For a summary measure of income mobility, Peter Hart and others have favoured an index based on the correlation between the logarithm of incomes in successive time periods. This paper examines the features of the Hart index and, in doing so, formulates a number of general properties that may be thought desirable in a measure of income mobility computed directly from individual income profiles rather than transition matrices. Set against these criteria, the Hart index performs well. It does, however, have one major deficiency: it is unable to decide whether a structure in which incomes are initially unequal, and then become equal, is highly mobile or completely immobile. Other mobility indices considered in the paper do not suffer from this problem and their overall performance is at least as good as the Hart index.