We present a general experimental method to investigate the relations between the density variations and the pressure variations (parallel and perpendicular to the ambient magnetic field) for one particle population of a hot collisionless plasma. The theoretical aspects of this problem have already been discussed in a recent paper [Belmont and Mazelle, 1992>. The aim of this letter is to provide a complete description of the data analysis technique for an experimental case, from GIOTTO electron and magnetic field data measured in the environment of comet P/Halley, used to verify the theory. The correlations between the electron characteristics, density and pressures (parallel and perpendicular), and the magnetic field strength are investigated. In this case, the method shows that the relations between the electron density and pressures can be satisfactorily represented by two polytropic laws. The values inferred for the polytropic indices strongly differ from those usually found in the literature, but are nevertheless fully quantitatively explained from the theoretical analytical calculations. ¿ American Geophysical Union 1993