Ulysses data in the high-speed solar wind that cover a wide range of l
atitudes centered on the solar poles were studied to test whether a po
lytrope law can be used to close the ion energy equation. Three approa
ches were taken, We determined the correlation between proton temperat
ure and density (1) in the free expansion of the highspeed solar wind
between 1.5 and 4.8 AU, (2) in steepened microstreams at high latitude
s, and (3) at the edges of the equatorial band of solar wind variabili
ty. Strong correlations were observed in all data subsets that are con
sistent with a single polytrope relation, T-p = aN(p)((gamma-1)), whe
re our best estimate gamma is between 1.5 and 1.7. The best fitting r
elation T-p = (2.0 +/- 0.13) x 10(5) N-p(0.57).