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CHAPTER
XVIII
OF THE
REFRACTION OF LIGHT, AND ASTRONOMICAL REFRACTION; AND OF PERSPECTIVE
1. THE Arabians applied themselves with much assiduity
to the study of the sciences, and the situation of their climate
led them to prefer astronomy, which they cultivated very early.
There are a considerable quantity of their writings in our large
repositories for books, which have never yet come under our notice,
having still remained in manuscript in their original language:
so great has been our neglect of them for some ages. Yet those
who have been at the pains curiously to ransack those manuscripts,
have been well rewarded for their trouble, by the acquisition
they have thence made of many new and original ideas, and the
information they have received of various inventions and discoveries,
useful and entertaining. A learned gentleman at Oxford, who carefully
examined the Arabian manuscripts in the famous library of that
university, gives his sanction to this in a manner that should engage others to imitate his example in such researches.
Among other motives naturally tending to produce the effect, he
says, “the advantages recommending the study of astronomy
to the people of the east were many. The serenity of their weather;
the largeness and correctness of the instruments they made use
of much exceeding what the moderns would be willing to believe;
the multitude of their observations and writings, being six times
more than what have been composed by Greeks and Latins; and,
in short the number of powerful princes, who, in a manner becoming
their own magnificence, aided them with protection. One letter
is not sufficient, says he, to show in how many respects the Arabian
astronomers detected the deficiency of Ptolomy, and the pains
they took correct him; how carefully they measured time by water-clucks,
sandglasses, immense solar dials, and even what perhaps will surpris
you. the vibrations of the pendulum; and with what assiduity and
accurately they conducted themselves in those nice attempts, which
do so much honour to human genius in the taking the distances
of the stars, and the measure of the earth.”
2. Hence it is manifest that the vibration of the pendulum
was employed by the ancient Arabians, long before the epocha we
ordinarily assign for its first discovery; and the use it was
applied to, was, exactly to measure time, the very purpose for
which we employ it.
3. The discovery of the refraction of light, is of more ancient
origin than is generally imagined; for the cause of it appears
to have’ been known to Ptolomy. According to Roger Bacon’s
account, that great philosopher and geometrician gave the same
explanation of that phenomenon, which Descartes has done since;
for he says, that a ray, passing from a more rare into a more
dense medium, becomes more perpendicular. Ptolomy, wrote a treatise
on optics, which was extant in Bacon’s time; and Alhazen
seems not only to have known that treatise of Ptolomy, but to
have drawn thence whatever is truly estimated in what he advances
about the refraction of light, astronomical refraction, and the
cause of the extraordinary size of planets when they appear on
the horizon. This last point, discussed with so much warmth between
Mallebranche and Regis, had already been adjusted by Ptolomy.
4. Ptolomy, and after him Alhazen, said, that “when a
ray of light passes from a more rare, into a more dense medium,
it changes its direction when it arrives upon the surface of the
latter, describing a line which intersects the angle made by that
of its first direction, and a perpendicular falling upon it from
the more dense medium.” Bacon adds, after Ptolomy, that the
angle formed by the coincidence of those two lines, is not always
equally divided by the refracted ray; because in proportion to
the greater or less density of the medium, the ray is more or
less refracted, or obliged to decline from its first direction.”
In this he approaches very near to the reason assigned by Sir
Isaac Newton, who deducing the cause of refraction, from the attraction
made upon the ray of light by the bodies surrounding it says,
“ that mediums are more or less attractive in proportion
to their density.”
5. Ptolomy, acquainted with the principle of the refraction
of light, could not fail to conclude, that this was the cause
also of what was called astronomic refraction, or of the appearance
of planets upon the horizon before they came there; having recourse
therefore to this principle, he accounted for those appearances
from the difference there was between the medium of air, and that
of ether winch lay beyond it; so that the rays of light coming
from the planet, and entering into the denser medium of our atmosphere,
must of course be so attracted as to change their direction, and
by that means bring the star to our view, before it really came
upon the horizon. Alhazen tells us of a method whereby we may
assure ourselves of this truth by observation. He bids us “take
an armillary sphere, and upon it measure the distance of any star
from the pole, when it passes nearest its zenith under the meridian,
and when it appears on the horizon. This last, he says, will be
its smallest distance.” He then makes it appear, that refraction
is the cause of this phenomenon. Yet Alhazen advances nothing
but what he derived from Ptolomy ; and neither one nor other of
them have applied this important discovery in astronomy. so as
to deduce from it, that the apparent elevation of the stars, when
near the horizon, necessarily requires to be corrected.
6. Roger Bacon, inquiring into the cause of that difference
of magnitude in stars when seen on the horizon, from what they
have when viewed over head, says, in the first place, that it
may proceed from this: “that the rays coming from the star
are made to diverge from each other, riot only by passing from
the rare medium of ether into the denser one of our surrounding
air, but also by the interposition of clouds and vapours arising
out of’ the earth, which repeat the refraction and augment
the dispersion of the rays, whereby the object must needs be magnified
to our eye." “Though, says he afterward there has been
assigned by Ptolemy and Alhazen, another cause for this; these
authors thought that the reason of a star’s appearing larger
at its rising or setting than when viewed overhead arose from
this: that when the star is over head, there are no immediate
objects perceived between it and us, so that we judge it nearer
to us, arid are not surprised at its littleness ; but when a star
is viewed on the horizon, it lies then so low, that all we can
see upon earth. interposes between it and us, which making it
appear at a greater distance, we imagine it larger than it is.
For the same reason the sun and moon, when appearing upon the
horizon, seem to be at a greater distance, by reason of the interposition
of those objects, which are upon the surface of our earth, than
when they are over head; and consequently, there will arise in
our minds an idea of their largeness, augmented by that of their
distance, and this of course must make it appear larger to us
when viewed on the horizon, than when seen in the zenith.
7. Most
of the learned deny the ancients the advantage of having known
the rules of perspective, or of having put them in practice although
Vitruvius makes mention of the principles of Democritus and Anaxagoras
respecting that science. in a manner that plainly shows they were
not ignorant of them. “Anazagoras and Democritus," says
he, “were instructed by Agatarchus the disciple of They both
of them taught the rules of drawing, so as to imitate from any
point of view the prospect that lay in sight, by making the lines
in their draught, issuing from the point of view there, exactly
resemble the radiation of those in nature; insomuch that, however
ignorant any one might be of the rules whereby this was performed,
could not but know at sight the edifices, and other prospects
which offered themselves in the perspective scenes they drew for
the deco ration of the theatre; where, though all the objects
were represented on a plain surface, yet they swelled out, or
retired from the sight, just as objects do endowed with all dimensions.”
Again, he says, “that the painter Apatarius drew a scene
for the theatre at Tralles, which was wonderfully pleasing to
the eye, on account that the artist had so well managed the lights
and shades, that the architecture appeared in reality to have
all its projections.” Plato, in two or three places of his
dialogues, speaks in such a manner of the effects of perspective,
as makes it evident that he was acquainted with its principles.
Pliny says, “that Pamphilus, who was an excellent painter,
applied himself much to the study of geometry, and maintained,
that, without its aid, it was impossible ever to arrive at perfection
in that art ;“ which holds certainly true with respect to
perspective. And a little farther he uses an expression, which
can allude to nothing-but perspective; when he says, “that
Apelles fell short of Asclepiodorus, in the art of laying down
distances in his paintings.” Lucian, in his dialogue of Zeuxis,
speaks of the effects of perspective in pictures. Philostratus,
in his preface to his drawing, or history of painting, makes it
appear that he knew this science; and in the description be gives
of Menoetuis' picture of the siege of Thebes, he places full in
sight the happy effects of perspective when studied’ with
care. There he extols the genius of this painter, who, in representing
the walls of the place invested, and scaled by soldiers, placed
some of them full in view, others to be seen only as far as the
knee, others only at- half length, and others whose heads only,
or helmets, were seen, till the whole ended in the points of the
spears of those who were not seen at all ; and he adds, that all
this was the effect of perspective, which’ deceives the eye
by means of the flexure of its lines which gradually approaching
one another as they seem to recede from view, proportionally diminish
the enclosed objects, and make them appear to retire.
8. Aristotle was the first who proposed the famous
problem respecting the roundness of that image of the sun, which
is formed by his rays passing through a small puncture, even though
the hole itself be square or triangular. Marolle, resolved this
about the middle of the fifteenth century, by demonstrating that
this puncture is the vortex 0f two cones of light, the one of
which has the sun itself for its base, and the other the refracted
image. Upon this, Mr. de Montucla ascribes
to him the whole honour of the solution of this optical problem,
formerly indeed proposed by Aristotle, but which that ancient
philosopher, says he, “according to his wonted way, had but
badly accounted for.” It is with regret that I find myself
obliged to animadvert upon some very material mistakes, into
which Mr. deMontuclahas slipt, whose judgment I so much revere
on other occasions. For first of all, from his manner of quoting
this problem of Aristotle, it appears that he neither consulted
the Greek text, nor even the Latin version that accompanies it:
insomuch, that I am at a loss to conceive where be came by this
problem of Aristotle, as he produces it; and still more where
he met with this obscure solution of it, which he imputes to that
ancient philosopher. Aristotle’s only inquiry is, “why
the sun, in transmitting his beams through a square puncture,
does hot form a rectilineal figure ?“ And Mr. de Montucla,
instead of this, makes him substitute quite another question,
respecting the sun in a partial eclipse: Why his rays, in passing
through such a puncture, should produce a figure exactly resembling
that part of his disk, which remains yet obscured? But of all
this, there is not one word in Aristotle. Mr. de Montucla afterward
affirms, that this question, the proper solution of which had
till then been despaired of by naturalists, reduced them all to
the necessity of saying with Aristotle, that “light naturally
threw itself into a round form, or resumed the resemblance of
the luminious body, as soon as ever it had surmounted the obstacle
which put it under constraint.” Now this again is what Aristotle
says nothing at all of. He gives two solutions of his own problem:
the first of which is certainly the foundation, if not the entire
substance of what Mr. de Montucla calls the discovery of Marolle.
To enable the reader to decide whether I have wronged Mr. de Montucla,
I present him with a literal ranslation of a passage of Aristotle’s,
containing in it his first solution of this problem. “ Why
is it that the sun, in passing through a square puncture, forms
itself into an orbicular, and not into a rectilineal figure, as
when it shines through a grate? Is it not because the efflux of
its rays, through the puncture, converges it into a cone whose
base is the luminious circle ” This may serve to confirm,
what I have formerly ventured to assert, that we but seldom do
justice enough to the ancients, either through our entire neglect
of them or from not rightly understanding them.
Chapter 19
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