In contributions to the theory of circulants this twenty-year period is found to have been still more fruitful than its fruitful predecessor, the number of writings belonging to it being, indeed, a fourth more, and the percentage of unoriginal communications much about the same. The language which appears oftenest is English, the next in order of frequency being Italian, French, German,—an unusual sequence: the American share of the first of these is considerable, and shows a tendency to increase. In our treatment of the subject papers on block circulants have not been kept separate from those on ordinary circulants: strict segregation has been found to necessitate considerable repetition, and the gain got from it in facility of reference is not so great as to overweigh this disadvantage.