With = 0,91 (Hydrogen)
and **v** = frequency

Then, We inserted it, in a software buckle containing
the 2eme law of Descartes. The difficulty of the simulation is essentially
due to the few of mathematical processor precision in the PCs. (Trigonometric
tables, and numerical computations where, at this time, 32 bits limited.
it is therefore better to achieve them with our own programs). besides
don't forget the rounded of calculations. In final here is the result in
the case of a sphere of gas of about hundred years light with a density
varying from

** ****10**^{-20} g/cm^{3}
to** 10**^{-10} g/cm^{3}.

The utilized growth law is in **x²**. Alone the central part is
represented here. Also notice that the simulation shows that the optical
frequency has a negligible role in densities of matter placed in game.

Not to hide anything, when I undertook this work, no
one believed there, me either.

**Conclusion**

If in the universe phenomena of refractivity are so,
possible in a gas bubble with g**radient of density of matter and with
refractive indice**, then, well evidently, it is strictly useless to
invoke, for every case of lens, some and solely gravitational lens.
However, the two phenomena are not certainly exclusive one of the other.
And, in this case they are accomplice and cumulative !