We present here rigorous analytical solutions for the Boltzmann-Poisson equation concerning the distribution of stars above the galactic plane. The number density of stars is considered to follow a behaviour n(m,0) ∼H(m - m₀)m^−x, wherem is the mass of a star andx an arbitrary exponent greater than 2 and also the velocity dispersion of the stars is assumed to behave as < v²(m)> ∼ m^−θ the exponent θ being arbitrary and positive. It is shown that an analytic expression can be found for the gravitational field K_z, in terms of confluent hypergeometric functions, the limiting trends being K_z∼z for z →0, while K_z→ constant for z → infinity. We also study the behaviour of < |z(m)|²>,i.e. the dispersion of the distance from the galactic disc for the stars of massm. It is seen that the quantity < |z(m)|²>∼ m^t-θ, for m→ þ, while it departs significantly from this harmonic oscillator behaviour for stars of lighter masses. It is suggested that observation of < |z(m)|²> can be used as a probe to findx and hence obtain information about the mass spectrum.

The on-going Parkes multibeam survey has been astoundingly successful (Manchesteret al. 2001), and its discovery of over 600 pulsars has opened up new avenues for probing the Galaxy’s electron content and magnetic field. Here we report on recent observations made with the Arecibo 305-m telescope, where 80 distant, high dispersion measure pulsars (of which 35 are from the multibeam survey) were studied at multiple frequency bands in the range 0.4–2.4 GHz, in order to determine their scattering properties, rotation measures and spectral indices. The results will be used to meet a variety of science goals; viz., creating an improved model of the electron density, mapping out the Galactic magnetic field, and modeling the pulsar population.