An explanation is given of what is meant by "sample-free" item calibration and by "item-free" person measurement as these terms are applied to the one-parameter logistic test theory model of Georg Rasch. When the difficulty of an item is calibrated separately for two different samples the results may differ; but, according the the model, the estimated item difficulty is invariant except for an arbitrary constant. Test equating with the Rasch model is the process of determining this constant. Two methods of test equating are described and illustrated by simple numerical examples and by equivalent graphic figures. Common-person equating is done when the same group of persons takes two different tests. Since the persons are assumed to have the same ability regardless of which test they take, the scores on the more difficult test may have a constant added to make them equal to equivalent scores on the easier test. Common-item equating assumes that a given item has only one difficulty. When two tests contain some items, common to both, then common item equating is appropriate. Any difference in the difficulty of the other items in the two tests may be adjusted by calibrating through the common items. Tests of the goodness of the fit of the data to the model are discussed. (Author/CTM)