The Notebooks of Leonardo Da Vinci (62 page)

888.

Take the measure of the sun at the solstice in mid-June.

889.

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.

Take a piece of paper and pierce holes in it with a needle, and look
at the sun through these holes.

On the luminousity of the moon (892-901).

892.

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.

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.

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.

It is impossible that at any distance the image of the sun cast on
the surface of a spherical body should occupy the half of the
sphere.

Here you must prove that the earth produces all the same effects
with regard to the moon, as the moon with regard to the earth.

The moon, with its reflected light, does not shine like the sun,
because the light of the moon is not a continuous reflection of that
of the sun on its whole surface, but only on the crests and hollows
of the waves of its waters; and thus the sun being confusedly
reflected, from the admixture of the shadows that lie between the
lustrous waves, its light is not pure and clear as the sun is.

[Footnote 38: This refers to the small diagram placed between
B
and
B
.—]. The earth between the moon on the fifteenth day and the
sun. [Footnote 39: See the diagram below the one referred to in the
preceding note.] Here the sun is in the East and the moon on the
fifteenth day in the West. [Footnote 40.41: Refers to the diagram
below the others.] The moon on the fifteenth [day] between the earth
and the sun. [41]Here it is the moon which has the sun to the West
and the earth to the East.

898.

The moon is not of itself luminous, but is highly fitted to
assimilate the character of light after the manner of a mirror, or
of water, or of any other reflecting body; and it grows larger in
the East and in the West, like the sun and the other planets. And
the reason is that every luminous body looks larger in proportion as
it is remote. It is easy to understand that every planet and star is
farther from us when in the West than when it is overhead, by about
3500 miles, as is proved on the margin [Footnote 7: refers to the
first diagram.—A =
sole
(the sun), B =
terra
(the earth), C =
luna
(the moon).], and if you see the sun or moon mirrored in the
water near to you, it looks to you of the same size in the water as
in the sky. But if you recede to the distance of a mile, it will
look 100 times larger; and if you see the sun reflected in the sea
at sunset, its image would look to you more than 10 miles long;
because that reflected image extends over more than 10 miles of sea.
And if you could stand where the moon is, the sun would look to you,
as if it were reflected from all the sea that it illuminates by day;
and the land amid the water would appear just like the dark spots
that are on the moon, which, when looked at from our earth, appears
to men the same as our earth would appear to any men who might dwell
in the moon.

[Footnote: This text has already been published by LIBRI:
Histoire
des Sciences,
III, pp. 224, 225.]

When the moon is entirely lighted up to our sight, we see its full
daylight; and at that time, owing to the reflection of the solar
rays which fall on it and are thrown off towards us, its ocean casts
off less moisture towards us; and the less light it gives the more
injurious it is.

899.

I say that as the moon has no light in itself and yet is luminous,
it is inevitable but that its light is caused by some other body.

900.

All my opponent's arguments to say that there is no water in the
moon. [Footnote: The objections are very minutely noted down in the
manuscript, but they hardly seem to have a place here.]

901.

Answer to Maestro Andrea da Imola, who said that the solar rays
reflected from a convex mirror are mingled and lost at a short
distance; whereby it is altogether denied that the luminous side of
the moon is of the nature of a mirror, and that consequently the
light is not produced by the innumerable multitude of the waves of
that sea, which I declared to be the portion of the moon which is
illuminated by the solar rays.

Let
o p
be the body of the sun,
c n s
the moon, and
b
the eye
which, above the base
c n
of the cathetus
c n m
, sees the body
of the sun reflected at equal angles
c n
; and the same again on
moving the eye from
b
to
a
. [Footnote: The large diagram on the
margin of page 161 belongs to this chapter.]