We present a study of the small-scale structure of the interstellar medium in the Milky Way .
We used HST STIS data to measure N ( H i ) in a pencil-beam toward 59 AGNs and compared the results with the values seen at 9′–36′ resolution in the same directions using radio telescopes ( GBT , Green Bank 140-ft and LAB survey ) .
The distribution of ratios N ( Ly \alpha ) / N ( H i ) has an average of 1 and a dispersion of about 10 % .
Our analysis also revealed that spectra from the Leiden-Argentina-Bonn ( LAB ) all-sky H i survey need to be corrected , taking out a broad gaussian component ( peak brightness temperature 0.048 K , FWHM 167 km s ^ { -1 } , and central velocity - 22 km s ^ { -1 } ) .
The column density ratios have a distribution showing similarities to simple descriptions of hierarchical structure in the neutral ISM , as well as to a more sophisticated 3D MHD simulation .
From the comparison with such models , we find that the sonic Mach number of the local ISM should lie between 0.6 and 0.9 .
However , none of the models yet matches the observed distribution in all details , but with many more sightlines ( as will be provided by COS ) our approach can be used to constrain the properties of interstellar turbulence .