ADVERTISEMENT. 



This memoir was presented to the Institution by Professor J. H. C. Coffin, 

 Superintendent of the American Nautical Almanac, and was afterwards submitted 

 to Prof. S. Newcomb of the Naval Observatory, both of whom recommended its 

 adoption as one of the Smithsonian Contributions to Knowledge. The appropria- 

 tion for printing at the time it was presented having been temporarily exhausted, 

 a friend of science, who does not allow his name to be mentioned, furnished the 

 means for its immediate publication. 



JOSEPH HENRY, 



Secretary. 



Smithsonian Institution, 

 May, 1'872. 



(iii) 



