VII-1-‘ INTERNATIONAL INLAND NAINGA’IION CONGRESS.
THE HAGUE, 1594.

6th QUESTION.
RIVER CURRENTS
AND THE
Configuration of river beds.
BY
L. |__r-i|_|AvsK|,
Engineer.
THE HAGUE,
Printed by Belinfante Bl“, late A. D. Schinkel,
PAVELJOENSGRACHT, 19.
18134.
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VIth International Inland Navigation Congress.
THE HAGUE, 1894.
Rllllll NJIIIIIINTS AND THE NlNllllllllAl‘lllN NI RNIIN BEDS
BY
L.LELIAVSKL
Engineer.
/
Nothwithstanding the great works of several mathematians, hydrodynamics
have not yet given a single exact formula absolutely adoptable to practical
combinations. This arises, in our opinion from the fact that the subject of the
displacement of fluids in the midst of resistances has not been sufficiently
examined in an experimental way; and that in the principles of mathematical
deductions there are admissions incompatible with reality. Observations show
that there is no one point in a fluvial current where the threads of water
have a direction completely parallel, but, as the laws on which the direction
\ _\ of the water—threads depend are unknown and their deviation from a parallel
\ine appears to be accidental, it has been generally admitted for the deduction
of hydrodynamic formulae that all water-threads run in parallel directions to
3 Q, //3.!/.¢<f
one another.
NAVIER, following the hypothesis of NEWTON that interior hydraulic frictions
are the lineal sunctions of relative speeds introduced into the equation of the
movement of fluids a coefficient of interior friction resultingfi-om the nature
of the fluid and of its temperature. BUSSINESK after a few unimportant changes
applied these formulae to the straight movement of parallel threads and has
drawn conclusions which agree nearly with the results of real and exact
experiments; but, the agreement is limited to capillary tubes, in which it
must be supposed that the threads run in an almost parallel line to the
guiding walls. For tubes of final transverse sections, and especially for canals
and rivers NAVIER’S formulae gives a considerably greater speed than has
been in reality observed. This phenomenon is attributed to the deviation of
the threads from their straight and mutually parallel direction, consequent on
accidental irregularities, such as inequalities in the walls, modification of
2
pressure on the free surface etc. The new resistance resulting here from, which
seems to be the result of accidental causes cannot be defined theoretically
with desirable exactitude and it diminishes with the reduction of the dimen-
sions of the transverse section of the bed. Nothing, however, proves that this
vague resistance really arises from accidental causes, for it always exists, even
when the walls are quite even and the current quite uniform. It should be
observed that all physical phenomena, so long as their reciprocal relations
have not been studied and determined, that is to say, so long as the laws
which regulate them have not been discovered have always appear to be
arbitrary. For this reason, the hydrodynamic problem in its present state must
comprise observations of the ‘deviations of water-threads from the parallel of
the walls of the tubes on the bottom and the banks of the fluvil bed, with
the view of discovering the laws which govern these deviations.
Based on the admission that the movement of the water takes place
according to straight and parallel threads, there have been deduced from the
I formula of NAVIER other formulae on the established and uni-form movement
of the water of rivers. Modified and simplified by several specialists, these
formulae give for the average speed of the current certain algebraical terms in
which enter several fixed coefficients dependent on the resistance of the
current. Such are the formulae of PRONY, DUPUIS, GIRARD, HAC-EN, WEISS-
BACH, EILLETT, CHEZY, DARCY, SAINT-VENAN, HYMPHREISS and ABBOT,
GAULKLER etc. The inexactitude of formulae arising from irregular admissions
in their foundation is rectified in their practical application by the value of
the coeflicients, which, therefore, must be determined with the greatest care.
The inexactitude of the formulae is manifested by the difference in the coeffi-
cients in conditions, which, i.f not identical, are very similar. Thus, for
example, the coefficient C for the formula of CHE'SY
I/=O\/_R—l_
has been defined by several investigators, and by each one differently, and
the diversity of this coefficient is above all strongly manifested in the calcul-
ation of the dimension of the bed. Consequently GANGUILFJ and KUTTER
considering this coeflicient as a variable quantity, which is modified according
to changes in the elements of the current which enter into the formula of
CHEZY have given for the coefficient C a term in which, besides the elements
designated enters still a new coefficient expressing the result of the calculation
of the degree of inequality of the bed. This coefficient must be obtained by
means of repeated measurements of the speed of the current and of the slopes
at different places. Such modification of the formula, although not adding to
its exactitude allows of its more approximate adoptation, to practical objects,
and it is for this reason that it is considered to be as the present day the
best mode for the solution of questions regarding works for the regulation of
rivers.
HELMHOLTZ working at the investigation of the science of the movements
3
of fluide, that is of the supposed movement independent of the force of
gravity, of friction and other resistances, and considering the possible modific-
ation of the elements of fluid to be infinitely small has found that these
modifications may result from a change of form in the elements, equally as
from their relative rotation.
HELMHOLTZ has further stated the following conclusions:
The commonest and infinitely small motion of fluid particles consists in a
continually advancing movement, rotation and extension.
The properties of the movement are as follows:
1°. A fluid particle that does not always rotate never rotates.
2°. If a line be drawn through a fluid particle every where parallel to its
axis of rotation, this line remains always and in all places parallel to the axis
of rotation. Every such line continually consists of the same particles. These
lines are the lines of motion. The lines which pass through a surface element
form a thread of motion.
3°. The product of the speed of motion and the section of a thread of
motion is constant.
4°. Threads of motion can only return into themselves or end on the
surface.
Since HELMHOLTZ, other mathematicians have studied these threads of
motion, but no clear explanation of the motion of the water has yet been
arrived at. The hypothesis of HELMI-IOLTZ has many partisans, but it is only
the j§ossz'lvz'lz'(y of moving lines and threads in moving fluids which can be
admitted, their real presence in flowing water is, however, not proved. The
rotation of the unfinitely small elements of fluid cannot be observed, and
observations by means of floats, of which we will speak later on do not
manifest any rapid rotary motion. The rotation of the floats is very slow and
is caused by the inequality of speed in the threads of water working on each
side of the float. It is to be remarked that the line followed by a floating
body never crosses itself, that is, it never takes the form of a knot, so that
completely closed circular movements can only occur in places where the
surface of the water is not under the influence of the current, as, for example
in small bays, behind bridge piles or in what are called dead corners at
junctions with confluent rivers etc. The rotary motion of the water in the
vortex is not analogous to the supposed movement of the fluid in the lines
and threads of HELMHOLTZ, for in the first case the axis of rotation is found
outside the moving body (axis of cylinder) and in the second it coincides
with the tangent of the line of direction, which, thus represents a curve enve-
loping the axes of rotation. The movement of the veins should rather be
called spiral, for this last definition would admit of resemblance to the move-
ment of aerial vortices, which in the same way as water-whirls move round a
vertical axis.
BUSSINCSK recognising the existance of a rotary motion of the molecules in
a current of water, considered their speed to be subjected to great irregularities,-
4
for facility of calculation he introduces a new admission of the existence of
average local speeds, nearly constant at all points of the mass of water,
allowing at the same time that the water threads are almost parallel to each
other. Like NAYIER, he introduces into the formula 21 coefficient of friction,
which is not constant for the total mass of moving water, but changes with
the alterations of the coordinates and is besides dependent on the size of the
radius under water, of the form of the section, of the velocity of the current
and of the value of the coefficient of interior friction. Thus BUSSINESK con-
siders the actual movement to be unequal and gradually changing. Ad his
admissions with regard to average velocities and, especiallly, as regards paral-
lelism of threads are not in accordance with reality, and those referring to
the variable value of the coefficient of friction are conjectural and arbitrary,
we find that notwithstanding the importance of his ‘works, which throw light
on several phenomena concerning the longitudinal section of rivers, many
things still remains unexplained and we have no exact formulae of the move-
ment of water adopted to a practical and precise application in the same way
as the formulae existing for the movement of solid bodies.
For researches concerning the displacement of fluvial alluvion it would be
very useful to have exact mathematical terms for the pression of a moving
liquid body on solid bodies; but unfortunately the empirical formulae in use
are not only inexact, but their correctness even is very doubtful.
According to the general opinion of those who have studied the subject
the question of the mutual pression of liquid and solid moving bodies is the
part of hydrodynamics, whlch has received the least attention.
The cause of this is principally the admission of the parallelism of threads.
The influence of this on the inexactitude of deductions is very strong, for not
only is there no parallelism in threads of moving in quietly flowing currents,
but shocks against solid bodies produce new movements of confusion,, accom-
panied by the formation of currents in all possible directions and which have
not been explored.
Absolutely exact as are the formulae relative to the movement of solid
bodies, little certain is up to the present known of the correctness of formulae
relativev to the shock of liquid bodies. Let us examine, for instance, the most
brief deduction of the most exact formula, representing the shock of a single
thread of water against a smooth surface which is perpendicular to it. Desig-
nating the acceleration of the moving point by [9, the time by Z, the space
by s, the speed acquired during the time 2‘ by 2/ the mass of the body by m,
the density A, the volume Q, the power of the shock .P, the gravity of the
weight of the body by G, the acceleration of the gravity by g and considering
that P = m - ]>, and G = m -- g, we shall have successively:
7/=j>-2‘,
therefore : 2‘ :=
‘sis.
5
2/ 2/2
5-:-——— !=——
2 X 21;
U2
further ,0 - s = —
27
212
j) m .s:77Z —
27
712
P-s=m- ~—
2)
the second part of the equation we name conditionally active power which is equal to
the force required to communicate to the mass /22 the speed 2/. If 1 = I, we obtain
7)
J :-—_
2:
G .-
therefore P -: m - 0 = —v = A - Q - L (1)
g g
In adapting these absolutely exact dynamic formulae to the power of the
shock of a single thread of water, it must be calculated that the volume Q
equals the efflux of which is expressed, as is known by the area of the trans-
verse section of the thread of water multiplied by the average speed of water.
That is to say T X 22; we obtain:

7,2
2 0'
P:2AT :2AT~/z, (2)
(3
in which k is the height of a colomn of water corresponding to the speed 21.
A similar application of the formula (I), which has reference to the shock of
a solid body to a liquid mass is irregular, because the efflux of water can be
equal to the average speed, multiplied by the area of the transverse section
of the thread of water, only in cases where the threads are in the same line
as _the smooth surface; this is however not possible, as the water threads are
not parallel to each other. However, experiments which have been made for
the verification of the above named formula by M. BIDON have given results
which approximate confirm its exactitude. This is to be attributed to the cir-
cumstance that the quantity of water directed in the tube can be immediately
measured, instead of being calculated by the multiplication of the area of the
active section by the speed of the water. (Plate I design I). Nevertheless, the
quantity of the pression on the surface depends much on the dimensions of
tha surface and above all on its distance from the orifice of escape of the
water from the tube, so that BIDOU when he placed the surface near the orifice
of the tube obtained the result P = 1,5 A - T- /z, and according to
Dnnors and LANGSDORFF P = only A - T - /z.
The force of the shock, in reality, is generally less than is calculated from
the formula and this results from the fact that by the shock of the liquid mass
a considerable part of the energy belonging to it is lost by the shock of the
separate threads against one another. With the shock of a liquid mass against
a solid the latter only receives directly the pression of the particles of liquid,
infinitely thin, which come in immediate contact with it, while the entire
6
mass of the liquid particles transmits a shock from one to the other of the
particles, in consequence of which the direction of their movement deviates
strongly from the direct line of the solid surface and there can be no question
of the parallelism of the threads. The greater the speed of the water, that is
to say the greater its pression in the tube, the more must be, with exact
experiments, the nearness of the coefficient in formula (2) to the given fig‘ure 2.
In the experiments of BIDON the speeds were very considerable, not less
than 8 metres per second; with small speeds it must be supposed that the
coeflicient of the formula (2) may be considerably less than the unit, even as
much as less than the half of the result of the calculation. So that the for-
mula of the shock of a single thread of water, looked upon as the most exact
of formulae concerning the shocks of liquid bodies really does not possess
the desired exactitude ; and the incompatability of the results of experiments
with these calculations proves the inexactitude of the admissions made in the
transformation of the formula Also, it should be observed, that the pres-
sion on the surface at the time of the commencement of the efflux of the
thread is more considerable than it is during the course of its flow. However
for a mathematical expression of the shock of an unlimited mass of water
we have no other means to apply than the formula (2) which is composed
for the shock of a single tread of water. Therefore for this part of hydrau-
lics we use the following phrase: [I is very jbroéable that we may admit that
the laws governing, the shock of an unlimited mass of water are the same
as those relating to that of a single thread of water. According to this sup-
position or admission the pression of a shock of water on a solid body on
the side of its affluent equals ‘
7,2
K, - A - .7"—;; .
<5
in which K, is the numerical coefficient defined by experiments and depen-
dant only on the form of the body. Besides should be taken into conside-
ration the relaxed pression or the want of pression (according to DUBOIS,
non-pression). This can be expressed in the same way as the pression on the
side of the affluent by the formula
92
K2-A-T—
2g
The hydrostatic pression being equal on each side of the body in opposite
directions may be left out of account. _
Therefore, the result of the pression of moving water on a solid body may
be expressed as follows: -
[i1-A-T———Ké-A-T—.=f<'-A-T—-. <3)
2g 2g 2g
All the coeflicients K, , K2 and K are to be defined by means of experi-
ments and will be certainly very different under various conditions and to
7
different observers. If for a single straight thread of water we may admit;
with a certain degree of approximation, the efflux of water to be equal to
the product of the area of section and the speed, such supposition can not
be admitted for the movement of an unlimited mass of water, for it is im-
possible to suppose that the entire quantity produces a shock against a solid
body through one cylinder which is separated from it and which has for
basis the transverse section of the body attacked. Even with parallelism of
threads the beds of moving water surrounding the cylinder participate in the
shock in consequence of their connection and in consequence of the adhesion
of the water to the eliminated cylinder. But as the threads of water have
convergent and divergent directions, and as it is not possible to separate from
the mass of water, the threads working at every moment on a solid body,
the formule (3) may give results which may diverge as much from the real
quantities as the volume of the cylinder may differ from the volumes of one
or several truncated cones. The convergence of the threads of water does not
conduce to condensation of the water, nor to the accleration of the speed of
the current, which, on the contrary is lessened by the shock of the threads
one against the other, and only causes an increase of pression on the solid
bodies encountered on the way of the moving water. As proved by repeated
observations the threads of water form curved lmes which are still more
curved when they turn around a solid body. When we say that a thread of
water shocks against a solid body we do not mean that all the mass of the
thread of water enters into contact with a solid body, but that on it is direc-
ted the action of the thread of water which is transmitted by the intermediary
beds of water. An indefinite quantity of threads may work upon a body from
different sides at any moment; they meet in their movement some resistance
from the solid body; this resistance being communicated to them by these
intermediate beds of water, they deviate from their direction and prolong this
movement around the solid body with decreasing speed.
As the laws which govern the direction of particles of water are unknown
to us, we cannot follow the threads which in the mass of water, press on the
solid body in the bed of the river. But in order to throw some light on pos-
sibile cases of transmission of pression, let us suppose that their laws are
known and we will represent them by lines as shown on Plate I fig. 2. Then,
suppose a solid body of small dimensions, for example a stone in the bed of
the river submitted to the hydraulic or, to the active pression of the body of
water moving towards it. In order to determine the strength of this pression,
we must seek out in the lines the points in which at a given moment are
found the moving particles of water; and iii these points draw tangents to
the lines, which tangents show the direction of the pressure at the given
moment. Looking at all these tangents, which cut the solid body we see a
mass of straight lines convergent or divergent, which form one or several
truncated cones, lying with their upper or lower end against the solid body.
In the first case the body will be submitted to the hydraulic pression of the
8
convergent threads and of the greatest number of the particles of water, in
the second to the pression of the divergent threads and of the smallest number
of particles of water. Supposing these particles of water to be mutually equal
in their mass, which we take as unit, if we define the average speed by 2)
and the number of particles by m, we flnd for the active power or the mecha-
nical work the mathematical term

and for the force of the shock (P)
P = m 2'),
in which the quantity m 2/ represents what is called the quantity of movement.
It is evident from what we have just said, that the figure 172, or the moving
mass of water on a solid body is a variable quantity and must not be elimi-
nated from the formula by substituting for it the product of the density of
the water with a determined volume. It is, also, evident that with the same
speed at the bottom, but with alteration of the mass of water producing the
pression. the alluvions may be submitted to a hydraulic pression different to
the flowing water according to the disposition of the threads.
Observations on water-threads show that in deep waters, ordinarily disposed
in the concave parts of the bed, all the water-threads move the floats towards
the concave banks, from which it is evident that the hydraulic pression moving
the floats is always directed towards these concave banks, while the particles
of water follow lines which never have a point of intersection with the bank.
So that the conception of the convergence and divergence of the threads of
water and of hydraulic pressions must not be identified with the idea of the
compression of the molecules of water, by the reunion of the threads of
water.
Directing themselves by curved lines and moving between themselves the
threads produce impulsions in two directions; firstly the tangent lines, which
we have examined above and, secondly, in the normal lines, so that impulsions
in the directions of the latter may induce rotary movements of molecules of
water contributing to the accumulation of alluvion. By the transformation of
0 I 2 I 0 I I I
the active force (1) in two directions its quantity must gradually be con-
2
sumed and proportionately more as the angle of the convergence of the water-
threads is larger. The reduction of the active force of each separate molecule
of water in the mass admitted as unit must be expressed by the reduction of
the speed of the current on all the bed.
In fact, as the curves of the bed are stronger the more remarkable is the
depth produced by a great pression of water on the bottom, caused by the
convergence of the water-threads towards the concave banks. The importance
of the increase of the mass of the converging water-threads is seen iu the
9
following of the fluvial bottom along the concave banks, which occurs with
the slackening of the current and causes the formation of a dead-water in the
longitudinal section of the river.
The cause of the reduction of speed and the increase of dead-water, is, as
has just been said, the consumption of a considerable part of the quantity of
active power for the shocks of the threads one against the other in the normal
directions of the molecules of water. On the contrary, in the deep parts where
the water-threads have divergent directions, opposite phenomena are manifested
and the displacement of alluvion in spite of the enormous speed of the current
is effected slowly. If we were to imagine in the direction of the tangents,
molecules of water as, for instance, thin threads of water moving against a
solid body, all the quantity of the mechanical force would at a given moment
be employed in the shock, of which the volume would perhaps be sufficient
not only to move the solid body forward, but even to crush it; and the mole-
cules or the mass of moving water towards upstream would be unlimited.
But in reality the shock of the moving water is transmitted in a different
way.
1° Each molecule approaching the solid body parts with, in the shock, only
a part of its active power and diverging sideways keeps by far the greatest
part of this power for its further flow.
2° Repeated observations have shown that the resistance of the solid body
to the free movement of the water flowing towards it does not extend to all
the mass of water flowing upstream, but that the deviations of the molecules
commences at a certain distance from it, so tbat neither theoretical calculations,
nor actual observations enable us to determine this distance.
It is probable that it depends on the velocity of the current, on the pro-
portion of the area of the greatest transverse section of the solid body to the
area of the transverse section of the bed, on the shape of the body and on
the disposition of the water-threads.
Examination of the pression exerted by flowing water on a solid immovable
body immerged in it has shown that there being no data by which the mass
of water transmitting the shock to the solid body and submitting to deviation
from the resistance offered to its free movement by the body could be deter-
.-,2
. . - . . (
mined, it l1as not yet been found possible to give to the expressions //1 ——
2
and 72/ v,.a propre form for practical calculation. These formulae, however. are
correct in their simple, form and very suitable for general decisions, relative
to transport of alluvion by flowing water. As we have already said, the part
of the flowing water working on a solid body, does not expend in the shock
2
all the quantity of its active power, as for its complete use //2 % would be
equal to O, and this is only possible if 21 : O, that is to say when the mass
of water is completely at rest. In reality it continues to flow with a some-
10
. . 1) 2
what relaxed speed 211 preserving a working power of //z —‘- so that the
2
quantity of power expended in the shock is
02 012
__ 2 2
//z_2 /u_2_(v __Z)1>. . . (4)
and the power of the shock = //z (21 —v1).
The greater the power used the stronger is the shock and thus greater the
possibility of removing the solid body from its place.
As the practical problem of the improvement of rivers consists above all in
the deepening of the bed we must next examine by what means an increase
in the value of the terms
25- (712—2112) and m (v—~v1) may be obtained.
Examining these terms we see that the work of deepening and the force
of the shock increase in proportion to the inerease m of the mass of molecules
of water directing their pression on the projections in the bed, in proportion
to the increase 2) of the speed of the flow of these molecules and in propor-
tion to the decrease 1/1 of the speed of these same molecules when they are
sent back by the resistance of the projections in the bed.
For the increase m it is necessary to direct to the suitable depth the largest
possible quantity of water-threads so as to concentrate their shock at this place.
In practice this is obtained by shutting of the lateral arms, as well as the
crossing threads which break themselves on the bottom, by means of regula-
tion works which form a guide for the direction of the lines of water.
The value 21 is the average speed, not of all the transverse section, but only
of that part of it, with which the hydraulic pression of the water extends to
the river bed. If the quantity 2) increases and decreases with the average speed
of all the section, it must be admitted that the decrease of the section must
serve to augment the quantity 2) and consequently to augment the deepening
power in the bed. With this object the narrowing of the bed is effected by
works of regulation, it must however be remarked that the reduction of the
width of the bed does not always give the desired reduction to the area of
the section, for the latter is often found in a manner non-normal to its projected
line but follows its curves in lines which are oblique, so that the water-threads
take also a direction not only non-parallel to the projected banks, but some-
times are nearly straight; so that the width of the transverse section passing
by the ridges of sandbanks may in these cases appear comparatively narrower
than its primitive widths. Consequently projects of the configuration of a river
compiled according to ordinary systems and the works of regulation executing
according to these projects do not afford the desired depth of bed. For this
reason it is necessary to take measures for the desired disposition of the water-
threads and with this object to form regulation works to direct the water-
threads so that they give the desired configuration. Besides, as is known, the
11
narrowing of the section has still the defect of causing with the deepening
of the bed, the lowering of the level of the water and the displacement or
considerable inclines of water towards neighbouring parts of the river, thus
again causing new hindrances to navigation. It is true, that this could be
remedied by submerged banks. which maintain the strong slopes in the regu-
lated sections; such constructions are, however, very dear and they may become
temporary hindrances to navigation if the amount of water diminishes or the
draught of the vessels increases. I
The quantity 1/1 that is the average speed of the molecules of water which
diverge in their movement under the influence of the resistance of the projec-
tions in the bed, against which they rush, enter in the mathematical expres-
sion for the power expended for the deepening of the bed with a negative
sign and for this reason in increasing the depth attention should be paid to
all possible reduction of the quantity 0,.
To examine this question let us suppose that a single thread of water is
directed in a tube against a solid body firmly fixed at its end. If the solid
body is not displaced by the force of the shock of the thread, the water in
the tube will be brought to a stillstand, 01 becomes —-= o, and the entire
2
quantity of the mechanical power 121% will be expended in the shock of which
the force will be equal to m 21. If the water-thread is not confined in a tube
but flows freely, the water surrounding easily the sides and the upper part
of the solid body, will keep after the shock a considerable part of its speed
and the shock be incomparably weaker.
When the water-thread working on the solid body is surrounded by other
threads nearly parallel among themselves or even divergent its action on the
solid body will be greater than that of an isolated thread, for its flow around
the solid body will be somewhat hindered by the resistance of the neigh-
bouring threads. If the direction of the neighbouring threads, even when they
do not direct their shock against a solid body, becomes convergent, it will
be still more diflicult for the attacking water-thread to turn at the side or
the body and it will then flow over it. This way will be difficult when there
are other water-lines in a position above the attacking line, for the latter
will have to lift them up. In the same degree as the difficulties in encircling
the solid body increase the speed of the water-thread '01 diminishes and the
shock increases. The more water-lines there are above the solid body, or
with other words the greater the depth of water, the more difficult it becomes
for the attacking line to lift up this mass of water, until at last, at a certain
depth it is no longer capable of this action, in which case 2), reaches its
minimum and the force of the shock its maximum.
It should be remarked that 2/I in the river bed never equals 0, for the
attacking water-thread may flow around the body increasing the speed of the
current of the neighbouring threads without lifting them up to any extent.
It is evident from what has been said above that the increase of depth and
12
the convergence of water-threads contribute to the increase of the action of
the water in the river bed, but it must not be concluded that an artificially
created channel in the river bed could be preserved and increased by the
action of the current; as for this to be effected would be required, n.ot only
the depth of water but, also, the disposition of the convergent threads of
water directed on the projections in the bed. And without this last condition
there would be scarcely any current in the channel, which would be obstructed
by particles of solid matter moving above and plunging into it on account
of their weight. ‘
The considerable influence of the depth on the formation of the river bed
is confirmed by observations on cuttings. When a cutting is formed at a
small depth, for instance, o.4 to 0.6 meters below the level of the water, the
deepening of the bottom takes place very slowly and this in spite of the
enormous incline existing at times of low-water and in spite of the consi-
derable speed of the current; but at high water when the fall is less the
operation of deepening becomes so strong that, as I have repeatedly had
occassion to observe on the _Dnieper and on the Pripet, the section-of the
cutting becomes in a very short time sufliciently large for navigation.
These results will show that the deepening power increases, not with the
speed of the current, but in accordance with the augmentation of the mass of
water working on the deepening, and especially at an increased depth, the
water by its gravity does not allow its lower beds to pass over the inequa-
lities in the bottom, but carries them away in descending the stream.
Generally, the more that the circuit of water around a solid body is
hindered, 7'1 is less and the force of the shock and the power expended by
the water for the shock is greater. We know, for example, that small streams
flowing in narrow beds with banks but little excavated often carry away
enormous stones. In the same way rainwater in the gutters of the streets
carries with it bricks and stones with a speed not much less than that of a
river current; but in wide river beds even small grains of sand remain. The
difference of the quantity of the power expended in the displacement of the
solid bodies in these two cases, does not depend so much on the speeds of
the current 2'), as on the quantity of the lost speed 2/—— 2'1], that is to say or
the quantity 2),, and the latter again depends upon the great difference in the
proportions of the transverse sections of the objects carried to the sections of
the beds, or to the quantity of the narrowing of the section of the current by
the transverse section of the body moved. If the bed be large and the size
of the solid body small, then 2/, differs very littie from 21 and the quantity
7” 2 0
2
is nearly :: O. If the current be narrow and the transverse section of the
object which obstructs the free movement of the water, larger, a considerable
delay in the movement will be caused, that is, 01 may become much less
than 21, and a part of the mechanical power of the Water whi_ch is expended
13
on the shock may attain a quantity suflicient to displace even heavy obstacles.
With regard to a closer examination of means for the diminution of the
quantity 2'1 let us suppose a flowing water in a gutter barred at its end by a
solid screen. After the shock of the water against the screen ,2), will be : O and the
shock complete, that all the active power of the water will be expended. If,
however, at the side of the screen a lateral piece of the gutter be removed the
power of the shock against the screen will not be complete and will be in
proportion as much less as the lateral opening is large. See plate I fig. 3.
If the screen be removed the water flowing direct exercises the least pos-
sible hydraulic pression on the walls of the tube. Exactly similar observations
have been made in fluvial beds. Lines of water flowing against ihe concave
bank and the part of the fluvial bed, which is contiguous to it being turned
back lose a great part of the speed employed for the shock, and for the
deepening of the bed at the side of the banks. On the contrary, in a straight
bed the loss of speed in the stream is comparatively insignificant; 2/1 is almost
= 2/, and the power of excavation consequently very small.
Therefore to obtain the quantity of the 1; (2/2——2/12) by the diminution 211
the straight parts of the projected configuration must be avoided and the
windings of the curves enlarged as much as possible, that is their radius
diminished. However this last measure has up to the present time not been
practically applied, for the object of the regulation of rivers does not consist
in the general deepening of the bed but, only the excavation of the bottom
at places where the depth of water is insufficient, which places are generally
found not in the concave elbows but at the points of inflexion of the bed. In
any case the application of such a measure should be restricted within certain
limits, depending; I) on the disadvantage of sharp curves for navigation
especially for steam tug navigation; 2) the underwashing of the banks; 3) the
washing away of the submerged banks by the water at high tides which seek
to follow a more direct line. '
Thus in projecting the trace of the banks we must principally follow the
configuration of natural concave banks, except in cases where their windings
are feeble and irregularly developed.
At the points of inflexion of the bed great divergency is generally found in
the directions of the water threads; and this affords them comparative faci-
lity in passing round obstacles. '
The loss of speed is, therefore not great, 2/, differs very little from 22 and
the transport of alluvion is weak,
T o augment the value of 21, we must unite the separate threads and give
them a convergent direction towards the projected line of the channel, so
that for the deepening of extensive beds the narrowing of the bed is not
sufllcient, but it is necessary to give the bed a configuration, which will
cause the water threads to take always a convergent direction.
Consequently we find it possible to increase the excavating power of the
14
river bed, not only by increasing 2/, that is the average speed of the current,
but also, by increasing the value of 222 and diminishing that of 2'1.
To increase 22 is not suflicient to narrow the section; it is necessary that
the water-threads have corresponding directions, and this is required, also for
the production of the desired influence on the quantities 222 and 221.
It is likewise acknowledged that the regulation of the bed may be effected,
not by narrowing it, but chiefly by guiding the water-threads in a suitable
direction, by which it is evident that a narrowing of the section will occur.
In examining the question of the action of the force of the current on the
deepening of the bed, we have considered the inert power of the water as
an independ.ant cause, while the active power is supplied by the force of
gravity of the water in its movement. We have, therefore, now to consider
to what extent we are able to dispose usefally of this force of gravity.
If Q be the efflux of water, A the density and H the slope, we obtain
as term for the force of gravitation theiproduct of A - Q - H.
The yearly efflux of water cannot be regulated, for this depends on meteo-
rological and climatic conditions; it is, however, known, that the cultivation
of forests conduces to the increase of moisture falling in the atmosphere.
But, for the maintainance of a navigation depth, it is not the general
quantity of moisture falling into the basin of the river which is of importance,
but much rather a suitable and regular supply of water. This is attained by
forest cultivation near to the basin of the river and by construction of reser-
voirs. The general slope of a river or of a more or less great part of it
cannot be altered; still, care should be taken that it be divided on the
length of the river as far as possible in such a way as to obtain uniformity
of the longitudinal section.
Formulae concerning the uniform movement of water teach us the necessity
of regulating the slopes so as to obtain uniformity of longitudinal section of
the bed of the river. But in the solution of practical questions of regulation
of rivers a complete levelling of the bed is not necessary; the possibility of
such Llevelling as well as of uniformity of the current is very doubt
full, as the condition of the stream in the curves is very different to that in
the inflexions. This disparaty is especially shown in the disposition of the
water-threads, and if we could succeed in obtaining in the inflexions a con-
vergence of threads such as are shown in the windings of the bed the ques-
tion of levelling would be considerably nearer to an ideal solution.
The above examination of the application of dynamic forms to river
currents shows the anomaly of the admission of parallelism of threads of
water.
The very great difference of movement and of shock of solid, elastic and
liquid bodies arrises from the fact that in the first the mutual position of the
molecules and of the distances between them does not vary either during the
movement or during the shock.
The direction of all the molecules is parallel or concentric, while in the
15
movement of liquid bodies, in consequence of the resistance of the surface,
on which they move and the surroundings in which the movement is effected,
there is in the interior of the liquid body a continual translation of molecules,
giving rise to interior independent currents, and this consumes a considerable
quantity of the stock of mechanical power acquired by the working of the
force of gravity. This loss of active force is especially great in the shock of
liquid bodies against solid bodies, since it consumes itself in the distribution
and the shock of the threads. In order to place hydrodynamics in the rank
of the exact sciences, abstract mathematical operations, such as those made
by NAVIER, HELMHOLTZ and their disciples, BUSSINECK and many others are
not sufficient.
It must be acknowledged that hydrodynamics is, just as physics, an expe-
rimental science and the bases of its conclusions must not be arbitrary admis-
sions, but data acquired by generalisation and direct experiments. As the
movement of liquid bodies in the midst of resistance are the result of laws,
which govern the movements of solid bodies, we consider it a principal
duty of those who make a study of the practical application of hydrodynamics,
to examine the combinations of the movement of water, resulting from the
configuration of the river bed and influencing its reformation, and especially
to pay attention to the particularities of the movements of the water, by which
liquids differ from solid bodies, that is, the interior translation of molecules
in bodies during their displacement. The researches made under our direc-
tion on the Dnieper near Kief have shown the possibility of examining the
direction of water threads relative to the surface of the water the particu-
larities then discovered concerning the direction of water-threads connected
wirh observations on the configuration of the relief of the river bed have
contributed to the explanation of the established law of the disposition of
isolated and independant currents appearing in every watercourse.
In order to solve the question as to the possibility of closing the lateral
bridge openings in the dike of the Dnieper on the causeway between Kief
and Tchernigoff and for the security of concentration of all the waters of
high tides in one principal bed at the right side of the town, so as to con-
duct them into the opening of the suspension bridge, we have made, in
addition to repeated measurements of the quantities of water, by means of
floats, definitions of the dispositions and the measurements of the speeds of
the water-threads on the surface of the water.
The floats are made round, of dry pine boards o,o6 m. in thickness, 0,25 in
diameter (see fig. I, Plate II). They are painted all round in awhite oil-colour,
the upper disk is divided in 4 sectors, varnished in different colours, so that
the direction of its rotation may be observed from a boat at acertain distance
and the number of revolutions counted.
An iron rod is passed through the float, having at its lower end an iron
screw on which is fixed es many iron plates as are suflicient to sink the float
nearly entirely in the water. At its upper end is placed a glass ball of bright colour.
16
Before commencing the compilation of a plan of the disposition of the
threads of water on the section under examination, transverse sections are
drawn up at a distance of 50 to 44 meters from each other according to the
importance of the section for the projected works, and according to the
variability of the character of the bed. These profiles are indicated on the
banks at each side of the bed by double stakes, as are shown on the plate.
Then a plan of the sheet of water is made on a scale of 25 or 50 m. to
o,or m. The entire section is divided into several parts, in such way that one
plan does not show more than 6oo to 7oo m. on each side, that is to say,
upstream and downstream, since at a greater distance with a KIPREGEL glass,
the glass balls of the floats cannot be distinctly seen.
In accordance with rough notes on the duration, of the courses of the
floats on the sections, plans have been made in two forms.
On the plans 22 are shown the directions of movements of floats and the
profiles of their speeds; on the plans [2 are shown, also, the directions of the
floats and their position at a certain lapse of time, after their passing the first
profile simultaneously, there were fixed on their lines of route, according to
their speed, the points at which they were at a lapse of 2, 4 or 5 minutes
after passing the first profiles; uniting these points we have the profiles of the
position of the floats at the end of these given intervals. From these points
in the direction of movement of the floats, the distances were traced which
they had travelled in the same interval according to the time. The union of
the points found, defined the second profile and so on.
In examining the positions of the lines of direction of the floats, it is im-
possible to overlook one particular characteristic, at the first view appearing a
strange one; namely, that all the floats move from the convex banks to the
channel and to the concave banks, and then their lines of direction cross.
And, as the points of these crossings have a certain fixedness, the fact
cannot be attributed to accidental causes, such as currents of wind, movement
caused by passing steamers, etc.; the more so, as these observations were
made in calm weather, and passing steamers were warned by means of a
speaking-trumpet to keep at a certain distance from the floats.
If the course of the float be considered as a water-thread, that is, as the
route followed by a certain mass of water, the intersection of these masses,
while they maintain each their own direction is evently impossible. For this
reason it is necessary to examine in how far the course of a float coincides
with that of the direction of a water-thread. Let us suppose a volume of water
in a spherical form or in the form of a rotating body with a vertical axis
placed 011 a quite smooth horizontal surface.
A fload placed horizontally above this rotating body will, after the water
has flown off descend vertically. According to its movement as seen on the
plan, we can only judge, that the water was quite motionless. If, however,
the surface~on which the water rests be not quite horizontal, or that there be
hollows or projections in the surface and inequalities in different directions,
1'7
by the increase of speed and of active force, the float will be drawn in the
direction of the greatest speed; from this, however, it does not follow that
the water does not move also in other directions.
Likewise, because the floats move towards the channel and towards the
concave banks, it does not follow that all the water moves in the same direc-
tion; it shows, however, that near the surface of the water the greatest speeds
of the current are not directed parallel to the banks, but obliquely to the
channel.
This deviation of the water-threads towards the channel is the reason that
the efflux of water, measured by us in different rivers gives sometimes results
very different from their true value. The difference in this respect is much
too great to be ascribed to want of precision in the instruments of l11€8.SIll‘€-
ment, for these may be brought to a great degree of perfection if the turning
wings are carefully attended to and the coefficient of fiiction correctly defined.
With the confluence of two watei-threads their masses unite and the further
movement follows in the direction of the result of both their speeds.
The complete union of the two masses of water can be judged by the
colour of the water, which is different on each river. Marshy rivers have a
dark brown colour, mountainous rivers are transparant, others yellow, of a
greenish shade and so on. This difference in colour at the confluence of two
rivers is only observable at a certain short distance from the place of union,
and gradually disappears as one thread of water connects itself with the
other.
The float at the junction of two water-threads moves in the direction of the
result of its own speed and that of the two threads. Thus, we find that at
the confluence of two water-threads the floats ca.rried by these threads will
not unite and will not float together, but their lines of direction will cross and
that if the place of union of the threads remains unchanged in a certain part
of the bed, the points of intersection of the lines of direction are not altered.
If a ship navigates a part of a river where another river or branch flows into
it at a sharp angle and where the concave banks form a point, it usually
passes into the thread issuing from the other arm.
The float receives at every instant a shock from the water which carries
it but it always tends to follow a straight line at a tangent to the curve of
the line of the thread. The mass of the water-threads oppose this movement of
the float and tend to draw it in the direction of their route. This opposition
is partly overcome by the active force of the float, so that the direction of
its movement does not entirely agree with the line of the water-thread and
the float deviates towards the concave bank and reaches it sooner than the
thread on which it had been launched.
Up to the present it has not been found possible to define to what extent
the float deviates from the direction of the thread which carries it, since the
direction of the current is only to be observed by the movement of the
floats. We will later on describe an apparatus which we have invented namely
L1iLIA.vsi\'I. 2
18
a submarine vane, by means of which the direction of the current at any point
of the transverse section of the bed may be determined.
If the density of the float were very nearly the same as that of the water
and its dimensions infinitely small, its direction would coincide exactly with
that of the water-thread.
It the float were of final and very small dimensions its directionwould
deviate very little from the movement of the mass of water surrounding it;
and we may, therefore, admit that the deviation of a solid floating body from
the direction of the mass of water which carries it, is to a certain extent
proportionate to the dimensions of the body. The deviation of the float results
from the power of inertia which is proportionate to the mass of the body,
that is to say to the quantity of three dimensions, and the resistance of the
water transmitted to the float by the shocks against its surface is proportionate
to the dimensions of the surface, that is, to the quantity, of the two measure-
ments ; so that the power resulting from inertia andresistance is proportionate
to a linear quantity, for example for floats, of equal height it is in proportion
to their diameter. From the deviations in direction of two floats of different
dimensions some idea may be formed of the extent of the error admitted,
when it is supposed that the direction of the float coincides with the position
of the water thread. 7
With the object of throwing light 011 this point we had a float made with
a diameter of one meter, that is tho say four times as large as the usual size.
Its organisation is shown on fig. 2, Plate II. .
Observations on the progress of this large float showed that in weak curves
it moved almost identically in the same way as floats of smaller dimensions.
When the configuration of the water-threads is more curved the larger floats
deviate more strongly than do the small ones towards the concavities of the
water lines. (See Plate IV thread NO. 5). ‘
Generally the progress of a large float is less subject to deviation by the
shock of lateral threads of water, than is a small float, therefore, it may be
accepted that the floats follow lines which differ but very slightly from the
directions of the water-threads.
We consider it here the appropriate place to give an explanation of the
expression 22/22222-//zr2'2r2z’s, an expression which we shall frequently use in the
following pages.
By water-threads we understand a mass of water of indefinite ‘amount, but,
with a determined direction. This direction usually agrees nearly with that of
the float. Its dimensions being undetermined, the water-thread is notaphysical
body, but a representation made ta explain the movement of the water.
In a river there are no separate water-threads of defined limits and extre-
mities. The movement of the water is the movement, not of a thread, but of
a mass, the same as the movement of a solid body, with this difference that
all the molecules of a solid body describe parallel and concentric directions,
while all the molecules of a liquid body, having different speeds describe
curved lines, not parallel and not concentric.
19
On further examination of the plans attached to this work, it is impossible
to overlook the characteristic particularity of the position of the water-threads
near the hanging bridge. In the neighhourhood of this bridge the threads
gradually move away from the banks. '
Thus, also, on the projection IX, Plates IV and V, all the floats are direc-
ted towards the right bank and against the concave part of it; the one excep-
tion being float NO. I on the left side, which only travelled a distance of
sixty meters from the concave part of the bed. The floats reaching the banks
_were obstructed by the fascines, only floats IV and VI glided on to a
smooth surface of the bank, floated off it and descended farther with the
stream. The inclination of all the surface of the water in the entire bed
towards the channel, and towards the concave banks, therefore, from the
shallow water towards the deep parts, is a great security to navigation.
Without this disposition of the character of upper currents, ships and floats
would ground on sandbanks, where as under the present circumstances a ship
has only to follow the stream and to take care that it does not strike against
the banks. The current itself does not allow the vessel to flow against the
sandban-ks on the convex side, Floats navigate on the Dnieper and its bran-
ches in calm weather without being steered. It is only on account of this
inclination of the water to stream towards the channel, that vessels find their
way between the shallows. We have often heard navigators say that the best
indication of the deepest waterway was shown by floating barrels filled with
tar and joined together. As soon as such a reft is launched on the surface
of the water it follows the deepest parts, except at curves where by the force
of converging water-threads it is moved towards the concave bank.
The French engineer FARGUE, proceeding from the idea that the convex
banks drive the water towards the channel, based on this his principal of the
curved configuration of the banks on the inflexions of the bed.
But, if the channel attracts to itself the threads of water and if the convex
banks reject them, we must ask from where comes the water on the convex
banks and where does it flow to from the channel and the concave banks?
We all know that the water on the convex bank is not stagnant but has
sometimes considerable speed of current; thus, for example, in the stream
where a part of the hanging bridge 011 the Dnieper was temporarily removed,
the current was so strong, that two tugs were required to draw a vessel
through it. '
The answer to the question is very simple. The water flowing towards the
channel and to the concave banks having no other possible issue, rises
slightly and forms a transversal declivity in the channel from the concave
towards the convex side and by its pressure on the under currents causes
them to flow in the inverse direction and obliquely to the banks.
The existence of such an under-current from the channel towards the banks
has not up to the present time been exactly determined, as correct instru-
ments for the purpose of measurement do not exist, but it is confirmed by
20
many observations. Thus, for example, the excavations in sandy concave beds,
by which large pieces of sandy, marshy soil are frequently carried away do
not cause sanding of the neighbouring parts, and the water flowing along such
banks apparently quite pure and transparent, while in the shallows it is cloudy
and lifts a quantity of alluvion from the bed. This is because the earth loo-
sened from the bank is carried away bythe under-current, which distributes
it not only over the lowest tongue on the same bank, but also in the direc-
tion of the opposite convex bank. In this way is explained the increase in the
number of the tongues of land under water on the convex bank and the
corresponding hollows in the concave banks in higher parts. The best proof
of the presence of the existence 'of an under-current is, however, obtained by
examination of the bottom of the bed.
If, in the bed there is a sandy elevation in the direction of the current,
the grains of sand of the ridge of this elevation are thrown on to the lower
slope down stream to be replaced by others brought from the upper parts of
the stream. The upper slope is levelled, takes a slight incline, coinciding with
the power of the water-flowing above it; and the lower slope, protected from
the shock, becomes of a less incline. By the levelling of the upper ridge to
a slight slope and by the increase of the lower slope, the sandy ridge gradu-
ally descends with the course of the current. As the displacement of the par-
ticles of soil is effected on the side of the water-curent, the top of the sandy
ridge is directed along the line of the water-threads, that is to say on the
bottom-current.
These well-known appearances afford us a certain means of fuiding the
direction of the stream from the configuration of the bottom of the bed.
The soft banks which are visible at low water present a row of sandy pro-
jections which against the stream have a very slight slope and are rather
steep on the side of the bank. This form of tongues of land on sandy banks which
is everywhere observable, shows that there is in every river with an alluvial
bed, a bottom current directed obliquely against the slighter sloped banks.
By examination, by means of a water-scale the direction of the sub marine
ridge can be defined and its limits determined. It is sometimes found that
these sandy deposits occupy the largest part of the width of the bed, rea-
ching even ‘to the channel; sometimes even they cross in the bed, so that at
such places no channel really exists, at least, no channel caused by conver-
ging currents. In this case, the upper water-streads have a divergent direction,
that is to say, that the upper convergent uniform current is replaced in these
parts by an under-current, fan-formed, extending over all the bed.
The cuniform current converging towards the concave banks engenders by
its shocks an under current in a direction lateral to the surface so that the
current of the bed appears to be a consequence of the current of the channel.
A more exact examination shows however that the working of both of the
currents is dependant on different causes.
If we represent the transverse section of the bed with the speeds given on
21
design 4, Plate I, we see that these lines divide the section in different beds
of water which move away gradually fiom the bottom and the banks towards
the channel; the bed of water nearest to the channel is generally the one
with the greatest speed.
The various speeds arise as is known from the exterior resistances to the
current of water represented principally by the friction against the bed and
partly against the air. If we leave the upper part of the bed out of notice
and consider only the bed of water which has the greatest speed relative to
the others we observe that flowing away over the others, it withdraws from
the smooth surface of the section. Then, to fill the place, of these removed
particles of water, all the molecules of the upper bed are thrown from upstream
into it. Thus, the current of the comparatively rapid channel absorbing the
water of all the bed is the cause of the deviation of the superficial current
towards the channel or towards the concave bank near to which it flows.
In this way the water-threads arrive at the concave bank by the force of
inertia and partly also by the result of centrifugal. Every bed and each thread
of water which moves more rapidly attracts a neighbouring bed or water-
thread; herefrom arises a deviation of the particles of water moving at a
comparatively.slow rate along the bank towards those moving more freely and
more quickly in the channel.
To find the cause of the deviation of the stream of the bed towards the
banks which have a slight slope we must consider the position of the water-
threads in a vertical smooth surface. As is known, the direction of the wind
blowing over the earth’s surface does not follow a line parallel to it but at an
angle to the horizon which is sometimes as much as 15°.
This arises from the friction of the air on the earth’s surface and on its
inequalities and projections. A similar phenomenon occurs with the movement
of the water. The lower beds of water are arrested by the roughness and
unequality of the bed; the upper beds pass in advance of the lower ones and
descend before them to the bottom; there they are again arrested by the
shock and the friction against the latter and overtaken by still higher beds of
water. Thus the position of a water-thread in a vertical plan should be inclined
towards the depth, so that the angle of deviation from the horizon gradually
increases towards the bottom. There is to be observed in the upper-water beds
a certain deviation in the water-threads from the horizon to the surface of the
water, which deviation arises from its friction against the air. Such deviation
of water threads from the horizontal direction is related to the shocks of
surface in friction with the bottom and with the air and, with the consequent
loss of mechanical power or of active force in the water-threads. This loss is
accompanied by a lessening of speed in the current. I
The upper current descending from the banks to the bed of the channel
has a direction almost parallel to the bottom and levels the bottom while
forming in it extensive longitudinal ridges; there are thus no isolated shocks
against the projections in the bed, and the speed of the bottom beds of water
22
differs but little from that of the upper beds. On the contrary when the move-
ment of the water is from a deep part to a shallow part, the lower water-
threads strike much more strongly, against the bottom and the loss of speed
be therefore more considerable. In fact the graphical representations of speeds
measured in a vertical plan, present convex lines very nearly approaching the
direction in the channel and have a considerable inclination towards the banks
which are slightly sloped and towards extensive shallows. The inclination of
the water-threads to the horizon increases the error in our calculations of the
efflux of water. We can only obtain a correct calculation by multiplication of
the speeds on a smooth surface with the normal sections, therefore the speeds
on smooth surfaces must be determined for curved sections as well as for
horizontal and vertical directions. As however it is very difficult to find in
nature the position of these to be determined points, it is necessary when a
section has been chosen to measure the direction of the threads at the same
time as the speed of the current and to multiply the section not with the
speeds, but with their projections on the perpendiculars on the plans of the
sections. As the rectangular projections of lines are always less than the lines
themselves, it follows that the actual efflux of water is really less than shown
by our measurements.
The water-threads directed towards the bottom are the cause of shocks
against it, they move grains of sand forward and rushing again upwards with
them carry them down the stream.
A particularity of this kind of movement of alluvion is the great speed
remarkable where there are extensive shallows. The power of the shock of
the water against the bottom is modified by the inequalities in the river-bed
and accordingly each mass of sand as it is carried forward cannot directly
cross the bed but forms single stripes of different forms which are in the
middle at their highest and lower towards the extremities. The slope which
is directed towards the upper stream is slight and the one towards the lower
stream is sharp. As by the increase of the lower slope the upper gradually
disappears, the masses of sand are thus continually moved down-stream; and
their height, their length and their position with regard to the profile of the
subject to continual change. These changes are caused by the fact that the
water which rushes against the sandbanks does not flow over them but flows
of at both sides where the height is less.
The water thrown of the sandbank forms a new stream which is directed
against the top and the two sides of the ridge and observations show that
the alluvion moves more in the directions of the two sides than over the top.
The smaller grains of sand are carried by the water from the top and deposi-
ted on the bed at some distance down stream where they form the beginning
of a new ridge. The movement of alluvion is thus caused more around the
ridges than over their summits.
The ridges formed lower down are opposite the upper ones. Generally the
ridges are not found on the horizontal part of the bed but on the slopes of
23
the banks. The water-threads flowing round the ridges have a greater speed
in the direction where the resistance is less; as the principal resistances of
the movement of the water-threads from above consists in the weight above
them, the water rather flows round the ridges sideways where the depth is
less, that is towards the bank.
By each shock of the bottom current the greater part of the water deviates
towards the bank; thus the union of the mass of these continually moving
impulsions, causes a deviation of the stream towards the bank and a flow of
water in a fan-like form towards the shallows.
With regard to the causes of these bottom and upper-currents, we acknow
ledge that they depend upon the form of the profile of the transverse section
of the bed, which is deep in the channel and has a soft incline on one or
both of the banks. We must, however, not conclude that these currents are
due to the existence of such a profile, on the contrary, the formation of the
profile of the bed arises exclusively under the influence of these currents,
without which that is to say, with aparallel waving movement of the water,
the transverse profile would be nearly a trapeze.
In consequence of the current of the cuneiform channel descending towards
the bottom, the smooth bed of the river within the limits of the stream must
have a triangular form of transverse section; the point of this triangle is only
observable in rivers with a more or less even efflux of water. Generally the
position of the axis of the stream of the channel varies in every river accord-
ing to the alteration in the height of the horizon and the efflux of water. This
is the. cause of the triangular profile becoming obtuse at the rounded points,
and at the lower sides, rather concave, so that the profile of its form approa-
ches a parabola.
The upper part of the slightly sloping banks form convex curves in the
transverse section, so that the active force carrying away the alluvion of the
channel towards the bank, gradually diminishes; therefrom the slope of the
bank on which the particles of sand are moved, becomes less sharp. By this
we are able to approximately determine, by means of the shape of the trans-
vers section; the limits between the converging and diverging currents, which
limits must be near the point of inflexion at which the concave part of the
profile becomes convex (Plate I design 5). With the translation of the channel
at the inflexions of the bed from one bank to the other, its transverse profile
may take all imaginable irregular curves. '
We are able to observe on a small scale the way in which flowing water
works on the profile of the bed, according to its movement in two streams,
the one in the channel and the one on the bank. For this purpose we have
only to follow the course of a mass of rainwater flowing in ground which is
easily hollowed out.
Even on the smooth places of the surface of the ground there are always
some parts which are lower, towards which the water firstly in a wide stream
directs its course.
2-1
Where the thickness of the stream is the greatest, is seen the greatest speed
in the upper water, because the resistance caused by friction and adhesion to
the surface of the ground upon it, has then its least influence.
In any case an accelerated movement of the water arises; this attracts the
threads of the neighbouring parts on the bed, hollows out the ground and
causes a deepening in the bed, in the parts, lying under the converging currents.
At the same time, appears a current on the bottom which, arises in conse-
quence of the shock of the water in the direction of its quickest threads.
The converging current causes longitudinal cavities, which are especially
deep in their curves, and the bottom current rejects the soil on the slightly
sloped banks and on the widenings of the bed, and that in a wavelike form.
In a very short time the bed has depth and sandbanks of great extent which
are distinctly visible when the bed is dry.
According to the laws of its current the water does not only follow its bed
in porous and dry grounds. but, also in those which are hard and rocky. Of
this proofs are found on the Dnieper. The old way, called the cossack-way
used by floats in the spring, flows in the deepest part of the rocky bed.
According to the explanations of persons well-acquainted with the cataract
district of the Dnieper these channels owe their origin to accidental fissures
in the rocks, these having suffered, in their less solid parts, destruction by the
rushing out of the water. If however, we examine carefully the conditon and
the direction of the old channel, it will be seen that this explanation of acci-
dental origin is unfounded.
The ancient waterway is situated near to the right bank and is the natural
channel of the Dnieper in the cataract district. The new channel at low water,
affords an excellent course for entering and leaving the canals. They are con-
structed near the left bank in parts which are less deep and less dangerous.
The natural deviation of the channel is in our opinion due to the action of
the northeast wind extending over centuries.
We have proved in a previous report that the steepness of the right banks
of rivers flowing southwards is not caused by the earth, rotation, but by
the influence of the wind at the time of the passing of the ice in autumn.
The greatest degrees of cold in our climate, which cause the ice on the rivers,
occur only with north and east winds. The culting power of the ice in autumn
is so great that it is sufficient after a few hours to divide a beam of 0,25 m. in
diameter. The current of the water itself has scarcely any effect of friction on wood.
The steepness of the right bank in the cataract district and the approach
of the old channel to this bank are therefore not due accidental causes but
almost entirely to the effect of the northeast wind.
The rocky bed of the cataracts has a depth for floats nearly sufficient for
their passage even at low tides. The obstacles are the summits of rocks, which
cross the bed in a straight line and are called la-222$. Throug these laves the
old channel takes its course towards deepcr parts where there are no rocks
rising out of the bed.
25
If these deep parts were of an accidental origin, the old channels in the
cataracts would be curved, and have a winding direction when passing from
one lave to the other; in reality however the channel runs in a straight line
through the mutually parallel rows of laves. It is impossible to suppose an
accidental piercing of the laves at all the cataracts in the same perpendicular
line; we must therefore be convinced that the deepening and the natural
washing away of the laves is caused by the water in the direction of the
channeh
The absorbing power of the converging stream is so great, notwithstanding
the small width of the channel (at most 40 to roo m. with a river-width of
7oo m. that a vessel launched at some distance from a cataract, in calm
weather finds, itsself, its way into the old channel; and is then carried by the
converging current over all the laves. pTo guide the vessel well, it is only
necessary to take care that it be not caught by any lateral current; for this
purpose a rudder is used which is formed of several planks.
If the converging currents were not as we have just described, the passage
of floats in the cataract districts could not be effected.
There exist, therefore, in the bed two currents; the upper one, convergent
and cuneiform, which, descending to the bottom of the channel causes there
longitudinal excavations, and might be compared to a plough throwing the
earth up on each side of it; and another at the bottom, divergent and fan-
shaped which gradually deviates from the convergent direction along the
channel to a direction nearly normal to the banks.
The soil washed ont by this second current and thrown on to the concave
banks forms slopes with slight declines and drives in zig-zag lines slantingly
over the ridges of sand.
If we could examine the direction of a single particle of water it would
at first sight appear to us to be very irregular especially on account of its
different and apparently accidental deviations from its normal direction, which
are caused by the projections in the bed and on the banks produced by the
continual variation in the flowing quantity of water.
A particle of water in the outer layer a short distance from the banks
takes a slanting direction towards the channel and when it has reached it,
falls slowly. down, and then travels quickly over the bottom, in a line almost
parallel to it. It then turns on one side and joins the bottom current, rushes
against the foot of the slightly sloped banks, thereby losing the active power
acquired in its movement along the channel. Now it springs sometimes upwards,
sometimes downwards and so continues on its way, until it joins again the
upper water bed, with which it again descends in the direction towards the
channél.
The sharper the curve of the concave bank, the more rapid is the descent
of the particle from the upper beds towards the bottom, the greater is the
active power acquired by the movement and the greater the excavation of
the bottom. For this reason the depth at the hollowed parts agrees in inverse
LELIAVSKI. Q*
26
ratio to the radius of the curve; still, the parts of greatest depth are not
found exactly opposite the largest curves of the concave bank, but slightly
lower down stream where the water particles which have the most active
power reach the bottom.
In this way arises the constant mixture of particles of water, without which,
that is, with a direction parallel to the threads, the rapid mixture of the coloured
or troubled water of the affluents with that of the river, would not be
explicable.
The upper converging current arising from the bottom current, aft_er depo-
siting the alluvion, directs itself towards the channel; therefore this upper
current is of clear water, which causes no deposits in the channel.
If the power of the converging current is strong enough to hollow out the
concave bank, this power is also sufficient to carry away the loosened earth
of the channel and without obstructing it, deposits this soil on the slight
slopes of the banks. Freed from this alluvion, the bottom current arises at
the surface of the water and is transformed into the upper current of a pure
form and flows again to the channel. In this direction of currents the channel
with the exception of accidental causes can never suffer from deposits of
sand. The sand can only descend in a tongue form upon them from up-stream.
Only at low-water and when the transverse section becomes exceedingly large
in proportion to the reduced quantity of water, the bottom may receive a
slight deposit of mud.
The depth and constancy of the navigable bottom are thus the effect of
the converging current, therefore, in regulation of rivers in the interests of
navigation care should be taken to grand to this stream the fullest possible
extent. It must, however, not be forgotten that to have a convergence of
waters, it is necessary to admit a free divergence by a bottom current on
the tongues and the slight slopes on the banks, considering that it is only
by its equal divergence that the bottom current can be translated into the
upper current, and proportionately supply the channel with the water threads
of the converging current. _
The converging currents are directed against the concave banks not in
consequence of centrifugal force; as is often seen and still more frequently
in regulated parts of rivers, there often exists a beautiful channel commencing
on the concave bank, and continuing along a great length of the convex
bank, which serves as a prolongation of the concave bank. The converging
current towards the concave banks results exclusively from the concave situa-
tion turning progressively to the side of the bed; it constantly reencounters
the current of the channel which deviates from it, divides again the water
threads flowing towards the concave bank and in consequence of the hydrau-
lic pressure hereby caused is directed towards the bottom which it excavates.
At the same time the bottom current following the convex bank, being
transformed into an upper current supplies new water threads to the bed
which flows towards the channel. For the maintainance of the converging
27
current, all that is necessary is to give a sufficient curve to the convex bank,
for a constant intersection with a direction of the returning water threads of
the converging upper current. Not only the concave bank may be treated in
this way. but on a proportionately short extent, also the convex; therefore
the convexity of the bank should project considerably in the bed and be
turned against the current with the object of meeting again the water-threads
flowing towards it. Therefore, the more the convexities forming the extremities
of the concave banks are developed, the more they retain near them the
convergence of the water.
We have verified this principal on the surfaces of the entire Dnieper and
of the Pripet and found every where that the more the upper parts of the
convex banks project, that is the sharper the water is driven by them against
the opposite concave banks the greater is the depth on the neighbouring
points of inflexion.
In natural non-consolidated beds the spring current being directed with
great speed on the tongues of sand forms frequently at the convexities of the
bancs convergent watersthreads which excavate the bank and cause, on the
sandy ridges near the banks, longitudinal holes with a gulf or a lake-like
form. Such a hollowing out of the convex bank is always accompanied with
a reduction of depth on the inflexions of the bed and in time projections are
formed which are a hindrance to navigation. From the point at which the
concave bank ceases to intersect the upper current, the convergence of the
water lessens and a dimunation of the depths of the channel results.
In proportion as the bank diviates from the general direction of the bed,
the angle of convergence of the water-threads lessens and finally instead of
converging, they diverge. At this place the longitudinal channel of the bed is
replaced by a superficial wave-formed bed, the depth of which diminishes by
degrees; the channel ceases to be the meeting-place of the converging water-
threads and the muddy bottom-stream rises to the surface of the water.
The characteristic phenomena of convergence of water-threads in an under
current, and the principals of their divergences near the junction of the two
opposite curves of the bed, may be followed on several plans made in accord-
ance with our investigations ou the Dnieper at Kief. These plans are not
shown here in order not to burden the report with a too great number of
supplements.
At the cessation of the convergent position of the water-threads, the fan-
shaped bottom currents reach the surface which then presents a boiling appea-
rance caused by impulsive local rising and falling back of the threads. The
displacement of alluvion is no longer effected directly but in zig-zag lines and
in the ridges of the sandbanks in a slanting direction. Banks disappear and
are replaced by others and in this way the bottom movement continues and
the banks moves down-stream. If the water flowing on the banks met with
no hindrances in its course, this movement of alluvion would be continual
as is seen in the deltas of sea-mouths.
28
In river-beds such an incessant descent cannot take place for at a short
distance from the ridge the water strikes against the bank of the river, whereby
the further removal of the bank is prevented. The ridge of each submarine
tongue at an inflexion of the bed unites the two banks, consequently the place
of its tangent with the bank which is left by the water is always situated
much lower down-stream as the point of the tangent of the ridge which meets
the bank towards which the current flows. (See design 3, Plate II).
On this plan the tangent point A on the ridge with the left bank is much
farther up stream than the tangent point B with the right bank. The water
flowing over the ridge at point A strikes against the bank and springing back
encounters the neighbouring water-threads, forming a convergence of water;
which are strengthened by the additional stream of water-threads flowing from
the right towards the concave bank.
By this convergence the extremity of the ridge is washed away, thus a
certain limit only is allowed to descend.
In consequence of the increase in the mass of the converging water-threads,
the power of their flow down stream is augmented and at the same time the
distance of the summit of the ridge from the concave bank becomes greater.
We know that the ridges in spite of the resistance offered by the bank
move farther downstream as the water becomes smoother. This has two causes,
first the excavation of the concave bank and second the reduction of the
power of convergence with the decrease of flow of water in the river.
If the curve of the left bank be sharp and long, so that is forms itself a
convergent current, as shown on the plan a deepness will arise. If the insuf-
ficiently developed curve of the concave bank cannot keep the convergence
of the water, a divergence to the right will result. If the right bank is at
some distance the diverging water meeting with no resistance diverges in dif-
ferent directions oblique to one another.
In consequence of the deviation of the stream in different directions the river be-
comes divided into several single currents, which often become independent arms.
The wider the bed the easier is the formation of new currents and the
developement of these into separate arms.
Generally, rivers which flow through meadows have the greatest tendency
to divide into separate arms, whereas rivers with high banks never divide
into more than two arms and that only at places where the bed becomes
wider. (See design 4).
In consequence of the divergence of the water at the widening of the bed
a tongue of land is formed, which if the bed is straight is placed inaslightly
convex form towards the lower part of the stream in a line nearly normal to
the banks. This convexity continually increases in consequence of the excava-
tion of the banks produced by the water flowing from the top of the ridge.
The longer the tongue of land, and the smoother the water, the nearer be-
come the water-threads to a direction normal to the banks, in consequence
of which the excavation and the widening of the bed is increased.
29
The spring water advancing with great power of inertia on the central part
of the tongue -of earth brings with it a mass of alluvion, so that in time an
island is formed, the height of which increases from one end to the other.
The difference between such a shallow or island and the shallow of a
river flowing in meadow grounds, (see Plate II). is that the first has nearly
always two submarine tongues, one at the beginning and the other at the end
of each arm; the second has only one submarine tongue, or when the bank
is very irregular an indefinite number of them.
The force of convergence is proportional to the active power of the moving
water, therefore the united water-threads can keep on banks which are but
slightly concave and at spring-tides even on convex banks when all the water-
threads flow against all the sandy shallows.
At low spring-tides the convergent current is limited to the concave parts
of the banks and a larger concavity is always required to retain the line of
the axis of the converging current directed along the channel.
Accidental elevations on the submarine tongues of land may cause separa-
tion and divergence of the water-threads and even the formation of isolated
currents.
On one of the attached plans (Plate II) are seen six dotted lines; these
indicate the direction of the axes of the converging currents at the deep places
and the most important depths above the elevations of the bed. The numbers
I to VI correspond to the gradual lowering of the level of the water.
Based on combinations confirmed by direct measurements we have pre-
sented on Plate II, design 3 six longitudinal profiles of the water surface in
the direction of the dotted axis-lines corresponding to the gradually descending
levels of water.
The increase of the superficial speed of the current and of the longitudinal
slope of the water depends on the angmentation of the divergence of the
water-threads, that is the flow of the water towards the wider parts of the
bed. When the sandy tongues are submerged at high-water the middle parts
of the deep places form eddies which extend to the extremities of the ele-
vation.
The divergence of the threads of the Spring-water begins at the point where
the distance between the summits of the ridges commences to increase and
near the point where the concavity of the bank ceases. (Point B on the plan).
The divergence of the threads of the Spring water induces a descent of the
water-level below the shallows, which extending a little upstream increases
the slope of the lower part of the deep channels of the river.
The convergence of the threads of the Spring water resulting from the
lessening of the distance between the summits of the banks, begins about the
middle of the shallows. The diminution of slope hereby caused extending over
the entire sand-bank, gradually increases the current in descending to the
middle of the deep part. The longitudinal profile resulting herefrom has in
the depths a concave form.
30
After the high-water has flown off and the Sandy tongues of land are dry
the current encounters an obstacle formed by the masses of soil brought down
by the spring water and deposited on the upper part of the shallow.
The sandy alluvion of the upper part of the stream gradually disappears
under the influence of the bottom current and re-appears at the lower end
of the shallow, where at the same time the fall of the water is considerably
concentrated.
In consequence of the drying of the deposits of sand, the point of division
of the water-threads descends more and more down stream; therefore, the
slopes below the deep parts and above the elevations are lessened. The dimi-
nution of the slope at this part is caused also by eddies, which are the result
of the accumulation of alluvion at the lower part of the shallows. On the
shallow, and particularly on the summit of the tongues of land, there is a
strong fall of water, the sleepness of which increases with the lowering of the
level of the water; the position of this fall on the longitudinal section moves
forward against the stream. So that, as the water lowers. the longitudinal
profile of the shallow from being concave becomes gradually convex. The
point of the strongest fall changes quickly after, the tongues of land become
dry. It passes suddenly from below a deep part to a place below a shallow,
then with a further lowering of the water it goes upstream, within the limits
of the summit of the submarine tongue of land.
The deposit of alluvion on the shallows is caused by the water at high
tide extending over the tongues of land; the deposit diminishes as the level
of the water is lowered, which results from the tongues laid dry diverting the
water-threads towards the middle of the bed and thus causing a narrowing of
the angle of their divergence.
At the beginning of this movement, when the mass of water has sufficient
power to displace large quantities of sand, the latter advance from the upper
part of the shallows in the direction of the greatest speed towards lower part
of the tongue or land (on our drawing on the right bank near the point B).
The increase of the summit of the submarine tongue at the point indicated
serves to turn the water in another direction (to the left) adding on one side
to the curve of the channel and on the other side to its depth and to the
intersection of the upper part of the submarine tongue. To this cause must be
attributed the well-known phenomena of the deepening of shallows with a
lowering of the level of the water.
After examining the direction of the fluvial currents, resulting from the con-
figuration of the ridges of the banks and the influence of these currents on
the form of the bed, we can determine with precision the form of bank which
corresponds best with the requirements af navigation and assists to the forma-
tion of a deep and constant channel.
We have already seen that in order to keep the converging current of the
channel on the concave bank, the latter must have a sufllciently developed
and continuous curve. Therefore the naturel parts must be provided with a
31
dressing, projections must be cut down and hollows covered by regulating
dikes, connected by transversel planks with the bank, the object of which is
to prevent the water threads at high tide extending across the dike and for-
ming behind at a converging current capable of excavating the bank and
increasing the dimensions of the hollows.
There is no converging current at the inflexions of the bed; there are, so
to speak, not even banks, for at these parts the bed being placed at nearly
a right angle to the tops of the banks is limited on one side by the parts of
the river downstream and on the other by those upstream. In order to form
in the inflexions of the bed a longitudinal cavity, durable and of sufllcient
depth it is necessary to have a converging current and for this purpose, taking
as a basis the combinations which we have shown, we must create an artifi-
cial bank, the direction of which must always intersect the flowing threads;
therefore, the banks should always be so constructed that the tangents of their
curves form at every point angles with the direction of the converging current.
The concave bank must have, as far as possibe, a concave form, but it may
have a certain convexity at the place where, projecting into the bed, it inter-
sects the direction of the threads. The length of the artificial bank should be
so fixed that the converging current directed by it, not expanding at low-
water may reach the concavity of the opposite bank, where the water having
flown off the rongue of earth has already formed a converging current. As
the extremety of the artificial bank is intended to direct the threads at low-
water, the height of the bank at this part should be as little as possible, in
order not to provoke a superfluous eddy at high water. The foot of the arti-
ficial bank, if it is submerged, should be constructed in masonry up to the top
of the bank, and when it is not under water to the highest water-level. I11
order to join easely the artificial with the natural bank, the foot of the first
must be in masonry at the part where the concavity decreases. As the object
of the artificial bank is to prevent the water flowing off on one side, to form
a convergence of the water-threads, and to return them near to it, a suitable
style of regulation must be selected and a proper position and profile given
to it. To retain the current of the channel along the bank the most suitable
system is found to the groins laid slantingly with their top against the current;
as the water-threads not only follow the shape of the tops but endeavour to
cross over them and wet each head on both sides.
The upper part of the artificial bank wich serves to throw back the spring
water-threads from the convexity of the natural bank can be best preserved
from excavation by the construction of a longitudinal dike attached by trans-
verse work to the bank.
Sharp sloping banks contribute to the retention of a convergent current
along the banks, while slight slopes induce divergence of the water-threads
and the formation of a bottom current; for this reason, it is necessary to give
a sharp slope to the heads of the groins laid along the converging current.
In an arrangement with fascines on the Dnieper and on the Pripet at
32
summer low-water wo gave the part or the heads above water an incline
almost vertical and placed the fascines with their thick ends upwards.
This arrangement of the upper part of the heads of the groins is of great
service in preventing as much as possible injury to the fascine work by the
number of enormous floats which drift about without any order. If the slope
of the heads be steep the converging stream directed downwards hollows out
the bottom to a great extent; to prevent this a layer of facines of large
dimensions is placed under the heads, so that deep excavations cannot occur.
Danger of collision from vessels is less when the bank is steep, than when
it is at a soft incline. Notwithstanding the active navigation both by day and
by night on the comparatively small channel of the Pripet it has, up to the
present never happened that a steamer or any other vessel has run againt the
heads on the concave bank. This is due to the fact that the converging cur-
rent allong the steep bank carries the vessel away from the bank and prevents
any collision, even if the distance of the vessel from the bank be small.
A configuration of the bank in a soft incline would cause the water-threads
to drive against the banks, and the vessel would run aground.
The bottom ends of the groins may be unbedded in the sand-banks, but
in order to prevent to hollowing out of the tongues of land by the spring
current, the bottom ends of the groins must be prolonged to the bank and
arranged perpendicularly to the convex bank. They will form a curve as
shown on Sketch 3, Plate II and their height should correspond with the
height of the projected bank, gradually diminishing as it descends the
current.
It cannot be doubted that with a configuration of converging bank as
represented on Sketch 3, Plate II a deep cavity is formed in the length of
the river-bed, its depth will, however, be less than the depth of the two
united current situated lower downstream, so that the form of the bank does
not provide a complete equalisation of depths. In order to lessen the depth
at the parts mentioned of the concave bank and at the same time to protect
the foundation from being hollowed out by the concentrated current, erections,
as shown by dotted lines in the plan may be applied, giving them a down-
stream direction, and thus change the converging current which is directed
downstream into a diverging one which tends upwards. In thus profiting of
the bottom elevations there is no danger of an increase of the hollowing of
banks, for the depths forming in the bottom beyond the elevations are of
but small width. The soil which is hollowed out is carried away by the
diverging threads. and heaped up at the foot of the bank, giving it a slight
incline.
In reviewing the measures to be taken in the construction of a projected
bank, it may be accepted as a rule that it is advisable to lengthen the con-
cave banks and to advance the convex extremities In the bed; the projection
of the upper part of the convex bank should be developed as much as
possible.
33
There is no fear of any danger arising from the retention of the water by
the artificial bank, as the height of the bank does nos exceed that of the
elevation situated lower downstream in the direction D E (Plate II). An
eddy of the spring waters is formed above the shallows and the eddies in the
depths are proportionately diminished, so that the lower concave section of
the high tides approaches the natural straight configuration, and the slope and
the surface speed become more regular. After the excavation of the submarine
sandy reach along artificial bank, the eddy of the summer water will diminish,
the surface will extent upstream over the lower part of a depth and down-
stream over the upper part of another depth. Nevertheless, the surface of the
summer water concentrates, itself at the sharp curve of the banks, as this
causes a strong eddy. This concentration of the slope on the deepened
shoals preserves the neightbouring depths from the undesirable transference
upon them of the fall of the water, which often occurs in the application of
the system of retaining the water for the regulation of the bed.
The rule laid down for the advancement of the extremities of concave
banks in the bed has been practically applied in the regulation of the bed of
the Pripet, as we have shown in a previous report to the assembly of Russian
hydrostatical Engineers. Primitively, the width given to the projected bed of
the Pripet was the considerable one of 200 m., and for the execution of the
work groins were built on each bank. These works were done in 1884 and
188 5. But the parts of the least depth moved from the shallows to the curves
of the bed. This result is inevitable, for, after the narrowing of the bed, when
the direction of the banks is divergent a divergence of threads and a deposit
of alluvion always ensues. Therefore it was necessary to narrow the bed
gradually up to the concavities by advancing the groins; and this explains
why the lengthening of the groins situated above the concave bank has no
influence on the deepening of the shallows; whereas the advancement of the
groins at the extremi'y of the opposite bank produces at once a deepening of
the channel and constancy in its position, especially as the number of bottom
elevations is increased by the construction of intermediate groins.
The correctness of the rule has also been confirmed by the construction
of groins on the Dnieper above Kiev, where in order to deepen the entrance
to the port of the town it was found necessary to advance considerably the
extremity of the slightly concave left bank into the bed. The shape of bank
and the position of the groins as represented on Plate II have been applied
to the regulation of the Pripet on the sandbank Proghnoiski, to which, however,
so much developement has not been given on the converging bank in order
to avoid the expensive powerful strengthening of the opposite bank, for which
a considerable depth was not necessary.
After the configurations described had been made in the course of the
Pripet near Tschernobyl on four sand-banks, the depth at the inflexions of
the canal was I. 5 times more than was desired if the summer water-level be
taken as a basis. No unfavourable results to the neighbouring parts were
84
caused, for a great part of the slope remained on the regulated reach, and
this on account of the eddies formed by the projections of the banks.
It is also, to be observed that these projections are far from being deve-
loped to the extent shown on Plate II; therefore, if a later deepening of the
bed became necessary, the convergence of the water could be strengthened
by strengthening the basis of the opposite banks. Thus the explanation given
of the positions of fluvial currents is quite confirmed by the data obtained in
practice, the manifestation of which preceded the theoretical explanation and
gave cause to examinations, observations and generalisation of the subject.
In order to have a considerable and stable deepening of the bed it is
necessary to give to the concave bank a regular form and a sufficient curve,
and by an artifial lengthening to conduct the water to the concavity of the
opposite bank, which has to be treated in the same manner. With this the
inflexions of the bed disappear and we obtain banks alternatively concave on
each side.
These banks may be designated conductors of the converging water-threads
and of the channel.
Up to the present we have spoken of concave banks, by the development
of which the inflexions of the bed can be obviated. The formation of such
banks is the principal means of regulating the current in the interests of steam
navigation; we must, however, also consider the opposite lying banks against
which the bottom current flows. The bottom current rising on the slight slopes
reaches the upper beds of water and is transformed into an upper current,
which with the threads converging towards the channel forms a channel-cur-
rent near the concave banks. In view of the transformation of bottom-current
into an upper-current, care must be taken that the water diverges proportion-
ately along the convex bank, so that the divergence arises of the threads from
the channel which is winding and of diminishing depth.
A particular obstacle to the uniforme divergence of water along slightly
sloping banks is the side-arms by which the bottom current flows away,
depriving the principal converging current of its threads, and, thus, diminish-
ing the convergence of the water towards the channel; in consequence of
which may be caused a divergence in the channel and even its entire ces-
sation.
The sanding of the arms has often been observed; this is a consequence
of the phenomenon described and is the reason why the side-arms should
be closed.
By these arms we understand those of which the direction, when they sepa-
rate from the principal bed, does not accord with the direction of its current,
flows into a side arm and is then changed into a converging current near to
one of the banks.
Besides the side-arms in the banks the transformation of the bottom current
into an upper current arises from the increase in the slight slope of the convex
bank, when the bottom current, flowing to a considerable distance from the
35
channel ceases to supply it to a suflicient degree with converging threads,
from which results a diminution of convergence, increase of the distance of the
channel from the concave bank, divergence of the upper water-threads and a
deposit of alluvion. This phenomenon is principally observed on the shallows
at widenings of the bed.
Even a considerable narrowing of the bed at these parts produces no impro-
vement and the channel has neither the desired depth nor a permanent posi-
tion. That is because artificial narrowing iufluences the consequence and not
the cause. The widening of the bed is not the primitive cause of the sanding
and instability of the channel; the cause is the irregular distribution of the
currents of the river. In narrowing the bed by advancing the two banks con-
verging currents are created on each bank and the channel cannot possibly
maintain a durable position near to one of them, and so flows in irrugular
curves from one bank to the other under the influence of the changes taking
place on the neighbouring parts of the river and the rising and falling of the
water-level.
Parallel, or nearly parallel lines look very well on the plan, but are in
reality not applicable, as the idea on which they are based is in contradiction
to the laws of movements of currents in rivers. According to plans of regula-
tion works executed or several foreign rivers it is seen that in these the
channel deviates systemattically from the position expected, that the windings
of the channel are arbitrary and temporary, that the channel often extends to
the convex banks and the concavities are covered with alluvion in the form
of moving tongues of land.
These consequences of the application of the system of hydraulic obstruction
on the shallows will be understood if we examine the influence which the
elevations advancing from the extremity of the convex bank has on the bottom
current. The bottom current reaching the heads of the groins cannot turn
towards the concave bank, but is inevitably changed into a converging current
descending towards the bottom, rushing towards the elevations and excavating
holes in them. Then becoming again a bottom current it diverges, carrying
the excavated soil into the channel, which in this way is not only not deepe-
ned, but may become sanded up. The groins confining the width of the
diverging current in a fan-like form can only increase the flow of water
towards the channel at a certain distance downstream; they must therefore
not be constructed nea.r to the tops of the submarine tongues, but are of much
more use when situated at the commencement of the shallows. The arrange-
ment and the profile of the groins near the convex bank must be quite diffe-
rent to the extremity of the concave bank, for their purpose is not to attract
the current of the channel, but on the contrary to direct it towards the
opposite bank, and, in particular, to reduce the angle of divergence of the
threads of the bottom current, so that it can be sooner changed into an upper
current, which increases the divergence near the tops of the tongues. For this
reason these groins must be inclined downstream, their extremities directed
86
against the current and their slope very slight. The arrangement of the groins
near the tongues downstream, just where a diminution of convergence is
desirable, in order to prevent the excavation of the bottom towards the con-
cave bank.
However, in order to utilise the watér-threads and to return them more
quickly to the channel, submerged works may be erected on the convex bank,
parallel to the bank. (Similar to those shown on Plate II).
It is to be supposed that such works in changing the longitudinal direction
of the bottom current into a transverse one may accelerate the transformation
of this current of upper water-threads into a current directed towards the channel.
In a natural bed the convergence and divergence of the water are unequal.
In the depths we observe a converging current and on shallows of great
extent a diverging current. The tendency of the regulation of the bed should
be to promote a proportionate partition of these currents along the river, to
accomplish which the current should be directed by a suitable construction
of the banks, in such way that a converging and a diverging current is ob-
tained in every transverse profile It is in the interests of navigation to have
a converging current all along the river, and, for this reason great care
should be taken in transforming the diverging currents on extensive elevations
into converging currents; but, it is also necessary to attend to the conformitv
of the divergence of the bottom current by reducing as required the angles
of the divergence of the threads, as will as to the increase or their divergence
in the depths in causing submerged erections.
Narrowing of the bed is of no use and is only the consequence of the
advancing of the guiding bank in the bed on the shoals themselves, and of
the concave bank above the shoals.
The theory exposed concerning the directions of river currents and the
rules which have been deduced for the rational regulation of rivers are
founded on observations on the effect of regulating works, observations on
the movement of floats and, generally on any Objects floating on the water,
on examinations of the forms of river-beds and on the transference of allu-
vion. A part of these observations has confirmed the correctness of the rules
deduced; and the results gathered by means of the formulae of dynamics
likewise prove the exactitude of the theory. Nevertheless, for the develope-
ment of this scientific theory in the interests of regulation works and in order
to obtain principles which are exactly in accordance with reality for the
mathematical treatment of hydrodynamics, it is requisite that future observa-
tions on the directions and positions of water-threads be more exact. Up to
the present such observations could not be made for want of suitable instru-
ments. We must consider that it has hitherto been impossible to determine
exactly the direction of a current even in an upper bed of water, since the
direction of the movement of a float is, as explained above, not in exact
accordance with the direction of the water-threads. Therefore, in order to
become an exact science, hydraulics demands instruments by which the direc-
37
tion of the movement of water at all points of the transverse section of the
bed may be determined.
To determine the direction of the wind a fane or weathercock is used, and
a similar apparatus may also serve for the direction of water-threads ; still,
the construction of such an instrument for use in water must be of a much
more complicated nature, than that of an aerial fane, and the observation of
the water-threads much more difificult. The aerial fane indicates the direction
of the wind in an horizontal surface while a submarine fane must show the
direction of the movement of the water at the same time horizontally and
vertically. The deviations in the directions of water-threads are made slowly
and are weak, it is, therefore, necessary that the instrument of measurement
be very sensitive and exact. The principal difliculty is, however, the fixing
and arrangement of the submarine apparatus and the observation of its indi-
cations. However securely a vessel may be layed to with anchors and ropes,
there always exists some swinging and rotative motion, which is the result of
the force of the current, of the wind or even caused by the moving about of
the people on board. For this reason the placing and using of the apparatus
on a boat would afford inexact and even quite erroneous results. It is impos-
sible to take direct observations of the movement of the submarine fane. The
use of instruments for the transmission of the movements is however diflicult,
because they hinder the free working of the fane and reduce its sensitiveness.
These observations show that such an apparatus must not but of ordinary
construction, but must, to answer its purpose be of a very complicated nature.
Researches made by a submarine fane should be executed, as faraspossible,
on an extensive scale, in order that exact deductions may be made from the
observations taken, leaving on one side accidental influences, which often so
complicate the phenomenon observed that it seems to be at first sight out of
all rule and subject to no definite laws.
Thus, for example, in order make clear the two kinds of currents in the
fluvial bed we have said that a part of the section is occupied by converging
and the other part by bottom or divergent water-threads. In reality, however,
it may happen that a convergence appears at several places and a divergence
may exist not only at two points, but at many points of a section.
In order to discover the causes of these complications we must examine
them with exactitude and in detail by means of repeated measurements at
points near to one another and on several adjacent transverse sections of
the bed.
For the execution of such examinations the writer of the present report has
projected two submarine fanes, one of wich is complete, and is found to be
quite suitable for its purpose. Designs of it are attached (See Plates VI, VII,
and VIII). It is composed of two steel arms A A, perpendicular to each
other, fixed across a steel rod P, which moves vertically, as well as horizon-
tally. To equalise the wings of the fane a leaden weight 15’ in the form of a
cone is placed at the other extremity of the rod.
38
A brass tube T serves as axis for the horizontal movement, with a conical
steel stop D at its lower end. The axis for the vertical movement passes
through the diameter E of this tube. The inner axis of the rests in a suppor-
ting steel socket S, fixed inside a brase ring Z. The ring Z ' screwed into
the lower end of the iron tube U, which serves as base for all the apparatus.
The brass tube passes through the centre of this supporting tube, so that the
geometrical axes of both agree. To the upper part of the principal tube, as
also to its lower part a bronze arch I is screwed at the upper extremity of
which is a steel screw with ‘a point and K supporting the upper part of
the middle tube.
Such a submarine fane gives the movement of a water-thread in horizontal
as well as in vertical diretions. The needle A shows the horizontal deviation.
This needle is fixed to the centre tube and to the index ./I! on the principal
tube. The water-thread having turned the wing of the the fane to the right
or to the left, turns the middle tube and consequently the needle, which
shows on the index the extent of the angle of deviation of the thread. By
means of the rod H and the index 0, the needle indicates the vertical
deviations of the threads. Both of these parts of the apparatus are fixed
on the middele tube; the needle moves on the axis and the index is immo-
vable. The vertical movements of the fane are transmitted to the needle by
two brass wires N N of equal length running parallel to one another from
the bend -of the rod of the fane to the needle. The correction and extension
of the brass wires is effected by means of screw-couplings P P.
‘For placing the fane at the desired depth the principal tube is marked out
in centimeters in colours.
To set the apparatus according to the profile designated by the indicators
on the bank pinules C are used attached to the side of the upper part,
and for placing it vertically a level G is employed which is fixed on a
horizontal index.
The entire length of the apparatus is about 6 m., so that it can be placed
in the water to a depth of 5 m.
For placing the fane we take a support with three legs which carries a
rectangular frame of hollow iron tubes, and is made of oak or other heavy,
solid wood. The supporting table has iron plates at its sides, with projecting
ends which serve as holes for the feet. The feet are coated at the sides on
all their length with iron and are fixed in the holes by means of compressing
screws 22 22 a. To prevent the feet sinking in the soft ground small iron cups
.5‘ SS are fixed at their extremities. These cups resting on their sharp edges
prevent the supports from slipping on stony soil. In order that the supports
may not separate from each other more than is desirable they are joined at
about half their height by ropes fibé. The ends of these ropes are free, so
that when the apparatus is placed in the water they may be pulled or slacke-
ned as required for the alteration of the position of the feet.
The frame by means of which the fane is let down is fixed on the upper
89
part of the support by means of a double hinge r so that it can move freely.
On the principal frame a small frame 2’ moves up and down on rollers. This
small frame has two cramp-irons e 2. A similar cramp-irion is placed on the
upper part of the principal frame g. The tube of the fane is placed in these
three cramp-irons. To keep the tube in a vertical position three tin cords
zzz issue from the lower part of the frame, each of which passes over the
pullies 22 at the end of the supporting feet, passing thence upwards along the
foot towards the winders and ratchet-wheels 222'. By winding up or unwin-
ding these three cords the fane is kept in a vertical position.
For raising and for letting down the fane a cord 12 is used issuing from
the frame 21’, which turns with the apparatus. The card passes over the pulley
A which is fixed to the upper part of the large frame to the winder /2’.
For observations to be made in one single place at different depths it is
not necessary to rearrange the pinules each time an observation be taken, as
the tube of the fane can be fixed to the cramping-irons 22 by the screws 22 22
at the commencement of the observations.
In order to give greater wheight to the apparatus, with the view of obtai-
ning greater fixety, a cylindrical iron reservoir 2 is suspended by a pulley in
the middle of the upper plate and underneath it. This reservoir can be filled
with water and emplied by means of an opening and a valve.
For the transport and fixing of the fane and the supports two boats are
required, fitted with scaffolding as seen on the sketch. Scaffolding of 3.5 m.
in height is sufficient to lift the supports out of the water. The lifting and
lowering is effected by means of a small windlass or capstan placed on the
bridge at the after part of the boat. Moveable platforms at each side of the
apparatus serve as standing places for the observers and are so elevated as
to be always near the upper end of the tube and in view of the indices,
The same windlass or capstan which works the apparatus also raises the
platforms. For this purpose are attached to the principal cable at point .5’
two side cables, which travel together over a fixed pulley T with three
wheels, placed at the top of the scaffold, thence under the pulleys D D,
over the pulleys E E and then descend to the platform.
For lifting and laying out the anchors a small boat is required. The
arrangement of the boats is shown on the plan.
With the aid of this apparatus measurement was effected in the months of
September and October 1893 of the direction of water-threads on the Dnieper
at jekaterinoslaw.
The results of these observations are embodied in a special report.

Inscriptions les Plancles.
PLANCHE I.
Les courants divergent.
,, ,, convergent.
PLANCHEIH.
Vert.
Jaune.
Rose.
Rouge.
Facade.
Profils longitudiuaux.
Monille.
Bane de sable.
A un niveau élevé de printernps.
A un has niveau de printemps.
A un niveau élevé d’été.
Au niveau d’étiage.
A un niveau bas.
Au niveau d’eau le plus bas.
PLANOHE III.
Embouchure du bras . . . .
Embouchure du golfe et an prin-
ternps du torrent Starik.
Digue conductrice des fils d’eau.
Cnlée fluviale.
,, du bord.
Quai.
Culée riveraine.
Les inscriptions sur les profils des
plans . . . désignent le nombre
de minutes écoulées du départ
des flotteurs du premier profil.
Les inscriptions sur les profils des
vitesses désignent la vitesse en
sagenes en une seconde.
Signes conventionnels.
Lnnrnvsm.
Inchriften IIBI‘ Zeichnmnen.
BLATT I.
Die Stromungen laufen auseinander.
,, ,, ,, zusammen.
'BLATTiL
Griin.
Gelb.
Rosa.
Roth.
Aufriss.
Langsprofile.
Tiefes VVasser.
Sandbank.
Bei hohem Friilijahrswasser.
,, niedrigem ,,
ho hem Sommerwasser.
niedrigstem ,,
VVasserstande.
dem niedrigsten ,,
BLATT III.
Miindung des Armes.
llliindung des Golfes und im Friih-
ling des 'Wildstromes Starik.
Leitditmme fiir die Striimung.
Flusspfeiler.
Landpfeiler.
Uferdamm.
Landpfeiler.
Die Inschriften auf den Profilen
. geben die Anzahl
welche seit
niedrigem
der Plane . .
der Minuten
Abgang der Schwimmer des ersten
Profiles verstrichen sind.
Die Inschriften auf den Geschwin-
digkeitsprofilen geben die Ge-
schwindigkeit in Saschenen per
Sekunde an.
an,
Zeichenerklarung.
llesniptlun of the Plates.
\\\\\ \'\
PLATE I.
The currents diverge.
,, ,, converge.
PLATE II.
Green.
Yellow.
Rose.
Red.
Elevation.
Longitudinal sections.
Deep water.
Sand-bank.
High spring level.
77 I‘)
High summer ,,
Low-water level.
At a low level.
At lowest level.
PL ATE III.
Mouth of the branch stream . . . .
Mouth of the gulf and rapids of
Starik in spring.
Dike regulating the current.
Abutment in the river.
,, on shore.
Wh&1‘f.
Abutment on the bank.
The references in the sections of
the projections. . . . indicate the
number of minutes spent from
the departure of the floats of the
first section.
The sections
showing the speed indicate the
references on the
speed in sa_q2‘:ncs per second.
Conventional signs.
2
PLANCHE IV.
Plan de disposition des ondes sur
le Dniépre à. Kief dressé selon
les recherches faites en Avril
1892, a un niveau + 1,09 Sagène
de la tringle de Phydromètre du
pont suspendu.
Profils des vitesses.
Limite naturelle de Natalka.
Voies des flotteurs.
Crue de Peau au niveau du prin-
temps.
Démarcation a un niveau bas.
Crête du bord.
Direction de la rotation des flot-
teurs, les chiffres marquent le
nombre de tours entre les deux
profils voisins.
Travaux couverts d’eau.
Flotteur au diamètre de . . .
Les chiffres
vitesses marquent la vitesse des
sur les profils des
flotteurs en sagènes en une se-
conde.
PLANCHE V.
Plan de la direction des fils d’eau
et profils de la direction des
flotteurs a Pexpiration d’in.ter-
valles de temps égaux.
Les chiffres sur les profils de direc-
tion des flotteurs marquent les
minutes écoulées depuis le départ
à. partir du premier.
(Pour les autres inscriptions, voir
les traductions „ Planche IV”.)
PLANCHE VI.
Dessin de la girouette sous-marine,
1/2 de la grandeur naturelle.
Section de Pextrémité du tuyau
par l’axe.
Vue de la partie postérieure.
(loupe par la ligne (4-1).
BLATT IV.
Darstellung der Wellenbewegung
auf dem Dnjepr bei Kiew, auf-
genommen nach im April 1892
bei einem Wasserstande
+ 1,09 Saschene
meter der Hängebrücke ange-
stellten Beobachtungen.
Geschwindigkeitsprofile.
Natürliche Grenze von Natalka.
Weg der Schwimmer.
VOIl
am Hydro-
Hochwasser im Fruhjahr.
Begrenzung bei niedrigem Wasser-
stande
Uferkamm.
Richtung der Drehung der Schwim-
mer, die Zifiern geben die Anzahl
der Umdrehungen zwischen zwei
benachbarten Profilen an.
Kunstbauten unter Wasser.
Schwimmer mit einem Durchmesser
von . . . .
Die Zahlen auf den Geschwindig-
keitsprofilen geben die Geschwin-
digkeit der Schwimmer in Sa-
schenen per Sekunde an.
BLATT V.
Richtung der Strömung und Pro-
file der Richtung der Schwimmer
nach Verlauf gleichmässiger Zeit-
intervallen.
Die Ziffern auf den Profilen der
Richtung der Schwimmer geben
die Anzahl der
welche seit Abgang des ersten
Minuten an ‚
verflossen sind.
(Die übrigen Inschriften
Uebersetzung zu Blatt IV.)
siehe
BLATT VI.
Zeichnung des Strömungsanzeigers
% der natürlichen Grosse
Querschnitt des aussersten Röhrenen-
des durch die Achse.
Ansicht des hinteren Theiles.
Schnitt in der Linie n—-b.
PLATE IV.
Projection of the state of the waves
on the Dnieper at Kiev drawn
up from investigations made in
April 1892, at a level of 1.09
sagéne above the rod of the hy-
drometer of the suspension bridge.
Sections showing the speed.
Natural limit of Natalka.
Ways taken by the floats.
Water-level during spring floods.
Limit at a low level.
Top of the bank.
Direction taken by the floats in
rotation, the figures indicate the
number of turns between the two
neighbouring sections.
VVorks under water.
Float of a diameter of . . . .
The figures on the sections showing
the speed mark the speed of the
floats in saqünes per second.
PLATE V.
Projection of the direction of the
current and sections of the direc-
tion taken by the floats at regular
intervals.
The figures on the sections showing
the direction taken by the floats
mark the minutes that elapse
after the departure of the first.
(For other references see transla-
tions under Plate IV.)
PLATE VI.
Sketch of the submarine vane, half
actual size.
Section of the extremity of the
tube made by the bed of the river.
Vue of the back.
Section at the line a-b.
PLANCHE VII.
Elévation de cote.
Vue de devant.
Dessin du support de la girouette
sous-marine.
Section du pied de support. _
Elévation de cote, 1/12 de la grandeur
naturelle.
PLANOH E VIII.
Dessin concernant le projet de la
girouette sous-marine.
Chaland et structure pour le trans-
port et le posage de la girouette
sous-marine.
Plan schématique du posage du
chaland par rapport an jalon.
Pin.
Chéne.
Fer.
Fonte.
Vue de devantj
Inscriptions souoent répétées.
Bras.
Dessin.
Pile.
Mesures.
1 sagene : 2,13 111. : 3 arsjines.
1 arsjine : 0,71 m. T. 16 verchoes.
1 verchoc : 0.0444 m.
3
BLATT VII.
Seitenansicht.
Vorderansioht.
Zeichnung des Stéinders des Strt5—
mungsauzeigers.
Querschnitt des Stiinderfilsses.
Seitenansicht 1/12 der natiirlichen
Grtisse.
BLATT VIII.
Zeichnung das Project eines Str6—
mungsanzeigers hetretfend.
Schute nebst Vorrichtung
Transport und zur Aufstellung
des Stromungsanzeigers.
Skizze der Aufstellung der Schuten
mit Hinsicht auf die Bake.
Tannenholz.
Eichenholz.
Eisen.
Zl1II1
Gusseisen.
Vorderansioht.
H1'i:.r/ig wiederholle A2(sd’r1'lc/ce.
Arm (eines Flusses).
Zeichnung.
Pfeiler.
M aasse.
1 Sasehenc: 2,13 m.: 3 Arschinen.
1 Arschine :0,71 ,, : 16 Werschok.
1 VVerschok :: 0,0444 n1.

PLATE VII.
Elevation of the side.
Front view.
Sketch of the support of the sub‘
marine fane.
Section of the foot of the support.
Elevation of the side 1/12 actual size.
PLATE VIII.
Sketch relating to the project of
the submarine fane.
Barge and arrangement for the
transport and fixing in posi-
tion of the submarine fane.
Projection of the scheme for the
fixing in position of the stake.
Pine.
Oak.
Iron.
Cast-iron. '
W ords f)"e(~/21011 ily repeated.
Branch.
Sketch.
Pile, pier.
11/Jeasmws.
1 sagene : 2.13 m. :: 3 arsjines.
1 arsjine : 0.71 m. :: 16 verchocs.
1 vercl1oc_ : 0.0444 111.


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PLANS DE LA DISPOSITION DES FILS D'EAU
profils des vitesses et positions des flotteurs?! Pexpiratlon des Intervalles de tumps égaux de leur flottement depuis le 10" profil sur le Dnlépre près du pont suspendu Nicolas
N 3 I (L , . N°11 dressés suivant les recherches fnîtes en aÿvril et mai 188G ù un horizon + 1,45 et + 0,93 selon la tringle ,du pont suspendu. 9 I 6
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___.______ 2 minutes. ._ ,._ 10 minutes Prqfik de la poxilion de: flotlmr: pour les plan: 50 m.. sur 0,01 m. sagènzs
~ Les inscnptzbns sur 1:: profils des vitesses dlsignmt 1a vitase en sagènzs en um semnde 4 I2 » à I’ ex;tiratz'an-
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..,_‘._.._.._. ô _______ marche dt: flatteurs. Q‘?/FLQ/£’£§’/O . ht-O-H-‘în ï '. : : Ê - g _ g J; j? 47"‘) "'
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Plan de la dlsposltlon des ondes
sur le’ Dniépre à Kjef.
dressé selon les recherches faites en avril 1892, à un niveau + 1.09
sagène de la tringle de Phydromètre du pont suspendu.
êcûeaz au pïan
100 m. par 0.01 m.
:00 100 0 200 400 000 m‘
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voies des flotteurs‘.
crue‘ de l'eau au niveau du primtemps + 1,00 sagènes.

Dtmarmtion à un niveau [ms de - 0,80 sagéne.
(rite du âord.
Direction de la rotation des flotteurs et les r/qfres marquent
le nombre de tours entre les deux profil: voisiru.
jbrafils des vitesses.
_ _-_ tmz/aux rmaurt: d ‘eau.
œ c’ flatteur au diamètre de (v zinc/tors.
Q O jiotteurs au diamètre de I arc/u'ne é’ vert/tors.




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—‘:] Crue [2 un m'2/eau + 1,14 sagénen.

0? _/iotteur diamc'trv 6 wrc/was.
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Piancizc N“. VI.
Dessin de la girouette sous-marine
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