No one of the libraries of the first class now in existence dates beyond the fifteenth century. The Vatican, the origin of which has been frequently carried back to the days of St. Hilarius in 465, cannot with any propriety be said to have deserved the name of library before the reign of Pope Martin V., by whose order it was removed in 1417 from Avignon to Rome. And even then a strict attention to exactitude would require us to withhold from it this title until the period of its final organization by Nicholas V. in 1447. It is difficult to speak with certainty concerning the libraries, whether public or private, supposed to have existed previous to the fifteenth century, both on account of the doubtful authority and indefiniteness of the passages in which they are mentioned, and the custom which so readily obtained in those dark ages of dignifying with the name of library every petty collection of insignificant codices. But many libraries of the fifteenth century being in existence, and others having been preserved long enough to make them the subject of historical inquiry before their dissolution, it becomes easier to fix with satisfactory accuracy the date of their foundation. We find, accordingly, that during the fifteenth century ten libraries were formed: the Vatican at Rome, the Laurentian at Florence, the Imperial of Vienna and Ratisbon, the University at Turin, the Malatestiana at Cesena, the Marciana at Venice, the Bodleian at Oxford, the University at Copenhagen, and the City at Frankfort on the Maine. The Palatine of Heidelberg was founded in 1390, dispersed in 1623, restored in 1652, and augmented in 1816. The increase of the libraries of Europe has generally been slowly progressive, although there have been periods of sudden augmentation in nearly all of them. They began with a small number of manuscripts; sometimes with a few, and often without any printed works. To these gradual accessions were made from the different sources which have always been more or less at the command of sovereigns and nobles. In 1455 the Vatican contained 5000 manuscripts. In 1685, after an interval of more than two centuries, the number of its manuscripts had only risen to 16,000, and that of the printed volumes did not exceed 25,000. In 1789, but little more than a century later, the number of manuscripts had been doubled, and the printed volumes amounted to 40,000. Far different was the progress of the Royal, or as it is now called, the National Library of Paris. The origin of this institution is placed in the year 1595--the date of its removal from Fontainebleau to Paris by order of Henry IV. In 1660 it contained only 1435 printed volumes. In the course of the following year this number was raised to 16,746, both printed volumes and manuscripts. During the ensuing eight years the library was nearly doubled; and before the close of the subsequent century, it was supposed to have been augmented by upwards of 100,000 volumes.