This study develops a weighted least squares method for transforming a logistic scale in such a way that the estimates of ability parameters on the tranformed scale are as comparable as possible with those on another scale. This scale tranformation process is referred to as equating of scales. Equating is an important procedure in studies involving the logistic model and the latent trait model in general; the equating method presented deals with situations in which there are two separately scaled tests that have only some items in common (vertical equating or horizontal equating) or all items in common (horizontal equating). The necessity for equating in the later case arises when two scales have been derived by using two different groups of examinees which may have different characteristics pertinent to the results of scaling. In the former case (only some items common), the groups of examinees may or may not be overlapped. As one of the optimum estimation procedures, a weighted least squares method is introduced and applied to an achievement scale and an intelligence test. An advantage of the method over previously proposed methods is that highly discriminating items tend to affect equating more strongly than less discriminating items. (Author/RL)