The Notebooks of Leonardo Da Vinci — Complete
wrote this note in 1508, and as the original Greek was first printed
in Venice in 1516, we must suppose him to quote here from the
translation by Guarinus Veronensis, which was printed as early as
1471, also at Venice (H. MULLER-STRUBING).]
Of the nature of Sunlight.
885.
OF THE PROOF THAT THE SUN IS HOT BY NATURE AND NOT BY VIRTUE.
Of the nature of Sunlight.
That the heat of the sun resides in its nature and not in its virtue
[or mode of action] is abundantly proved by the radiance of the
solar body on which the human eye cannot dwell and besides this no
less manifestly by the rays reflected from a concave mirror,
which--when they strike the eye with such splendour that the eye
cannot bear them--have a brilliancy equal to the sun in its own
place. And that this is true I prove by the fact that if the mirror
has its concavity formed exactly as is requisite for the collecting
and reflecting of these rays, no created being could endure the
heat that strikes from the reflected rays of such a mirror. And if
you argue that the mirror itself is cold and yet send forth hot
rays, I should reply that those rays come really from the sun and
that it is the ray of the concave mirror after having passed through
the window.
Considerations as to the size of the sun (886-891).
886.
The sun does not move. [Footnote: This sentence occurs incidentally
among mathematical notes, and is written in unusually large
letters.]
887.
PROOF THAT THE NEARER YOU ARE TO THE SOURCE OF THE SOLAR RAYS, THE
LARGER WILL THE REFLECTION OF THE SUN FROM THE SEA APPEAR TO YOU.
[Footnote: Lines 4 and fol. Compare Vol. I, Nos. 130, 131.] If it is
from the centre that the sun employs its radiance to intensify the
power of its whole mass, it is evident that the farther its rays
extend, the more widely they will be divided; and this being so,
you, whose eye is near the water that mirrors the sun, see but a
small portion of the rays of the sun strike the surface of the
water, and reflecting the form of the sun. But if you were near to
the sun--as would be the case when the sun is on the meridian and
the sea to the westward--you would see the sun, mirrored in the sea,
of a very great size; because, as you are nearer to the sun, your
eye taking in the rays nearer to the point of radiation takes more
of them in, and a great splendour is the result. And in this way it
can be proved that the moon must have seas which reflect the sun,
and that the parts which do not shine are land.
888.
Take the measure of the sun at the solstice in mid-June.
889.
WHY THE SUN APPEARS LARGER WHEN SETTING THAN AT NOON, WHEN IT IS
NEAR TO US.
Every object seen through a curved medium seems to be of larger size
than it is.
[Footnote: At A is written _sole_ (the sun), at B _terra_ (the
earth).]
890.
Because the eye is small it can only see the image of the sun as of
a small size. If the eye were as large as the sun it would see the
image of the sun in water of the same size as the real body of the
sun, so long as the water is smooth.
891.
A METHOD OF SEEING THE SUN ECLIPSED WITHOUT PAIN TO THE EYE.
Take a piece of paper and pierce holes in it with a needle, and look
at the sun through these holes.
III.
THE MOON.
On the luminousity of the moon (892-901).
892.
OF THE MOON.
As I propose to treat of the nature of the moon, it is necessary
that first I should describe the perspective of mirrors, whether
plane, concave or convex; and first what is meant by a luminous ray,
and how it is refracted by various kinds of media; then, when a
reflected ray is most powerful, whether when the angle of incidence
is acute, right, or obtuse, or from a convex, a plane, or a concave
surface; or from an opaque or a transparent body. Besides this, how
it is that the solar rays which fall on the waves of the sea, are
seen by the eye of the same width at the angle nearest to the eye,
as at the highest line of the waves on the horizon; but
notwithstanding this the solar rays reflected from the waves of the
sea assume the pyramidal form and consequently, at each degree of
distance increase proportionally in size, although to our sight,
they appear as parallel.
1st. Nothing that has very little weight is opaque.
2dly. Nothing that is excessively weighty can remain beneath that
which is heavier.
3dly. As to whether the moon is situated in the centre of its
elements or not.
And, if it has no proper place of its own, like the earth, in the
midst of its elements, why does it not fall to the centre of our
elements? [Footnote 26: The problem here propounded by Leonardo was
not satisfactorily answered till Newton in 1682 formulated the law
of universal attraction and gravitation. Compare No. 902, lines
5-15.]
And, if the moon is not in the centre of its own elements and yet
does not fall, it must then be lighter than any other element.
And, if the moon is lighter than the other elements why is it opaque
and not transparent?
When objects of various sizes, being placed at various distances,
look of equal size, there must be the same relative proportion in
the distances as in the magnitudes of the objects.
[Footnote: In the diagram Leonardo wrote _sole_ at the place marked
_A_.]
893.
OF THE MOON AND WHETHER IT IS POLISHED AND SPHERICAL.
The image of the sun in the moon is powerfully luminous, and is only
on a small portion of its surface. And the proof may be seen by
taking a ball of burnished gold and placing it in the dark with a
light at some distance from it; and then, although it will
illuminate about half of the ball, the eye will perceive its
reflection only in a small part of its surface, and all the rest of
the surface reflects the darkness which surrounds it; so that it is
only in that spot that the image of the light is seen, and all the
rest remains invisible, the eye being at a distance from the ball.
The same thing would happen on the surface of the moon if it were
polished, lustrous and opaque, like all bodies with a reflecting
surface.
Show how, if you were standing on the moon or on a star, our earth
would seem to reflect the sun as the moon does.
And show that the image of the sun in the sea cannot appear one and
undivided, as it appears in a perfectly plane mirror.
894.
How shadows are lost at great distances, as is shown by the shadow
side of the moon which is never seen. [Footnote: Compare also Vol.
I, Nos. 175-179.]
895.
Either the moon has intrinsic luminosity or not. If it has, why does
it not shine without the aid of the sun? But if it has not any light
in itself it must of necessity be a spherical mirror; and if it is a
mirror, is it not proved in Perspective that the image of a luminous
object will never be equal to the extent of surface of the
reflecting body that it illuminates? And if it be thus [Footnote 13:
At A, in the diagram, Leonardo wrote "_sole_" (the sun), and at B
"_luna o noi terra_" (the moon or our earth). Compare also the text
of No. 876.], as is here shown at _r s_ in the figure, whence comes
so great an extent of radiance as that of the full moon as we see
it, at the fifteenth day of the moon?
896.
OF THE MOON.
The moon has no light in itself; but so much of it as faces the sun
is illuminated, and of that illumined portion we see so much as
faces the earth. And the moon's night receives just as much light as
is lent it by our waters as they reflect the image of the sun, which
is mirrored in all those waters which are on the side towards the
sun. The outside or surface of the waters forming the seas of the
moon and of the seas of our globe is always ruffled little or much,
or more or less--and this roughness causes an extension of the
numberless images of the sun which are repeated in the ridges and
hollows, the sides and fronts of the innumerable waves; that is to
say in as many different spots on each wave as our eyes find
different positions to view them from. This could not happen, if the
aqueous sphere which covers a great part of the moon were uniformly
spherical, for then the images of the sun would be one to each
spectator, and its reflections would be separate and independent and
its radiance would always appear circular; as is plainly to be seen
in the gilt balls placed on the tops of high buildings. But if those
gilt balls were rugged or composed of several little balls, like
mulberries, which are a black fruit composed of minute round
globules, then each portion of these little balls, when seen in the
sun, would display to the eye the lustre resulting from the
reflection of the sun, and thus, in one and the same body many tiny
suns would be seen; and these often combine at a long distance and
appear as one. The lustre of the new moon is brighter and stronger,
than when the moon is full; and the reason of this is that the angle
of incidence is more obtuse in the new than in the full moon, in
which the angles [of incidence and reflection] are highly acute. The
waves of the moon therefore mirror the sun in the hollows of the
waves as well as on the ridges, and the sides remain in shadow. But
at the sides of the moon the hollows of the waves do not catch the
sunlight, but only their crests; and thus the images are fewer and
more mixed up with the shadows in the hollows; and this
intermingling of the shaded and illuminated spots comes to the eye
with a mitigated splendour, so that the edges will be darker,
because the curves of the sides of the waves are insufficient to
reflect to the eye the rays that fall upon them. Now the new moon
naturally reflects the solar rays more directly towards the eye from
the crests of the waves than from any other part, as is shown by the
form of the moon, whose rays a strike the waves _b_ and are
reflected in the line _b d_, the eye being situated at _d_. This
cannot happen at the full moon, when the solar rays, being in the
west, fall on the extreme waters of the moon to the East from _n_ to
_m_, and are not reflected to the eye in the West, but are thrown
back eastwards, with but slight deflection from the straight course
of the solar ray; and thus the angle of incidence is very wide
indeed.
The moon is an opaque and solid body and if, on the contrary, it
were transparent, it would not receive the light of the sun.
The yellow or yolk of an egg remains in the middle of the albumen,
without moving on either side; now it is either lighter or heavier
than this albumen, or equal to it; if it is lighter, it ought to
rise above all the albumen and stop in contact with the shell of the
egg; and if it is heavier, it ought to sink, and if it is equal, it
might just as well be at one of the ends, as in the middle or below
[54].
[Footnote 48-64: Compare No. 861.]
The innumerable images of the solar rays reflected from the
innumerable waves of the sea, as they fall upon those waves, are
what cause us to see the very broad and continuous radiance on the
surface of the sea.
897.
That the sun could not be mirrored in the body of the moon, which is
a convex mirror, in such a way as that so much of its surface as is
illuminated by the sun, should reflect the sun unless the moon had a
surface adapted to reflect it--in waves and ridges, like the surface
of the sea when its surface is moved by the wind.
[Footnote: In the original diagrams _sole_ is written at the place
marked _A; luna_ at _C,_ and _terra_ at the two spots marked _B_.]
The waves in water multiply the image of the object reflected in it.
These waves reflect light, each by its own line, as the surface of
the fir cone does [Footnote 14: See the diagram p. 145.]
These are 2 figures one different from the other; one with
undulating water and the other with smooth water.