Vertical profiles of scalar horizontal winds have been measured at high resolution (10m) in the 13 to 37 km region of the stratosphere. This resolution (at that range of altitude) represents the state-of-the-art, and is unique. Our goal was to ascertain whether or not the internal waves of the stratosphere behave consistently with the Garrett-Munk model which was originally created for oceanic internal waves. The power spectral densities (PSD's) of five profiles are presented and it is found that (a) they closely fit a straight line on a log-log graph even to wavelengths as small as 40m, and (b) the average slope is -2.7¿.2 (standard error =0.1. We conclude that (a) stratospheric internal waves obey the Garrett-Munk model for vertical wave numbers, and (b) there is no statistically significant evidence for a break in the curve at high wave numbers when due allowance is made for aliasing effects.