THE SMITHSONIAN INSTITUTION. 21 



any time is proportional to the sine of the sun's altitude above the 

 horizon. The subject was also investigated by Euler in 1*739, in the 

 Petersburg Commentaries, with some improvements upon the metliod 

 of Halley, but owing to the introduction of false hypotheses, it was 

 not brought to a successful conclusion. More recently, Fourrier and 

 Poisson have discussed the problems of terrestrial heat at great length, 

 but in so general a way as to leave very much yet to be accomplished. 



The present memoir, avoiding hypotheses, proceeds entirely in ac- 

 cordance with the principle that the intensity of the heat and light 

 radiated from the sun to the earth, is inversely proportional to the 

 square of the distance. By strict adherence to this primary law, the 

 principles of the astronomical branch of meteorology are deduced in a 

 connected series with geometrical precision, while at the same time an 

 account is taken of all the modifying circumstances of which the effects 

 are definitely known, such as the geographic latitude, the changes of 

 the sun's distance from the earth, the changes of the sun's altitude or 

 oblique direction of the solar beams, and changes in the length of the 

 day. 



Among the more interesting results thus obtained are the simple 

 expressions for annual intensity and the duration of sunlight and twi- 

 light, and a more full delineation of the peculiar increase of summer 

 heat around the poles, first pointed out by Halley. 



The secular changes of solar heat^ or those which relate to long 

 periods, are also analyzed in accordance with the received variations 

 of astronomical elements, particularly those given by Leverrier^ and 

 extended to very remote epochs. This part of the investigation is in- 

 timately connected with the geology of the globe, and the question as 

 to the amelioration of the climate of America since the period of our 

 colonial history. The paper is accompanied by a number of graphical 

 illustrations, which, besides exhibiting the general results, show the 

 reflex agency of the earth and its atmosphere in modifying the direct 

 heat of the sun, and the progressive change of climates, and the seasons 

 of the year. A small appropriation was made to defray the expense 

 of the arithmetical calculations necessary for deducing the numerical 

 values from the general formula. 



7. In a previous report it was stated that a small appropriation had 

 been made to defray, in part, the expense of some special geological 

 explorations, under the direction of Professor E. Hitchcock, of Amherst 

 College, Massachusetts. The papers containing the result of these in- 

 vestigations have been presented to the Institution for publication. 

 They all relate to surface geology^ or the geological changes which 

 have taken place on the earth's surface since the tertiary period. 



The first paper treats of the unconsolidated terraces, beaches, sub- 

 marine ridges, &c., that have been formed along the shores of the 

 ocean, lakes, and rivers, since the last submergence of the continents. 

 The author has given the heights of a great number of these above 

 the ocean, and the rivers, and a map of those in the valley of the Con- 

 necticut river. The evidence they afford of a submergence of this 

 continent, at least, and a part of Europe, since the Drift Period, is re- 

 garded by the author as one of his most important conclusions. But 



