Documentary History of New-York.--The forthcoming (third) volume of this State contribution to our historical literature will well sustain the reputation of its predecessors and of its zealous editor. Dr. O'CALLAGHAN is an enthusiast in his zeal for lighting up "the dark ages of our history," as Verplanck called the Dutch period; and he has done as much as any man living to rescue the fast perishing memorials of the founders of the Empire State. It is fortunate for the State that his industry and patient research are secured for the proper arrangement of the Archives--too long neglected and subject to loss and mutilation. The new volume has come to hand too late for any elaborate notice or review of its contents; but a glance at the list of papers and illustrations alone warrants the opinion we have expressed. We notice particularly the account of Champlain's explorations in Northern New-York, &c., from 1609 to 1615--translated from the edition of 1632. The historical student cannot fail to note the coincidence of discovery and exploration by the Dutch and French; and the credit due to the "Founder of New France;" to which we have alluded in the article on the Jesuit Relations. The translations of the extracts from Wassenaar (1624, etc.), give an interesting cotemporaneous view of the progress of the European discoveries and settlements in America. A chapter on Medals and Coins contains attractive matter, particularly that portion which relates to the "Rosa Americana coins," connected as they are with the "Wood's half-pence," immortalized by Dean Swift. The notes and biographical sketches by the editor, scattered through the volume, add materially to its value--as also the numerous maps and engravings. We have heard hints that some small suggestions of disinterested economists of the public money, or other considerations less creditable, have been brought to bear against the continuation of this publication--but we trust that they will end when they begin. New-York owes it to her own great history to make its material accessible to all. * * * * *