The report of the Secretary, Professor Henry, states that at tho last session of the board it was resolved to memorialize Congress, asking that the usual appropriation of $4,000 for the maintenance of the National Museum might be increased to $10.000, and also that $25,000 might be appropriated towards fitting up the large room, in the second story of the building, for the better exhibition of the Government collections. The request was refused and only the usual appropriation was made. In view of the facts that $4,000 was the sum appropriated when the museum was under the charge of the Patent Office, that since its removal to tho Institution its size has been trebled, that the currency is greatly depreciated, and that the amount expended since the fire of 1885, is over $140,000, the greater part of which was for the accommodation of the National Museum, it is hard to see why, if the sustaining of this museum is considered necessary, the moderate request of the Regents should not have been granted. The fact that $20,000 of the $140,000 expended since 1865, were paid out of the last $,nHuarincome, renders the results attained during the year particularly praise-worthy. The funds of the institution are reported in better condition than they were at the time of the preceding report by $18,000. The total capital of the Institution after payment of all liabilities is $697,000, a gain upon the original bequest of Mr. Smithson of over $155,000. The fifteenth volume of the " Smithsonian Contributions to Knowledge " has been published and distributed to institutions of learning in this country and in Europe. A large number of valuable and interesting papers are in hand, and will form parts of the sixteenth volume of the same publication. The general appendix to this report contains a large amount of valuable scientific matter, together with biographic sketches of scientific men. These latter comprise a memoir of Cuvier, with a history of his Works ; a memoir of Oersted ; a notice of Christian Frederic Schoenbein, the discoverer of ozone, with an appendix giving an account of the principal discoveries of that distinguished investigator ; a memoir of Encke ; and a memoir of Eaton Hodgkinson, the celebrated English engineer, with reviews of many of his inquiries and demonstrations. These are followed by a translation of a very important paper on " Recent Progress in relation to the Theory of Heat," by A. Cazin, and another one from the pen of Dr. Joh. Millier on the " Principles of the Mechanical Theory of Heat," with a large number of illustrations, the execution of which fully entitles their perpetrator himself to execution. The subject matter, however, of this paper, and the thoroughness and perspicuity with which it is treated, render it one of the most valuable works upon heat ever published in English. The next contribution in order is a short but valuable paper on the "Continuous Vibratory Movement of all Matter, Ponderable and Imponderable," by L. Magrini, of the Museum of Florence. In this paper the attempt is made to prove that movement is a fundamental property of matter in whatsoever state it exists, that the movement always has existed, and, though the author does not draw this inevitable and logical conclusion from his argument, always will exist so long as matter exists. We may at some future period review this paper at length We are next given a lecture by Dr. John Tyndall before the University of Cambridge, May 16, 1865, on the subject of Radiation, of which, having given the author's name, it is unnecessary for us to say it is a comprehensive and exhaustive discussion, exhibiting in a marked degree the peculiarly felicitous style characteristic of Mr. Tyndall's efforts. The remainder of the volume is filled with records of scientific experiments, reports of learned societies in various parts of the world, archselogical discoveries, etc., etc. ; the whole making a volume which the Secretary might justly hope “would show the results attained to have been little inferior in value or extent to those of any preceding year.”