Radzievskii,V.V.
and Kagalnikova, I.I. Bull. Vsesoyuz. Astronomo. Geol. Obshchestva.

(Moscow) __26__,
3 (1960)

Translation
in U.S. Govt. tech. report FTD-TT-64-323/1+2+4 (AD-601762)

**THE NATURE OF
GRAVITATION**

**V.** **V.** **Radziyevskiy** **and** **I.** **I.** **Kagal'nikova**

__Introduction__

The discovery of the
law of universal gravitation did not

immediately
attract the attention of researchers to the question

of the physical
nature of gravitation. Not until the
middle of

the 18th century did M. V. Lomonosov (1) and several years later,

Lesage [2, 3]*,* make the first attempts to interpret the phenome-

non of gravitation on the basis of the hypothesis of
"attraction"

of one body to another by means of
"ultracosmic" corpuscles.

The hypothesis of Lomonosov and Lesage, thanks to its great

simplicity and physical clarity quickly attracted the general

attention of naturalists and during the next 150 years served as

a theme for violent polemics. It
gave rise to an enormous number

of publications, among which the most interesting are
the works

of Laplace [4], Secchi (5), Leray (6), V. Thomson (7), Schramm (8),

Tait (9), lsenkrahe (10), Preston (11, 12), Jarolimek (13), Waachy

(14)* ,* Rysanek (15), Lorentz (16), D.
Thomson (cited in (17),

Darwin (18), H. Poincare {19, 20), Majorana (21-25), and

-1-

Sulaiman (26, 27).

** **In the course of these polemics, numerous authors proposed

various modificatlons to
the theory of Lomonosov and Lesage.

However, careful
examination of each of these invariably led to

conclusions which were
incompatible with one or another concept

of classical physics. For this reason, and also as a result of

the successful elaboration
of the general theory of relativity,

interest In the
Lomonosov-Lesage hypothesis declined sharply at

the beginning of the 20th
century and evidently it would have

been doomed to complete
oblivion, if in 1919-1922 the Italian

scientist Majorana had not
published the results of his highly

interesting
experiments. In a series of extremely
carefully

prepared experiments,
Majorana discovered the phenomenon of

gravitational absorption
by massive screens placed between inter-

acting bodies, a
phenomenon which is easily interpreted within

the framework of classical
concepts of the mechanism of gravita-

tion, but theretofore did
not have an explanation from the point

of view of the general
theory of relativity.

The famous experimenter,
Michelson (28), became interested

in the experiments of
Majorana. However, his intention to

duplicate these
experiments faded, evidently as a result of the

critical article of Russel
(29), in which it was shown that if

the Majorana's
gravitational absorption really did exist, then the

intensity of ocean tides
on two diametrically opposite points on

the earth would differ
almost 400 fold. On the basis of this

calculation of Russel,
Majorana's experimental results were taken

to be groundless in spite
of the fact that the experimental and

technical aspect did not
arouse any concrete objections.

-2-

In acquainting ourselves with the whole
complex of pre-

relativity
ideas about the nature of gravitation, we were compelled

to
think of the possibility of a synthesis of the numerous classical

hypothesis,
such that each of the inherent, isolated, internal con-

tradictions
or disagreements with experimental data might be suc-

cessfully
explained. The exposition of this
"synthesis." i.e.,

unified
and modernized classical hypothesis of
gravitation created

primarily from the work of
the authors cited above and supplemented

only to a minimum degree
by our own deliberations, is the main

problem of this work. The other motive which has impelled us to

write this article is that
we have discovered the above mentioned

objections of Russel
against Majorana's experimental results to

be untenable; from the point of view of the classical
gravitation

hypothesis no differential
effect in the ocean tides need be

observed. Therefore we must again emphasize that
Majorana's experi-

mental results deserve the
closest attention and study. It seems

to us that duplication of
Majorana's experiments and organization

of a series of other
experiments which shed light on the existence

of gravitation absorption
are some of the most urgent problems of

contemporary physics. Positive results of detailed experiments

could Introduce
substantial corrections into even the general

theory of relativity
concerning the question of gravitation absorp-

tion within the framework
of this theory, while still remaining

a blank spot.

Evidently a strict interpretation of the Majorana phenomenon

la possible only from the
position of a quantum-relativistic theory

of gravitation. However, insofar as this theory is still
only

being conceived it seems
appropriate, as a first approximation, to

-3-

examine an interpretation of this problem on the
basis of the

"synthetic hypothesis"
presented below, especially as the last

includes the known
attempts at a theory of quantum gravitation.

We shall begin with a
short exposition of the history of the

question.

1. Discussion of the Lomonosov-Lesage hypothesis

According to the
Lomonosov-Lesage hypothesis, outer space is

filled with
"ultracosmic" particles which move with tremendous

speed and can almost
freely penetrate matter. The latter
only

slightly impedes the
momentum of the particles In proportion to

the magnitude of the
penetrating momentum, the density of the

matter, and the path
length of the particle within the body.

Thanks to spatial isotropy
in the distribution and motion of

ultracosmic particles, the
cumulative momentum which is absorbed

by an isolated body is
equal to zero and the body experiences only

a state of
compression. In the presence of two
bodies (A and B)

the stream of
particles from body B, impinging on body A, is

attenuated by absorption
within body B. Therefore, the surplus

of the flux striking body
A from the outer side drives the latter

toward body B.

In connection with the Lomonosov-Lesage hypothesis, the

question of the mechanism
of momentum absorption immediately

arises. Generally speaking the following variants
are possible:

1. The overwhelming
majority of particles pass through

matter without loss of
momentum, and an insignificant part are

either completely absorbed
by the matter or undergo elastic

reflection (Schramm (8)). Evidently, in the first
case constant

"scooping"
of ultracosmic particles by matter must take place,

-4-

leading to secular decrease in the gravitation
constant. In

addition, as it is
easy to show, in this case an inadmissable

rapid increment of
the body's mass must occur. If the speed of the

ultracosmic particles
is close to that of light. In the
second

case as Waschy (14)
showed, the reflected particles must compensate

for
the anisotropy in the motion of the particles, which was

created by the
interacting bodies. In other words, the
driving

of the bodies in this
caae would be completely compensated for by

the repulsion of the
reflected particles and no gravitation would

result.

2. All particles passing through matter
experience something

like friction, as a
result of which they lose part of their

momentum owing to a
decrease in speed (Lesage (2, 3), Leray (6),

Darwin [18], and
others). Evidently in this case there
would also

be a gradual
weakening of the gravitational interaction of the

bodies (lsenkrahe
(10)).

A way out from the
described difficulty was made possible by

the proposal of
Thomasin (cited in (19, 17)), D. Thomson (cited in

(17)),
Lorentz (15), Brush (30), Klutz (31), Poincare (19, 20),

and others, for a new
modification of the Lomonosov-Lesage hypothe-

sis, according to
which the ultracosmic particles are replaced by

extremely hard and
penetrating electromagnetic wave radiation.

If in this case we
assume that matter is capable of absorbing only

primary radiation and
radiates secondary radiation, which still

posesses great penetrating
power, then the Waschy effect (repulsion

of secondary
radiation) may be eliminated.*

_______________________________

*
However, in order that a secular
decrease in the gravitation

constant does not occur It
is necessary to suppose that the quanta

of secondary radiation,
after being radiated, decompose to primary

radiation and, as a
consequence, at some distance, depending on the

duration of their lives,
the gravitational interaction between bodies

approaches zero.

-5-

The next question which
arises in connection with the Lomonosv-

Lesage hypothesis concerns
the fate of the energy which is absorbed

by the body along
with the momentum of the gravitational field.
As

Maxwell (32) and
Poincare (19, 20) have shown, if we attribute to

gravity a speed not
less than the speed of light, then in order to

ensure the
gravitational force observed in nature it is necessary

to
accept that momentum is absorbed which is equal to an amount of

energy that can
transform all material into vapor in one second.

However,
these ideas lose their force when the ideas of Thomasin,

G. Thomson,
and Lorentz are considered,
according to which the

absorbed energy is
not transformed into heat, but is reradiated as

secondary radiation
according to laws which are distinct from the

laws of thermal
radiation.

There was still one
group of very ticklish questions connected

with the astronomical
consequences of the Lomonosov-Lesage hypothe-

sis. As Laplace has shown [4], the propagation of
gravitation with

a finite speed must
cause gravitational aberration, giving rise to

so many significant
disturbances in the motion of heavenly bodies

that
it would be possible to miss them only if the propagation

velocity of
gravitation exceeded the velocity of light by at least

several million times.

Poincare (20)
directed attention to the fact that the motion

of
even an isolated body must experience very significant braking

as a result first of
the Doppler effect (head-on gravitons become

harder
and consequently have more momentum than ones which are

being
overtaken) and second, the mass being absorbed sets the body

In motion and a part
of the body's own motion is communicated to

the mass. So
that this braking not be detected by observation, it

-6-

is necessary to assume that the speed of gravitational
radiation

exceeds the speed of light by 18 orders. This idea of
Poincare

is considered to be one of
the strongest arguments against the
Lomonosov-Lesage hypothesis.

Not too long ago a modification to the Lomonosov-Lesage

hypothesis was suggested
by the Indian academician Sulaiman.

According to this
hypothesis, an isolated body A radiates

gravitons in all possible
directions isotropically, experiencing

a resultant force equal to
zero. The presence of a second body B

slows the process of
graviton radiation by body A more strongly,

the smaller the distance
between the bodies. Therefore the
quanti-

ty of gravitons being
radiated from the side of body A facing

body B will be less than
from the opposite side. This gives rise

to a resultant force which
is different from zero and tends to

bring body A and body B
together.

Further, Sulaiman
postulated invariability of the graviton

momentum with respect to a
certain absolute frame of reference.

Here the moving body must
experience not braking, but rather accel-

eration coinciding with
the direction of speed and being compensated

by the braking influence
of the medium.

Sulaiman's hypothesis is very interesting. Unfortunately, it

does not examine the
question of decreasing mass of the radiating

bodies or the question of
the fate of the radiated gravitons.

As can easily be shown by elementary calculation, so that the

impulse being radiated by
the body can secure the observed force

of interaction between
them, it is necessary that they lose their

mass with an unacceptably
great speed. It is completely clear
that

no combination of longitudinal and transverse masses
can save the

-7-

thesis. There is a well-defined relationship between
the relativ-

istic expressions of the momentum and the energy (33), and it is

impossible to imagine that a body radiating energy E (i.e., mass

*E/c*^{2}*)* could with this momentum radiate more than E/c.

If we suppose that the radiation of the mass is compensated

by the corresponding reverse process of graviton absorption, then

we return to a more natural elementary variant of the Lomonosov-

Lesage hypothesis. Graviton
absorption and the screening effect

which is inescapably linked with it guarantee a gravitational

attraction force without the additional concept of anisotropic

graviton radiation by one body in the presence of another.

2. Majorana's experiment,
Russel's criticism.

Majorana did not insist in his investigations on a concrete

physical interpretation of the law of gravitation. He simply

started from the supposition that if there is a material screen

between two interacting material points A and B, the force of their

attraction is weakened by gravitational absorption of this screen

[21, 22, 25). As in the
Lomonosov-Lesage hypothesis, Majorana

took attenuation of the gravitational flux to be proportional to

the value of the stream itself, the true density of the substance

being penetrated by it, and the path length through the substance.

The proportionality factor __h__ in this relationship is known as the

absorption coefficient. It is
evident that with the above indi-

cated supposition the relationship of the gravitational flux value

to the path length must be expressed by an exponential law.

Let us imagine a
material point which is interacting with an

extended body. Since any element of this body's mass will
be

attracted to the
material point with a force attenuated by screening

-8-

of that part of the body
which is situated between its given

element and the
material point, on the whole the heavy mass of

this body will
diminish in comparison with its true or inert mass.

In his work (21),
Majorana introduced a formula for the

relationship between the
heavy (apparent) mass M and the inert

(true)
mass M_{u} of a spherical body of radius R and a constant

true density d_{u}

M_{α }= ΨM* _{ν}*
=

where u = hδ* _{ν}*R.

Expanding (1) into a
series, it is easy to see that when

U →0, M_{α}→ M* _{ν}*, and when u→¥,
M

h __<__
πR^{2}/ M_{α}_{
}(2)

Applying the result
of (2) in the case of the sun, which is a

body with the most
reliably determined apparent weight, Majorana

obtained

h __<__ 7,65 •^{ }10^{-12} CGS. (3)

To experimentally
determine the absorption coefficient __h__

it is theoretically
sufficient to weigh some "material point" with-

out a screen and then
determine the weight of this "material screen"

after placing it in
the center of a hollow sphere. If in
the first

case we obtain a
value __m__ then in the second case we will register

a decreased value as a
result of gravitational absorption by the

-9-

walls of the hollow sphere

m_{a} =
me^{-h}^{dl}
» m
(1-^{ }hdl), (4)

where d is the density of the material from which the
screening

sphere is made, and __I__
is the thickness of its walls.
Designating

ε as the weight
decrease __m__ - __m___{a}, we easily find that

h = ε/mdl .
(5)

To
determine the absorption coefficient value by formula (5),

Majorana began, in 1919, a
series of carefully arranged experiments,

weighing a lead sphere
(with a mass of 1274 g*)* before and after

screening with a layer of
mercury or lead (a decimeter thick).

After scrupulous consideration of all the corrections it

turned out that, as a
result of screening the weight of the sphere

had decreased in the first
series of experiments by 9.8 • 10^{-7}
g

which yields, according to
(5), h = 6.7 • 10^{-12}. In the
second

series of experiments, h =
2,8 • 10^{-12 }was obtained.

As already mentioned, in 1921 Russel came out with a critical

article devoted to
Majorana's work.

Assuming that the interaction force between two finite bodies

is expressed by the
formula:

F = Gm_{1}ψ_{1}M_{2}
ψ_{2} /r^{2 } (6)

where, in accordance with
expression (1)

-10-

ψ = ¾(1/u – 1/2u^{3}
+ e^{-2u}(1/u + 1/2u^{3}))

and assuming at first that the decrease in weight as a result of

self-screening occurs
while leaving the inert masses unchanged,

Russel obtained on
the basis of (6) the third law of Kepler in the

form

a^{3}_{1}/ a^{3}_{2}
= T^{3}_{1}/ T^{3}_{2} (ψ^{3}_{1}/
ψ^{3}_{2})
(7)

The value
of ψ, calculated by Russel with the absorption

coefficient h = 6,73 •^{ }10^{-12}
found by Majorana for several bodies

of the solar system,
is equal to:

Sun **.** **.** **.** 0.33

Jupiter **.** **.** 0.951

Saturn . **.** 0.978

Earth **.** **.** **.** 0.983

Mars . .
. 0.993

Moon . . .
0.997

Eros . .
. 1.000

From this it follows that the true density of the sun
is not 1.41,

but 4.23 g/cm^{2}**.**

Using the above
tabulated values of ψ and Kepler's law, Russel

showed convincingly
that the corresponding imbalance between the

heavy and inert
masses of the planets would lead to unacceptably

great deflections of their
motions. In order that the deflection

might remain unnoticed, it
would be necessary for the absorption

coefficient __h__
to be 10^{4 }times the value found by Majorana. From

this Russel came to
the undoubtedly true conclusion that if as a

result of
self-screening the weight decrease found by Majorana did

occur, then there
would have to be a simultaneous decrease in their

-11-

inert masses.

Russel made this conclusion the basis of the second part of

his
article which was devoted mainly to investigation of the

question of the
influence of gravitational absorption on the

intensity of lunar
and solar tides. Following Majorana's
ideas,

Russel suggested that
a decrease in attraction and necessarily

also a decrease in
the inert mass of each cubic centimeter of

water In relation to
the sun or noon would occur only if they

were below the
horizon. If this is admitted, then
sharp anomalies

In
the tides must be observed, viz., the tides on the side of the

earth where the
attracting body is located must be less intense

(2
times for lunar tides and 370 times for solar tides) than on

the opposite side of
the earth. In conclusion Russel
contended

that his calculations
demonstrated the absence of any substantial

gravitational
absorption and that consequently Majorana's results

are in need of some
other interpretation, Russel himself,
however,

did
not come to any conclusions in this regard.

While acknowledging
the ideas presented in the first part of

Russel 's work to be
unquestionably right, we must first of all

state that the
self-screening effect and the weight decrease

associated with It cannot
be seen as a phenomenon which is contra-

dictory to the
relativistic principle of equivalence:
any change

in a heavy mass must
be accompanied by a corresponding change in

the inert mass of the
body. But is it possible to agree with
the

results of the second
part of Russel's article, according to which

gravitational
absorption on the scale discovered by Majorana is

contradicted by the
observation data of lunar and solar tides?

Let us remember that
Russel came to this conclusion starting from

-12-

the freshly formed Majorana hypothesis of
gravitational absorption

only under the condition
that the attracting bodies are on dif-

ferent sides of the
screen. Meanwhile, application of the
Lomonosov-

Lesage hypothesis which
painted a physical picture of gravitational

absorption leads, as we will show in the following
section, to

conclusions which are
completely compatible with Majorana's experi-

mental results and with
the concepts set forth in the first part

of Russel's article,
but at the same time, all of the conclusions

about tide anomalies lack
any kind of basis. Skipping ahead some-

what let us say in short
that according to the Lomonosov-Lesage

hypothesis, the weakening
of attraction between two bodies must

occur when a screen
intersects the straight line joining them,

regardless of whether
there are gravitational bodies on various

sides or on one side
of this screen.

3. The "Synthetic" Hypothesis

Let us suppose that outer
space is filled with an isotropic

uniform gravitational
field which we can liken to an electro-

magnetic field of
extremely high frequency. Let us
designate ρ

as the material density of
the field, keeping in mind with this

concept the value of the
inert mass contained in a unit volume of

space. Evidently the density of that part of the
field which is

moving in a chosen direction within the solid angle
dω is ρdω/4π

Under these conditions a mass of

dμ =
dScρdω/4π (8)

carrying a momentum

dp = dSc^{2}ρdω/4π (9)

-13-

will pass through any area element dS in its normal
direction with-

in the solid angle dω
in unit time.

The mass flux (8) will
fill an elementary cone, one cross

section of which serves as
the area element dS. At any distance

from this area element,
let us draw two planes parallel to it

which cut off an
elementary frustrum of height dl, and let us

imagine that the frustrum
is filled with material of density d.

It is evident that the
portion of the flux (8) absorbed by this

material will be

d(dμ) = dμ hd dl (10)

or

d(dμ) = hρc (dω/4π) dm

where dm = d dSdl is the mass of the elementary frustrum.

Let us imagine a "material point" of mass __m__
in the form of a

spherical body of density d and of sufficiently small dimensions

so that it is possible to
neglect the progressive character of

the absorption within
it and to consider that the absorption

proceeds in conformity
with formula (11). Let us divide the
sec-

tion of this spherical
body into a number of area elements and

construct on each of them
an elementary cone with an apex angle dω,

Applying formula (11) to
these cones, and integrating with respect

to the whole mass of the
material point, we obtain

Δ(dμ) = hρc (dω/4π) dm (12)

-14-

Fig. 1.
Diagram for calculation

of mass absorption of the
flux

of a material field.

Formula
(12) determines the value of the absorbed portion of

the field mass which has
passed in unit time through a cone with

an apex angle dω,
which Is circumscribed around a sufficiently

small spherical body of
mass __m__.

To obtain the total rate of increment in the mass of the
point,

it is necessary to take
into consideration absorption of the field

impinging on it from all
possible directions, which is equivalent

to integration (12) over
the whole solid angle ω. This
gives

dm/dt = hρcm. (12’)

Returning to formula (10), Imagine that the field flux inside

the
cone circumscribed around material point __m__,
penetrates the

material
throughout the finite section of the path AB = L (fig. 1)

Integrating (10) from B to A, we obtain
an expression which

determines
the total absorption within the cone AB when δ = const

(dμ)_{1} =
dμe^{-h}^{δL}
(13)

-15-

Let dμ be the mass of the field striking cone AB from side
B,

and
(d μ)_{i} be the mass of the field exiting this
cone and impinging

on body __m__. The decrease in the mass of the flux because
of

absorption
in AB is equivalent to the decrease in its density up

to the value

ρ_{1} = ρe^{-h}^{δL}. (14)

Thus from the left
flux of density ρ (its absorbed portion is

expressed by formula
(12)) strikes material point m and from
the

right, a flux of
density ρ_{1}. The portion
which is absorbed will be

Δ(dμ)_{1 }= hρe^{-h}^{δL} (dω/4π) m. (15)

Calculating (15) and
(12) and multiplying the result by __c__ we

obtain a vector sum
of the momentum absorbed by point __m__ in unit

time equal to the value
of force dF, from which point __m__ is "attrac-

fed"
to cone

dF = hρc^{2}(dω/4π) ( 1 - e^{-h}^{δL}) (16)

It would not be hard to show that with such a force,
cone AB is

"attracted" to point __m__.

point __m__ to a cone of elementary length

d(dF) = h^{2}ρc^{2}(dω/4π)mddL
(17)

As can be seen, force (17) at the assigned values of d, dω, and dL

Depends neither on the distance between point __m__
and the attracting

-16-

elementary frustrum, nor
on the mass of the latter. This result

corresponds
completely to the data of Newton’s theory of gravity

and is explained by the
fact that the mass of the frustrum being

examined is directly
proportional to the square of its distance

from point __m__.

Differentiating (16)
with respect to L, we obtain the value

of the attraction
force of point __m__ to element C of cone AB, which

also does not depend
on the position of this element

d(dF) = h^{2}ρc^{2}(dω/4π)me^{-h}^{δL} ddL
(18)

Comparison of (18) with
(17) shows, however, that element C

attracts point __m__
with a weakened force and the degree of its weak-

ening depends on the
general thickness L of the screening material,

regardless of whether
point __m__ and element C are on different or on

the same side of the
screen. The latter result is
mathematical

evidence of the
groundlessness (within the frame of the Lomonosov-

Lesage hypothesis) of
the critical ideas in the second part of

Russel's article.

Let us now determine
the total attraction force of material

point __m__ to a
spherical homogeneous body of mass M.
Multiplying

the right side of
(16) by cos φ for this purpose
and taking into

account that L = 2 (R^{2}
–r^{2 }sin^{2} φ)^{1/2} and dω = 2 π** **sinφ dφ , we

easily find that

arcsin R/r
_{1/2}

F = hρc^{2}m/2 = ∫_{0} (1
– e ^{–2hδ(}R^{2 –}r^{2 }sin^{2 φ)} )cos φ sin φ dφ =

(h^{2}ρc^{2}/4π) (LmψM/r^{2}), (19)

where

ψ = ¾(1/u – 1/2u^{3} + e^{-2u}(1/u^{2}
+ 1/2u^{3})) (20)

-17-

In which u = hdR.

As has already been noted above, Ψ ≈ 1 whence
follows that

the value

G = h^{2}ρc^{2}/4π (21)

plays the role of a
gravitational constant. The value
ψ which

depends on progressive
gravitation absorption within the body M

must be considered to be
the weight decrease coefficient of the

latter.

In correspondence with the later experinents of Majorana, let

us suppose that the
coefficient of gravitation absorption is

h = 2,8 • 10^{-12 } (22)

Then on the basis of (21) we easily find that

ρ = 1,2 • 10^{-4} g/cm^{3} (23)

Such a relatively high
material density for outer space cannot

meet objections, since the material of the gravitational field can

almost freely penetrate any substance and is noticeable only in

the form of the phenomenon of gravitational interaction of bodies.

Now let us see how this business fares with the Doppler and

aberration effects. It is quite
evident that if the material

behaves like a "black body" i.e., __i__f it absorbs
gravitational

waves
of any frequency equally well, then the Doppler effect will

cause inadmissably intense braking of even an isolated body moving

in
a system, relative to which the total momentum of the gravita-

tional
field is equal to zero. Therefore, we are forced to admit

-18-

that matter absorbs gravitational waves only within a
definite

range of frequencies
Δ*ν* which is much greater than the Doppler

frequency shift
caused by motion, and at the same time substantially

overlaps that region of
the field spectrum adjacent to Δ*v,* whose

intensity may be
considered to be more or less constant.
It is

easy to see that under
these conditions, a moving body will not

experience braking,
just as a selectively absorbing atom moving

in an isotropic field with
a frequency spectrum having a surplus

overlapping the whole
absorption spectrum of the atom, does not

exhibit the
Poynting-Robertson effect.

Actually, in system
Σ which accompanies the atom, the observer

will detect from all sides
absorption of photons of the same

frequency corresponding to
the properties of the atom. From the

point of view of this
observer, the resulting momentum borne by

the photons which are
absorbed by the atom will be equal on the

average to zero. The mass of photons being absorbed in system
Σ

is not set in motion
and therefore does not derive any momentum

from the atom. On the other hand an observer in system S
relative

to which the field is
isotropic, will detect that the moving atom

is overtaken by harder
photons and is met by softer photons.
In

other words it will seem
to him that the atom absorbs a resulting

momentum which differs
from zero and is moving in the direction of

the motion of the atom and
compensates the loss of momentum, which

is connected with the transmission of its absorbed
mass of photons.

In this manner the observer in system S will also fail to

observe either braking or acceleration of the atom's
motion.

As concerns the effect of aberration, according to the apt

remark of Robertson (34),
which is completely applicable to a

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gravitational field, consideration of this phenomenon
is the worst

method of observing the
Doppler effect. Actually an isolated
body

such as the sun is a sink
for the gravitational field being absorbed

and a source for one not
being absorbed. Since we are interested

only in the form, we may
say that In the presence of a body, some-

thing analogous to
distortion of the gravitational field occurs:

at each point of the field
there arises a non-zero resulting

momentum directed towards
the center of the sink. Evidently such

a momentum may collide
with any other body only in a direction

towards this
center. The very fact of motion, as
follows from the

aforementioned
considerations, cannot cause the appearance of a

transversal force component.

Thus it is possible to see that the modernized Lomonosov-

Lesage hypothesis
presented here is not in conflict with a single

one of the empirical facts
which up to now have been discussed In

connection with this
hypothesis. At the same time, of course,
it

is impossible to guarantee
that a more detailed analysis of the

problem will not
subsequently lead to discovery of such conflicts.

The Lomonosov-Lesage hypothesis not only makes it possible to

easily interpret the
Majorana phenomenon, but also in clarifying

the essence of gravity it
opens up perspectives for further inves-

tigations of the internal
structure of matter and for a study of

the possibility of
controlling gravitational forces, and consequent-

ly the energy of the
gravitational field. To illustrate the
power

of the energy, it suffices
to recall that in the Majorana experi-

ments the weight of the
lead sphere, when introduced into the

hollow sphere of mercury,
decreased by 10^{-6} g, which is equivalent

to the liberation of twenty million calories of
gravitational

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energy.

Most recently the authors have become aware of the experiments

of the French engineer
Allais who discovered the phenomenon of

gravitational absorption
by observations of the swinging of a

pendulum during the total
solar eclipse on June 30, 1954. In con-

nection with this we feel
compelled to mention that towards the

end of the 19th century,
the Russian engineer I. 0. Yarkovskiy

(35) was busying
himself with systematic observations of the changes

in the force of gravity,
which resulted in the discovery of diurnal

variations and a sharp
change in the force of gravity during the

total solar eclipse on
August 7, 1887.

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