  Column densities for H I, Al III, Si IV, C IV, and O VI toward 109 stars and
30 extragalactic objects have been assembled to study the extensions of these
species away from the Galactic plane into the Galactic halo. H I and Al III
mostly trace the warm neutral and warm ionized medium, respectively, while Si
IV, C IV and O VI trace a combination of warm photoionized and collisionally
ionized plasmas. The much larger object sample compared to previous studies
allows us to consider and correct for the effects of the sample bias that has
affected earlier but smaller surveys of the gas distributions. We find Si IV
and C IV have similar exponential scale heights of 3.2(+1.0, -0.6) and
3.6(+1.0, -0.8) kpc. The scale height of O VI is marginally smaller with h =
2.6+/- 0.6 kpc. The transition temperature gas is ~3 times more extended than
the warm ionized medium traced by Al III with h = 0.90(+0.62, -0.33) kpc and
~12 times more extended than the warm neutral medium traced by H I with h =
0.24 +/- 0.06 kpc. There is a factor of 2 decrease in the dispersion of the log
of the column density ratios for transition temperature gas for lines of sight
in the Galactic disk compared to extragalactic lines of sight through the
entire halo. The observations are compared to the predictions of the various
models for the production of the transition temperature gas in the halo. The
appendix presents a revision to the electron scale height proposed by Gaensler
et al. (2008) based on electron dispersion measures.
