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Infinite self-gravitating cylinders with pressure and density related by the equation P = constant p1+11" are considered; the purpose is to find the equilibrium distributions of pressure, density, and gravitational potential. Solutions in closed form are obtained for n = 0 (liquid), n = 1, and n = (isothermal perfect gas). It is proved that for all 0 < n < the mass per unit length and the radius are finite; for n = the mass per unit length is finite, but the radius is not. Graphical and tabular material is included showing the run of density with radius, and the variation of radius, mass per unit length, and halfradius (radius within which half the mass is contained) as a function of polytropic index n.
Jeremiah P. Ostriker (Thu,) studied this question.