The principle on which this Memoir was compiled lay in the careful comparison of the Museum Catalogues with the best special bibliographies, and with the Catalogues of other Libraries. In Jurisprudence, for example, the national collection was tested by the _Bibliotheca Juridica_ of LIPENIUS, SENCKENBERG, and MADAHN; by the list of law-books inserted in DUPIN’S edition of CAMUS’ _Lettres sur la profession d’Avocat_, and by the _Bibliothèque diplomatique choisie_ of MARTENS. In Political Economy, by BLANQUI’S list given in the _Histoire de l’Economie politique en Europe_. The Mathematical section of the Library was compared with ROGG’S _Handbuch der mathematischen Literatur_. In British History, the _Bibliotheca Grenvilliana_, and the _Catalogue of the Library of the Writers to the Signet_, were examined, for those sections of the subject to which they were more particularly applicable, and so on in the other departments. The facts thus elicited were striking. It was shown that much had been done since 1836 to augment almost every section of the Library; but that the deficiencies were still of the most conspicuous sort. In a word, the statement abundantly established the truth of the proposition that ‘the Collection of Printed Books in the British Museum is not nearly so complete and perfect as the National Library of Great Britain ought to be ...’ and it then proceeded to discuss the further question: ‘By what means can the collection be brought with all proper despatch to a state of as much completeness and perfection as is attainable in such matters, and as the public service may require?’ It was shown that no reliance could be placed upon donations, for the filling up those gaps in the Library which were the special subject of the Memoir. Rare and precious books might thus come, but not the widely miscellaneous assemblage still needed. As to special grants for the acquisition of entire collections, not one of ten such collections, it was thought, would, under existing circumstances, be suitable for the Museum. The Copyright-tax has no bearing, however rigidly enforced, save on current British Literature. There remained, therefore, but one adequate resource, that of annual Parliamentary grants, unfettered by restrictions as to their application, and capable of being depended upon for a considerable number of years to come. Purchases might thus be organized in all parts of the world with foresight, system, and continuity. In the letter addressed by the Trustees to the Treasury, it was stated that, ‘for filling up the chasms which are so much to be regretted, and some of which are distinctly set forth in the annexed document, the Trustees think that a sum of not less than ten thousand a year will be required for the next ten years,’ in addition to the usual five thousand a year for the ordinary acquisitions of the Library.