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The spatial distribution of plasma electrons in the ISX-B Tokamak has been determined by Abel-inverting vertical integral data from far infrared (FIR) laser-phase shift measurements. The calculational method for performing the Abel inversion is discussed and the results of the inversion of several sets of data are compared with Thomson scattering measurements of the pointwise electron density, and with the 2-mm interferometer measurement of the horizontal-midplane line-integral electron density. The inversion method used is essentially that described by Demas et al. This method is an extension of the method described by Yasutomo et al. The main difference is that the inversion method used here can treat plasmas with any outer boundary shape as long as the radius of the surface is single valued. In this regard it is more general than the inversion method of Wetzer, which is restricted to using an elliptical outer-plasma boundary.