The sole in-situ measurement of a giant planet atmosphere comes from the Galileo probe, which plunged through Jupiter's weather layer at 6.5 degrees N and measured a remarkably stable atmospheric temperature profile. Horizontal winds were observed to substantially increase from 1 to 3 bars, in a region of relatively low static stability. Using geostrophic coordinates developed for terrestrial frontogenesis, we generalize an expression to determine lapse rates along constant angular momentum surfaces for deep atmospheres at any latitude. We show that this high shear region indicates the best possibility of slantwise convection, and suggest that the fluid here is likely adiabatic, in spite of the observed static stability.