Using Active Magnetospheric Particle Tracer Explorers/Ion Release Modu
le data from 10 magnetosheath crossings in the 11-13 LT sector, we hav
e investigated the behavior of the proton temperature and the proton t
emperature anisotropy between the bow shock and the magnetopause. The
proton anisotropy increases toward the magnetopause. Comparison with e
arlier predictions, however, shows that this increase is much more mod
est than was predicted by assuming the double adiabatic equations. It
is shown that neither of the two double-adiabatic equations holds sepa
rately. We conclude that energy is transferred between the perpendicul
ar and the parallel component of the proton temperature. It is well es
tablished that instabilities such as the mirror and the ion-cyclotron
instability show such a behavior and lead to a decrease in the tempera
ture anisotropy. Our data show that in the magnetosheath proper, the t
hreshold for the onset of the mirror instability is always marginally
met. We show that we can give an empirical relation between the temper
ature anisotropy and beta(perpendicular to), as long as beta(perpendic
ular to) is not less than 1.