In the report he submitted to the Acad\'emie des Sciences, Poisson imagined a
set of concentric spheres at the origin of the Earth's magnetic field. It may
come as a surprise to many that Poisson as well as Gauss both considered the
magnetic field to be constant. We propose in this study to test this surprising
assertion for the first time evoked by Poisson (1826). First, we will present a
development of Maxwell's equations in the framework of a static electric field
and a static magnetic field in order to draw the necessary consequences for the
Poisson hypothesis. In a second step, we will see if the observations can be in
agreement with Poisson (1826). To do so, we have chosen to compare 1) the polar
motion drift and the secular variation of the Earth's magnetic field, 2) the
seasonal pseudo-cycles of day length together with those of the sea level
recorded by different tide gauges around the globe and those of the Earth's
magnetic field recorded in different magnetic observatories. We then propose a
mechanism, in the spirit of Poisson, to explain the presence of the 11-year in
the magnetic field. We test this mechanism with observations and finally we
study closely the evolution of the g10 coefficient of the IGFR over time