THE ELECTROGRAVITATIONAL THEORY (EGT)
PART ΙΙ
THE CAVENDISH EXPERIMENT OF THE EGT

REMAINDER OF CONSTANTS G_o, τ_o, k_o, μ_o of the EGT

As discussed earlier, (See Electrogravitational Theory, PART I), constants G_o, τ_o, k_o, μ_o play a fundamental role in the development of this Theory.
To calculate these constants we proceed as follows:
Let us consider (Fig. 1) the apparatus of the Cavendish experiment.
At the two ends Α and Β of the fixed rod ΑΒ = 2a, we place respectively two unequal spheres of radius r₁ and r₂, (r₁ < r₂ ), which are filled with liquid hydrogen.
Similarly, at the ends C and D of the rotating rod CD = 2a, we place respectively two equal spheres of radius r_o which are also filled with liquid hydrogen.

fig. 1

 As it is well known, the rotating rod CD is suspended from a metallic fiber S, while rod ΑΒ is secured in place and is not suspended from metallic fiber S.

Let us assume that:

are respectively the equal masses of the liquid hydrogen, contained in spheres C and D of the rotating rod CD.

Similarly:

are the unequal masses of the liquid hydrogen, contained in spheres Α and Β of the fixed rod ΑΒ, where
We now move the rotating rod CD close to the fixed rod ΑΒ.
In this case, fiber S, twisted, resists and the two rods ΑΒ and CD balance under an angle φ, lying at a distance r from one another.
Therefore:
According to the EGT, force F₁ by which they attract one another, mass found at the end Α of the fixed rod ΑΒ and mass Μu found at the end C of the rotating rod CD is:

Similarly, force F2 by which they attract one another, mass   found at the end B of the fixed rod ΑΒ and mass Mu found at the end D of the rotating rod CD, is:

Yet, because from relations (4) and (5) we have F₁ < F₂ , where f_Α is the material constant of the liquid hydrogen.
As it can be observed, the pair of forces F₁ and F₂, imparts to fiber S a moment Μ, which is:

However, according to what we know:

where D is the directing torque of fiber S and φ is the angle through which fiber S twists, at which the two rods ΑΒ and CD balance.
Therefore, relations (4), (5), (6) and (7), yield:

Moreover, for the rotating rod CD, the following relation applies:

where Τ is the period of oscillation of the rotating rod CD, and Θ is its moment of inertia.

Yet, because

from relations (1) and (10) we obtain:

However, according to the EGT:

Thus, on the basis of relation (12), relation (11) yields:

Also, on the basis of relations (13) and (9), relation (8) yields:

We will call Relation (14) “basic relation of the Cavendish experiment”, according to the EGT.

After everything analyzed above, we proceed as follows: 
We conduct the Cavendish experiment (Fig. 1) in four different phases and in the manner described below:

We keep the equal masses Mu found at the ends C and D of the rotating rod CD secured in place and we vary the unequal masses  and found at the ends Α and Β of the fixed rod ΑΒ.
At the same time, however, we vary in each phase the length a of rods ΑΒ and CD, on the condition that in each phase the two rods ΑΒ and CD have the same length, that is, ΑΒ = CD = 2a_i, where i = 1,2,3,4.

So, one example is the following:

where, a₁ , a₂ , a₃, a₄ are the known lengths of the rods that we selected for each phase respectively.
r₁, r₂, r₃, r₄ are the distances between masses Mu – and Mu – , when the rods ΑΒ and CD balancing under angle Φ₁, Φ₂, Φ₃, Φ₄ in each one of these four phases.
Therefore, for the above four phases, the basic relation (14), yields respectively:

Note: Apparently, because , of the four phases of relations (15) are similar to one another, then their pure masses and will also be similar to one another and thus the above relations (16) are formulated.
As we can observe, in the system of the four equations of relations (16), the unknown dimensions are G₀, τ₀, f_A, M₀.
The rest, i.e. are known and are measured respectively in the above-mentioned four phases during the performance of the experiment.
Consequently, by solving the system of the four equations (16), relative to the unknown G₀, τ₀, f_A, M₀ we find their values.
So, having calculated the values G_o and τ_o, we can easily calculate the value of constant k_o, since as it is known the following relation applies:

By calculating from relation (17) the value of constant k_o, we can easily calculate the value of constant μ_o, since as it is known the following relation applies:

Therefore, after everything explained above, based on the Cavendish experiment we have calculated the values of every constant G₀, τ₀, k_o, μ_o of the EGT.

THE HYDROGEN ATOM

1. As mentioned above, solving the system of equations (16) allowed us also to calculate the material constant f_A of mass Mu of the liquid hydrogen contained in spheres Α, Β, C, D.
Because, however, mass Mu of the liquid hydrogen is an aggregate of hydrogen atoms, this signifies that the material constant f_A calculated in our experiment is equal to the material constant  f_Η of the hydrogen atom, that is:

f_A=f_Η                (19)

because  mass m_u,H of a hydrogen atom and mass Mu of the liquid hydrogen contained in spheres Α, Β, C, D are similar masses and as we know, similar masses have the same material constant.
Therefore, on the basis of the foregoing, we have also calculated the material constant f_Η of the hydrogen atom.

2. Knowing now the material constant f_Η of the hydrogen atom, we can easily calculate the material constant f of every chemical element, for as it is known

where Μ and Ζ are respectively the mass and atomic number of this chemical element.
Therefore, based on relation (20), we know the material constants of all chemical elements in the Periodic table and we can easily represent them graphically.

3. Moreover, when solving the system of relations (16), we also calculated the pure mass Μ_ο of the liquid hydrogen contained in spheres C and D, (of radius r_o) of the rotating rod CD.

Consequently, in 1 cm³ the pure mass m_o of the liquid hydrogen is:

Yet, because number Ν of the liquid hydrogen’s atoms contained in 1 cm³ is known, the pure mass m_ο,H of the hydrogen atom is:

4. Furthermore, because the material constant f_H of the hydrogen atom is known, then from the EGT relation

and on the basis of relation (22), relation (23) yields

Relation (24) gives us the absolute value of the total electric charge of the hydrogen atom.

5. Thus, from relations (22) and (24) we can easily calculate the Newtonian mass m_u,H of the hydrogen atom, which is:

Note: In the Cavendish experiment elaborated above we use the electrogravitational system of units (EGS).

By summing up everything discussed above, we come to the following conclusion:

CONCLUSION

The above described Cavendish experiment (according to the EGT) is of major importance to Physics, since its conduct allows us to easily calculate the following:

1. The values of the fundamental constants of the EGT, which play a basic role in Physics, both in the microcosm and macrocosm.
2. The material constant of the hydrogen atom.
3. The material constant f of all chemical elements.
4. The pure mass m_ο,H of the hydrogen atom.
5. The absolute value of the total electric charge 2q of the hydrogen atom.
6. The Newtonian mass m_u,H of the hydrogen atom.

Finally, with the aid of modern technology, it is certain that the conduct of the Cavendish experiment as described above will yield reliable results that will pave the way for the EGT in modern Physics.

Copyright 2007: Christos A. Tsolkas                           Christos Α. Τsolkas
                                                                                       March 2007

©  Copyright 2001 Tsolkas Christos.  Web design by Wirenet Communications