The Notebooks of Leonardo Da Vinci (53 page)

[Footnote: See Pl. CIV.]

771.

The cracks in walls will never be parallel unless the part of the
wall that separates from the remainder does not slip down.

The stability of buildings is the result of the contrary law to the
two former cases. That is to say that the walls must be all built up
equally, and by degrees, to equal heights all round the building,
and the whole thickness at once, whatever kind of walls they may be.
And although a thin wall dries more quickly than a thick one it will
not necessarily give way under the added weight day by day and thus,
[16] although a thin wall dries more quickly than a thick one, it
will not give way under the weight which the latter may acquire from
day to day. Because if double the amount of it dries in one day, one
of double the thickness will dry in two days or thereabouts; thus
the small addition of weight will be balanced by the smaller
difference of time [18].

The adversary says that
a
which projects, slips down.

And here the adversary says that
r
slips and not
c
.

The part of the wall which does not slip is that in which the
obliquity projects and overhangs the portion which has parted from
it and slipped down.

When the crevice in the wall is wider at the top than at the bottom,
it is a manifest sign, that the cause of the fissure in the wall is
remote from the perpendicular line through the crevice.

[Footnote: Lines 1-5 refer to Pl. CV, No. 2. Line 9
alle due
anteciedete
, see on the same page.

Lines 16-18. The translation of this is doubtful, and the meaning in
any case very obscure.

Lines 19-23 are on the right hand margin close to the two sketches
on Pl. CII, No. 3.]

772.

That wall which does not dry uniformly in an equal time, always
cracks.

A wall though of equal thickness will not dry with equal quickness
if it is not everywhere in contact with the same medium. Thus, if
one side of a wall were in contact with a damp slope and the other
were in contact with the air, then this latter side would remain of
the same size as before; that side which dries in the air will
shrink or diminish and the side which is kept damp will not dry. And
the dry portion will break away readily from the damp portion
because the damp part not shrinking in the same proportion does not
cohere and follow the movement of the part which dries continuously.

Arched cracks, wide at the top and narrow below are found in
walled-up doors, which shrink more in their height than in their
breadth, and in proportion as their height is greater than their
width, and as the joints of the mortar are more numerous in the
height than in the width.

The crack diminishes less in
r o
than in
m n
, in proportion as
there is less material between
r
and
o
than between
n
and
m
.

Any crack made in a concave wall is wide below and narrow at the
top; and this originates, as is here shown at
b c d
, in the side
figure.

1. That which gets wet increases in proportion to the moisture it
imbibes.

2. And a wet object shrinks, while drying, in proportion to the
amount of moisture which evaporates from it.

[Footnote: The text of this passage is reproduced in facsimile on
Pl. CVI to the left. L. 36-40 are written inside the sketch No. 2.
L. 41-46 are partly written over the sketch No. 3 to which they
refer.]

773.

The walls give way in cracks, some of which are more or less
vertical and others are oblique. The cracks which are in a vertical
direction are caused by the joining of new walls, with old walls,
whether straight or with indentations fitting on to those of the old
wall; for, as these indentations cannot bear the too great weight of
the wall added on to them, it is inevitable that they should break,
and give way to the settling of the new wall, which will shrink one
braccia in every ten, more or less, according to the greater or
smaller quantity of mortar used between the stones of the masonry,
and whether this mortar is more or less liquid. And observe, that
the walls should always be built first and then faced with the
stones intended to face them. For, if you do not proceed thus, since
the wall settles more than the stone facing, the projections left on
the sides of the wall must inevitably give way; because the stones
used for facing the wall being larger than those over which they are
laid, they will necessarily have less mortar laid between the
joints, and consequently they settle less; and this cannot happen if
the facing is added after the wall is dry.

a b
the new wall,
c
the old wall, which has already settled; and
the part
a b
settles afterwards, although
a
, being founded on
c
, the old wall, cannot possibly break, having a stable foundation
on the old wall. But only the remainder
b
of the new wall will
break away, because it is built from top to bottom of the building;
and the remainder of the new wall will overhang the gap above the
wall that has sunk.

774.

A new tower founded partly on old masonry.

775.

Stones laid in regular courses from bottom to top and built up with
an equal quantity of mortar settle equally throughout, when the
moisture that made the mortar soft evaporates.

By what is said above it is proved that the small extent of the new
wall between
A
and
n
will settle but little, in proportion to
the extent of the same wall between
c
and
d
. The proportion will
in fact be that of the thinness of the mortar in relation to the
number of courses or to the quantity of mortar laid between the
stones above the different levels of the old wall.

[Footnote: See Pl. CV, No. 1. The top of the tower is wanting in
this reproduction, and with it the letter
n
which, in the
original, stands above the letter
A
over the top of the tower,
while
c
stands perpendicularly over
d
.]

776.

This wall will break under the arch
e f
, because the seven whole
square bricks are not sufficient to sustain the spring of the arch
placed on them. And these seven bricks will give way in their middle
exactly as appears in
a b
. The reason is, that the brick
a
has
above it only the weight
a k
, whilst the last brick under the arch
has above it the weight
c d x a
.

c d
seems to press on the arch towards the abutment at the point
p
but the weight
p o
opposes resistence to it, whence the whole
pressure is transmitted to the root of the arch. Therefore the foot
of the arch acts like 7 6, which is more than double of
x z
.

777.

An arch constructed on a semicircle and bearing weights on the two
opposite thirds of its curve will give way at five points of the
curve. To prove this let the weights be at
n m
which will break
the arch
a
,
b
,
f
. I say that, by the foregoing, as the
extremities
c
and
a
are equally pressed upon by the thrust
n
,
it follows, by the 5th, that the arch will give way at the point
which is furthest from the two forces acting on them and that is the
middle
e
. The same is to be understood of the opposite curve,
d g
b
; hence the weights
n m
must sink, but they cannot sink by the
7th, without coming closer together, and they cannot come together
unless the extremities of the arch between them come closer, and if
these draw together the crown of the arch must break; and thus the
arch will give way in two places as was at first said &c.

I ask, given a weight at
a
what counteracts it in the direction
n
f
and by what weight must the weight at
f
be counteracted.

778.

The window
a
is the cause of the crack at
b
; and this crack is
increased by the pressure of
n
and
m
which sink or penetrate
into the soil in which foundations are built more than the lighter
portion at
b
. Besides, the old foundation under
b
has already
settled, and this the piers
n
and
m
have not yet done. Hence the
part
b
does not settle down perpendicularly; on the contrary, it
is thrown outwards obliquely, and it cannot on the contrary be
thrown inwards, because a portion like this, separated from the main
wall, is larger outside than inside and the main wall, where it is
broken, is of the same shape and is also larger outside than inside;
therefore, if this separate portion were to fall inwards the larger
would have to pass through the smaller—which is impossible. Hence
it is evident that the portion of the semicircular wall when
disunited from the main wall will be thrust outwards, and not
inwards as the adversary says.

When a dome or a half-dome is crushed from above by an excess of
weight the vault will give way, forming a crack which diminishes
towards the top and is wide below, narrow on the inner side and wide
outside; as is the case with the outer husk of a pomegranate,
divided into many parts lengthwise; for the more it is pressed in
the direction of its length, that part of the joints will open most,
which is most distant from the cause of the pressure; and for that
reason the arches of the vaults of any apse should never be more
loaded than the arches of the principal building. Because that which
weighs most, presses most on the parts below, and they sink into the
foundations; but this cannot happen to lighter structures like the
said apses.

[Footnote: The figure on Pl. CV, No. 4 belongs to the first
paragraph of this passage, lines 1-14; fig. 5 is sketched by the
side of lines l5—and following. The sketch below of a pomegranate
refers to line 22. The drawing fig. 6 is, in the original, over line
37 and fig. 7 over line 54.]

Which of these two cubes will shrink the more uniformly: the cube
A
resting on the pavement, or the cube
b
suspended in the air,
when both cubes are equal in weight and bulk, and of clay mixed with
equal quantities of water?

The cube placed on the pavement diminishes more in height than in
breadth, which the cube above, hanging in the air, cannot do. Thus
it is proved. The cube shown above is better shown here below.

The final result of the two cylinders of damp clay that is
a
and
b
will be the pyramidal figures below
c
and
d
. This is proved
thus: The cylinder
a
resting on block of stone being made of clay
mixed with a great deal of water will sink by its weight, which
presses on its base, and in proportion as it settles and spreads all
the parts will be somewhat nearer to the base because that is
charged with the whole weight.

779.

The arch is nothing else than a force originated by two weaknesses,
for the arch in buildings is composed of two segments of a circle,
each of which being very weak in itself tends to fall; but as each
opposes this tendency in the other, the two weaknesses combine to
form one strength.

As the arch is a composite force it remains in equilibrium because
the thrust is equal from both sides; and if one of the segments
weighs more than the other the stability is lost, because the
greater pressure will outweigh the lesser.

Next to giving the segments of the circle equal weight it is
necessary to load them equally, or you will fall into the same
defect as before.

An arch breaks at the part which lies below half way from the
centre.

If the excess of weight be placed in the middle of the arch at the
point
a
, that weight tends to fall towards
b
, and the arch
breaks at 2/3 of its height at
c e
; and
g e
is as many times
stronger than
e a
, as
m o
goes into
m n
.

The arch will likewise give way under a transversal thrust, for when
the charge is not thrown directly on the foot of the arch, the arch
lasts but a short time.

780.

The way to give stability to the arch is to fill the spandrils with
good masonry up to the level of its summit.

An arch of small curve is safe in itself, but if it be heavily
charged, it is necessary to strengthen the flanks well. An arch of a
very large curve is weak in itself, and stronger if it be charged,
and will do little harm to its abutments, and its places of giving
way are
o p
.