We have used the Arecibo telescope to measure the HI absorption spectra of eight pulsars. We show how kinematic distance measurements depend upon the values of the galactic constants R_o and Theta_o, and we select our preferred current values from the literature. We then derive kinematic distances for the low-latitude pulsars in our sample and electron densities along their lines of sight. We combine these measurements with all others in the inner galactic plane visible from Arecibo to study the electron density in this region. The electron density in the interarm range 48 degrees < l < 70 degrees is [0.017 (-0.007,+0.012) (68% c.l.)] cm^(-3). This is 0.75 (-0.22,+0.49) (68% c.l.) of the value calculated by the Cordes & Lazio (2002) galactic electron density model. The model agrees more closely with electron density measurements toward Arecibo pulsars lying closer to the galactic center, at 30 degrees<l<48 degrees. Our analysis leads to the best current estimate of the distance of the relativistic binary pulsar B1913+16: d=(9.0 +/- 3) kpc. We use the high-latitude pulsars to search for small-scale structure in the interstellar hydrogen observed in absorption over multiple epochs. PSR B0301+19 exhibited significant changes in its absorption spectrum over 22 yr, indicating HI structure on a ~500 AU scale.
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