Especial emphasis has been laid upon the connection between the vaulting and lighting problem. Some vaults, such as those of six-part and five-part form, are shown to have probably derived this form from the clerestory, while other vaults of nave, apse, and ambulatory are proved to be very closely related to the position of the windows beneath them. In the discussion of Romanesque vaulting, a number of churches are suggested as forming a “School of the Loire,” in addition to the schools which are generally listed. Suggestions are made regarding the form of the centering employed in Perigord, and there is a somewhat extended account of the purpose served by the triforia of Auvergne. In dealing with ribbed vaults the use of caryatid figures for the support of the ribs, the non-essential character of the wall rib, the origin and development of six-part vaulting, and the types of chevet vaults are subjects especially treated. But these and other novelties are all subordinate to the real purpose of the work, which is to give in a compact and systematic form a thorough résumé of all the principal forms of vaulting employed in the middle ages. For the sake of this systematic treatment the different portions of the church, nave and aisles, choir and transepts, apse and ambulatory have been taken up in separate chapters, though in each case there has been an effort to keep as closely as possible to the chronological sequence of the monuments. This matter of chronology has, in fact, led to an effort to date as accurately as possible all the buildings mentioned. For this purpose the author has consulted many authorities and in the case of doubtful monuments has arrived at the dates given only after an analysis of the various claims advanced. The illustrations are in large measure from photographs taken by the author or purchased in Europe. The following, however, are from publications, Figs. 31, 34 and 39 from Gurlitt, _Baukunst in Frankreich_ (J. Bleyl Nacht, Dresden); Fig. 12 from Baum, _Romanische Baukunst in Frankreich_ (Julius Hoffmann, Stuttgart); Fig. 38, from Bond, _Gothic Architecture in England_ (Batsford, London), and Fig. 63 from Moore, _The Mediaeval Church Architecture of England_ (Macmillan, New York). The drawings are largely based upon plates in Dehio and Von Bezold, _Kirchliche Baukunst des Abendlandes_ (Cotta, Stuttgart), supplemented by the author’s own notes. Of course, only a limited number of illustrations were possible and for this reason less well known examples, and those not previously published, were in most cases chosen. To make it possible for the reader to supplement the illustrative material references are made in the footnotes to publications in which reproductions of many of the churches mentioned may be found. The books chosen for reference have, where possible, been those easily accessible to the student.