calls it, is
closed, which Berenger had discovered, and Vesalius confirmed
(though the bulk of anatomists long afterwards adhered to Galen’s
notion of perforation), and consequently, that some other means
must exist for restoring the blood from the left division of the
heart to the right, he should not have seen the necessity of a
system of vessels to carry forward this communication.
|To Columbus.|
14. Columbus is acknowledged to have been acquainted with the
pulmonary circulation. He says of his own discovery, that no one had
observed or consigned it to writing before. Arantius, according to
Portal, has described the pulmonary circulation still better than
Columbus, while Sprengel denies that he has described it all. It is
perfectly certain, and is admitted on all sides, that Columbus did not
know the systemic circulation: in what manner he disposed of the blood
does not very clearly appear; but, as he conceived a passage to exist
between the ventricles of the heart, it is probable, though his words
do not lead to this inference, that he supposed the aerated blood to
be transmitted back in this course.[648]
[648] The leading passage in Columbus (De Re Anatomica,
lib. vii., p. 177, edit. 1559), which I have not found quoted by
Portal or Sprengel, is as follows: Inter hos ventriculos septum
adest, per quod fere omnes existimant sanguini a dextro
ventriculo ad sinistrum aditum patefieri; id ut fieret facilius,
in transitu ob vitalium spirituum generationem demum reddi; sed
longa errant via; nam sanguis per arteriosam venam ad pulmonem
fertur; ibique attenuatur; deinde cum aere una per arteriam
venalem ad sinistrum cordis ventriculum defertur; quod nemo
hactenus aut animadvertit aut scriptum reliquit; licet maximè et
ab omnibus animadvertendum. He afterwards makes a remark, in
which Servetus had preceded him, that the size of the pulmonary
artery (vena arteriosa) is greater than would be required for the
nutrition of the lungs alone. Whether he knew of the passages in
Servetus or no, notwithstanding his claim of originality is not
perhaps manifest: the coincidence as to the function of the lungs
in aerating the blood is remarkable; but, if Columbus had any
direct knowledge of the Christianismi Restitutio, he did not
choose to follow it in the remarkable discovery that there is no
perforation in the septum between the ventricles.
|And to Cæsalpin.|
15. Cæsalpin, whose versatile genius entered upon every field of
research, has, in more than one of his treatises relating to very
different topics, and especially in that upon plants, some remarkable
passages on the same subject, which approach more nearly than any we
have seen to a just notion of the general circulation, and have led
several writers to insist on his claim as a prior discoverer to
Harvey. Portal admits that this might be regarded as a fair
pretension, if he were to judge from such passages; but there are
others which contradict this supposition, and show Cæsalpin to have
had a confused and imperfect idea of the office of the veins.
Sprengel, though at first he seems to incline more towards the
pretensions of Cæsalpin, comes ultimately almost to the same
conclusion; and giving the reader the words of most importance, leaves
him to form his own judgment. The Italians are more confident:
Tiraboschi and Corniani, neither of whom are medical authorities, put
in an unhesitating claim for Cæsalpin as the discoverer of the
circulation of the blood not without unfair reflections on
Harvey.[649]
[649] Tiraboschi, x., 49. Corniani, vi., 8. He quotes, on the
authority of another Italian writer, il giudizio di que illustri
Inglesi, i fratelli Hunter, i quali, esaminato bene il processo
di questa causa, _si maravigliano della sentenza data in favore
del loro concittadino_. I must doubt, till more evidence is
produced, whether this be true.
The passage in Cæsalpin’s Quæstiones Peripateticæ is certainly
the most resembling a statement of the entire truth that can be
found in any writer before Harvey. I transcribe it from Dutens’s
Origine des Découvertes, vol. ii., p. 23. Idcirco pulmo per venam
arteriis similem ex dextro cordis ventriculo fervidum hauriens
sanguinem, eumque per anastomosin arteriæ venali reddens, quæ in
sinistrum cordis ventriculum tendit, transmisso interim aere
frigido per asperæ arteriæ canales, qui juxta arteriam venalem
protenduntur, non tamen osculis communicantes, ut putavit Galenus
solo, tactu temperat. Huic sanguinis circulationi ex dextro
cordis ventriculo per pulmones in sinistrum ejusdem ventriculum
optimè respondent ea quæ ex dissectione apparent. Nam duo sunt
vasa in dextrum ventriculum desinentia, duo etiam in sinistrum:
duorum autem unum intromittit tantum, alterum educit, membranis
eo ingenio constitutis. Vas igitur intromittens vena et magna
quidem in dextro, quæ cava appellatur; parva autem in sinistro ex
pulmone introducens, cujus unica est tunica, ut cæterarum
venarum. Vas autem educens arteria est magna quidem in sinistro,
quæ aorta appellatur; parva autem in dextro, ad pulmones
derivans, cujus similiter duæ sunt tunicæ, ut in cæteris
arteriis.
In the treatise De Plantis we have a similar, but shorter
passage. Nam in animalibus videmus alimentum per venas duci ad
cor tanquam ad officinam caloris insiti, et adepta inibi ultima
perfectione, per arterias in universum corpus distribui agente
spiritu, qui ex eodem alimento in corde gignitur. I have taken
this from the article of Cæsalpin in the Biographie Universelle.
|Generally unknown before Harvey.|
16. It is thus manifest that several anatomists of the sixteenth
century were on the verge of completely detecting the law by which the
motion of the blood is governed; and the language of one is so strong,
that we must have recourse, in order to exclude his claim, to the
irresistible fact that he did not confirm by proof his own theory, nor
announce it in such a manner as to attract the attention of the world.
Certainly, when the doctrine of a general circulation was advanced by
Harvey, he both announced it as a paradox, and was not deceived in
expecting that it would be so accounted. Those again who strove to
depreciate his originality, sought intimations in the writings of the
ancients, and even spread a rumour that he had stolen the papers of
Father Paul; but it does not appear that they talked, like some
moderns, of plagiarism from Levasseur or Cæsalpin.
|His discovery.|
17. William Harvey first taught the circulation of the blood in
London, in 1619; but his Exercitatio de Motu Cordis was not published
till 1628. He was induced, as is said, to conceive the probability of
this great truth, by reflecting on the final cause of those valves,
which his master, Fabricius de Aquapendente, had demonstrated in the
veins; valves whose structure was such as to prevent the reflux of the
blood towards the extremities. Fabricius himself seems to have been
ignorant of this structure, and certainly of the circulation; for he
presumes that they serve to prevent the blood from flowing like a
river towards the feet and hands, and from collecting in one part.
Harvey followed his own happy conjecture by a long inductive process
of experiments on the effects of ligatures, and on the observed motion
of the blood in living animals.
|Unjustly doubted to be original.|
18. Portal has imputed to Harvey an unfair silence as to Servetus,
Columbus, Levasseur, and Cæsalpin, who had all preceded him in the
same track. Tiraboschi copies Portal, and Corniani speaks of the
appropriation of Cæsalpin’s discovery by Harvey. It may be replied,
that no one can reasonably suppose Harvey to have been acquainted with
the passage in Servetus. But the imputation of suppressing the merits
of Columbus is grossly unjust, and founded upon ignorance or
forgetfulness of Harvey’s celebrated Exercitation. In the proœmium to
this treatise he observes, that almost all anatomists have hitherto
supposed with Galen, that the mechanism of the pulse is the same as
that of respiration. But he not less than three times makes an
exception for Columbus, to whom he most expressly refers the theory of
a pulmonary circulation.[650] Of Cæsalpin he certainly says
nothing; but there seems to be no presumption that he was acquainted
with that author’s writings. Were it even true that he had been guided
in his researches by the obscure passages we have quoted, could this
set aside the merit of that patient induction by which he established
his own theory? Cæsalpin asserts at best, what we may say he divined,
but did not know to be true; Harvey asserts what he had demonstrated.
The one is an empiric in a philosophical sense, the other a legitimate
minister of truth. It has been justly said, that he alone discovers
who proves; nor is there a more odious office, or a more sophistical
course of reasoning, than to impair the credit of great men, as Dutens
wasted his erudition in doing, by hunting out equivocal and insulated
passages from older writers, in order to depreciate the originality of
the real teachers of mankind.[651] It may indeed be thought wonderful
that Servetus, Columbus, or Cæsalpin should not have more distinctly
apprehended the consequences of what they maintained, since it seems
difficult to conceive the lesser circulation without the greater; but
the defectiveness of their views is not to be alledged as a
counterbalance to the more steady sagacity of Harvey. The solution of
their falling so short is that they were right, not indeed quite by
guess, but upon insufficient proof; and that the consciousness of this
embarrassing their minds, prevented them from deducing inferences
which now appear irresistible. In every department of philosophy, the
researches of the first inquirers have often been arrested by similar
causes.[652]
[650] Pæne omnes huc usque anatomici medici et philosophi
supponunt cum Galeno eundem usum esse pulsus, quam respirationis.
But though he certainly claims the doctrine of a general
circulation as wholly his own, and counts it a paradox which will
startle everyone, he as expressly refers (p. 38 and 41 of the
Exercitatio) that of a pulmonary transmission of the blood to
Columbus, peritissimo, doctissimoque anatomico; and observes, in
his proœmium, as an objection to the received theory, quomodo
probabile est (_uti notavit Rualdus Columbus_) tanto sanguine
opus esse ad nutritionem pulmonum, cum hoc vas, vena videlicet
arteriosa (hoc est, uti tum loquebantur, arteria pulmonalis)
exsuperet magnitudine utrumque ramum distributionis venæ cavæ
descendentis cruralem, p. 16.
[651] This is the general character of a really learned and
interesting work by Dutens Origine des Découvertes attribuées aux
Modernes. Justice is due to those who have first struck out, even
without following up, original ideas in any science; but not at
the expense of those who, generally without knowledge of what had
been said before, have deduced the same principles from reasoning
or from observation, and carried them out to important
consequences. Pascal quotes Montaigne for the shrewd remark, that
we should try a man who says a wise thing, for we may often find
that he does not understand it. Those who entertain a morbid
jealousy of modern philosophy, are glad to avail themselves of
such hunters into obscure antiquity as Dutens, and they are
seconded by all the envious, the uncandid, and by many of the
unreflecting among mankind. With respect to the immediate
question, the passages which Dutens has quoted from Hippocrates
and Plato, have certainly an appearance of expressing a real
circulation of the blood by the words περιοδος [periodos] and
περιφερομενου αἱματος [peripheromenou ahimatos]; but others, and
especially one from Nemesius, on which some reliance has been
placed, mean nothing more than the flux and reflux of the blood,
which the contraction and dilatation of the heart was supposed to
produce. See Dutens, vol. ii., p. 8-13. Mr. Coleridge has been
deceived in the same manner by some lines of Jordano Bruno, which
he takes to describe the circulation of the blood: whereas, they
merely express its movement to and fro, _meat et remeat_, which
might be by the same system of vessels.
[652] The biographer of Harvey in the Biographie Universelle
strongly vindicates his claim. Tous les hommes instruits
conviennent aujourd’hui que Harvey est la véritable auteur de
cette belle découverte.... Césalpin pressentoit la circulation
artérielle, en supposant que le sang rétourne des extrémités au
cœur; mais ces assertions ne furent point prouvées; elles ne se
trouvèrent étayées par aucune expérience, par aucun fait; et l’on
peut dire de Césalpin qu’il divina presque la grande circulation
dont les lois lui furent totalement inconnues; la découverte en
était réservée a Guillaume Harvey.
|Harvey’s treatise on Generation.|
19. Harvey is the author of a treatise on generation, wherein he
maintains that all animals, including men, are derived from an egg. In
this book, we first find an argument maintained against spontaneous
generation, which, in the case of the lower animals, had been
generally received. Sprengel thinks this treatise prolix, and not
equal to the author’s reputation.[653] It was first published in 1651.
[653] Hist. de la Médecine, iv., 299. Portal, ii., 477.
|Lacteals discovered by Assellius.|
20. Next in importance to the discovery of Harvey, is that of
Assellius as to the lacteal vessels. Eustachius had observed the
thoracic duct in a horse. But Asellius, more by chance, as he owns,
than by reflection, perceived the lacteals in a fat dog whom he opened
soon after it had eaten. This was in 1622, and his treatise, De
Lacteis Venis, was published in 1627.[654] Harvey did not assent to
this discovery, and endeavoured to dispute the use of the vessels; nor
is it to his honour that even to the end of his life he disregarded
the subsequent confirmation that Pecquet and Bartholin had
furnished.[655] The former detected the common origin of the lacteal
and lymphatic vessels in 1647, though his work on the subject
was not published till 1651. But Olaus Rudbeck was the first who
clearly distinguished these two kinds of vessels.
[654] Portal, ii., 461. Sprengel, iv., 201. Peiresc soon
after this got the body of a man fresh hanged after a good
supper, and had the pleasure of confirming the discovery of
Asellius by his own eyes. Gassendi, Vita Peirescii, p. 177.
[655] Sprengel, iv., 203.
|Optical discoveries of Scheiner.|
21. Scheiner, the Jesuit, proved that the retina is the organ of
sight, and that the humours serve only to refract the rays which paint
the object on the optic nerve. This was in a treatise entitled,
Oculus, hoc est, Fundamentum Opticum, 1619.[656] The writings of
several anatomists of this period, such as Riolan, Vesling, Bartholin,
contain partial accessions to the science; but it seems to have been
less enriched by great discoveries, after those already named, than in
the preceding century.
[656] Sprengel, iv., 270.
|Medicine--Van Helmont.|
22. The mystical medicine of Paracelsus continued to have many
advocates in Germany. A new class of enthusiasts sprung from the same
school, and calling themselves Rosicrucians, pretended to cure
diseases by faith and imagination. A true Rosicrucian, they held, had
only to look on a patient to cure him. The analogy of magnetism,
revived in the last and present age, was commonly employed.[657] Of
this school the most eminent was Van Helmont, who combined the
Paracelsian superstitions with some original ideas of his own. His
general idea of medicine was that its business was to regulate the
archæus, an immaterial principle of life and health; to which, like
Paracelsus, he attributed a mysterious being and efficacy. The seat of
the archæus is in the stomach; and it is to be effected either by a
scheme of diet or through the imagination. Sprengel praises Van
Helmont for overthrowing many current errors, and for announcing
principles since pursued.[658] The French physicians adhered to the
Hippocratic school, in opposition to what Sprengel calls the
Chemiatric, which, more or less, may be reckoned that of Paracelsus.
The Italians were still renowned in medicine. Sanctorius, De Medicina
Statica, 1614, seems the only work to which we need allude. It is
loaded with eulogy by Portal, Tiraboschi, and other writers.[659]
[657] All in nature, says Croll of Hesse, one of the principal
theosophists in medicine, is living; all that lives has its vital
force, or astrum, which cannot act without a body, but passes
from one to another. All things in the macrocosm are found also
in the microcosm. The inward or astral man is Gabalis, from which
the science is named. This Gabalis or imagination, is as a magnet
to external objects, which it thus attracts. Medicines act by a
magnetic force. Sprengel, iii., 362.
[658] Vol. v., p. 22.
[659] Portal, ii., 391. Tiraboschi, xi., 270. Biog. Univ.
SECT. III.
_On Oriental Literature--Hebrew Learning--Arabic and other Eastern
Languages._
|Diffusion of Hebrew.|
23. During no period of equal length, since the revival of letters,
has the knowledge of the Hebrew language been, apparently, so much
diffused among the literary world as in that before us. The frequent
sprinkling of its characters in works of the most miscellaneous
erudition, will strike the eye of every one who habitually consults
them. Nor was this learning by any means so much confined to the
clergy as it has been in later times, though their order naturally
furnished the greater portion of those who laboured in that field.
Some of the chief Hebraists of this age were laymen. The study of this
language prevailed most in the protestant countries of Europe, and it
was cultivated with much zeal in England. The period between the last
years of Elizabeth and the Restoration, may be reckoned that in which
a knowledge of Hebrew has been most usual among our divines.
|Language not studied in the best method.|
24. Upon this subject, I can only assert what I collect to be the
verdict of judicious critics.[660] It seems that the Hebrew language
was not yet sufficiently studied in the method most likely to give an
insight into its principles, by comparing it with all the cognate
tongues, latterly called Semitic, spoken in the neighbouring parts of
Asia, and manifestly springing from a common source. Postel, indeed,
had made some attempts at this in the last century, but his learning
was very slight; and Schindler published in 1612 a Lexicon
Pentaglottum, in which the Arabic, as well as Syriac and Chaldaic,
were placed in apposition with the Hebrew text. Louis De Dieu, whose
“Remarks on all the Books of the Old Testament,” were published at
Leyden in 1648, has frequently recourse to some of the kindred
languages, in order to explain the Hebrew.[661] But the first
instructors in the latter had been Jewish rabbis; and the Hebraists of
the sixteenth age had imbibed a prejudice, not unnatural though
unfounded, that their teachers were best conversant with the language
of their forefathers.[662] They had derived from the same source an
extravagant notion of the beauty, antiquity, and capacity of the
Hebrew; and, combining this with still more chimerical dreams of a
mystical philosophy, lost sight of all real principles of criticism.
[660] The fifth volume of Eichhorn’s Geschichte der Cultur is
devoted to the progress of Oriental literature in Europe, not
very full in characterising the various productions it mentions,
but analytically arranged, and highly useful for reference.
Jenisch, in his preface to Meninski’s Thesaurus (Vienna, 1780),
has traced a sketch of the same subject. We may have trusted in
some respects to Simon, Histoire Critique du Vieux Testament. The
biographical dictionaries, English and French, have, of course,
been resorted to.
[661] Simon, Hist. Critique du Vieux Testament, p. 494.
[662] This was not the case with Luther, who rejected the
authority of the rabbis, and thought none but Christians could
understand the Old Testament. Simon, p. 375. But Munster, Fagius,
and several others, who are found in the Critici Sacri, gave way
to the prejudice in favour of rabbinical opinions, and their
commentaries are consequently too Judaical, p. 496.
|The Buxtorfs.|
25. The most eminent Hebrew scholars of this age were the two Buxtorfs
of Basle, father and son, both devoted to the rabbinical school. The
elder, who had become distinguished before the end of the preceding
century, published a grammar in 1609, which long continued to be
reckoned the best, and a lexicon of Hebrew, Chaldee, and Syriac, in
1623, which was not superseded for more than a hundred years. Many
other works relating to these three dialects, as well as to that of
the later Jews, do honour to the erudition of the elder Buxtorf; but
he is considered as representing a class of Hebraists which, in the
more comprehensive Orientalism of the eighteenth century, has lost
much of its credit. The son trod closely in his father’s footsteps,
whom he succeeded as professor of Hebrew at Basle. They held this
chair between them more than seventy years. The younger Buxtorf was
engaged in controversies which had not begun in his father’s lifetime.
Morin, one of those learned protestants who had gone over to the
church of Rome, systematically laboured to establish the authority of
those versions which the church had approved, by weakening that of the
text which passed for original.[663] Hence, he endeavoured to show,
though this could not logically do much for his object, that the
Samaritan Pentateuch, lately brought to Europe, which is not in a
different language, but merely the Hebrew written in Samaritan
characters, is deserving of preference above what is called the
Masoretic text, from which the protestant versions are taken. The
variations between these are sufficiently numerous to affect a
favourite hypothesis, borrowed from the rabbis, but strenuously
maintained by the generality of protestants, that the Hebrew text of
the Masoretic recension is perfectly incorrupt.[664] Morin’s opinion
was opposed by Buxtorf and Hottinger, and by other writers even of the
Romish church. It has, however, been countenanced by Simon and
Kennicott. The integrity, at least, of the Hebrew copyist, was
gradually given up, and it has since been shown that they differ
greatly among themselves. The Samaritan Pentateuch was first published
in 1645, several years after this controversy began, by Sionita,
editor of the Parisian Polyglott. This edition, sometimes called by
the name of Le Jay, contains most that is in the Polyglott of Antwerp,
with the addition of the Syriac and Arabic versions of the Old
Testament.
[663] Simon, p. 522.
[664] Id. p. 522. Eichhorn, v., 464.
|Vowel points rejected by Cappel.|