REPORT OF THE SECRETARY. 23 



A fifth set of the sheets was used for representing the geology of the 

 United States and Territories. 



There now remain on hand several sets of the original prints of this 

 large outline map, available for purposes similiar to the foregoing, and 

 which it is proposed to dispose of to institutions or associations willing, 

 by a small proportionate outlay, to aid in the re-imbursement of the 

 original expenses. 



Annual report. — The annual report of the operations of the Institution 

 for the year 1875 was presented to Congress on the 7th of April, 1870, but 

 the extra copies ordered as usual were not delivered to the Institution 

 until December, and their distribution has therefore only just now com- 

 menced. An edition of 10,500 copies was printed, 1,000 for the use of 

 the Senate, 2,000 for the House of Representatives, and 7,500 for the 

 Institution. The appendix to the report contains translations of Arago's 

 eulogy on Volta; DeCandolle on the probable future of the human race; 

 the annual report for 1873-*71: on the transactions of the Geneva Society 

 of Physics and Natural History ; a lecture on the past and future of 

 geology, by Prof. Joseph Prestwich, of England; a report on the dimi- 

 nution of the water of rivers and streams, by a committee of the Eoyal 

 Academy of Vienna; an original communication on the refraction of 

 sound, by Wm. B. Taylor, of Washington; a letter by Professor Henry 

 on the organization of local scientific societies, intended to furnish an 

 answer to numerous letters addressed to the Institution on this subject; 

 a translation of a proposed international code of symbols for charts of 

 prehistoric archaeology, by Profs. Mortillet and Chantre ; an article on 

 characteristics pertaining to ancient man in Michigan, by Henry Gill- 

 man ; and a memoir on the stone-age in New Jersey, by Dr. C. C. Abbott. 



RESEARCHES. 



It has been stated in previous reports that an annual appropriation 

 was made for several years to enable Professor Newcomb, of the Na- 

 tional Observatory, to employ accountants for the reduction of the 

 mathematical expressions of the orbits of the planets Uranus and Nep- 

 tune to numerical tabular results. 



Although the representation of the observations of Uranus by the 

 tables presented to the Smithsonian Institution four years ago, was 

 regarded by astronomers generally as highly satisfactory, it was not so 

 considered by the author, owing to the systematic character of the mi- 

 nute discrepancies. He therefore desired to ascertain whether these 

 discrepancies arose from errors in the computation of the perturbations 

 of Uranus, and, if not, whether they could be due to the action of an 

 ultra-Neptunian planet. The first step in the investigation was to have 

 a complete duplicate computation of the perturbations from 1753 until 

 the present time, by the method of mechanical quadratures, with which 

 to compare the results computed from the tables. An appropriation 



