56 PROCEEDINGS OF THE AMERICAN ACADEMY 



explained except by a failure in the phenomenon itself, especially when 

 it is considered that the early settlers of New England were not likely 

 to have overlooked appearances which they could so readily associate 

 with the religious or political events of their heaven-determined des- 

 tiny. A preliminary discussion of the subject was first published in 

 the American Almanac for 1860, and afterwards, with some modifica- 

 tion, in the Memoirs of the Academy, Vol. IX. p. 101. But I was 

 soon satisfied that no satisfactory solution of a vast problem could be 

 reached, which was built on anything less than the richest materials 

 that could be gathered from the records of science. Much time has 

 been expended, therefore, in preparing and printing a complete cata- 

 logue of all the auroras observed from the earliest times down to the 

 present year, — a catalogue which comprises about ten thousand inde- 

 pendent auroras and fifty thousand observations. 



The discussion of these materials, so far as it has yet progressed, 

 relates especially to the distribution of auroras between the different 

 days and months of the year, and the accuracy with which this distri- 

 bution may be expressed by a periodical function. The subject is 

 considered, not only for the whole earth, but also separately for the 

 two hemispheres, and for each place where a series of observations 

 has continued long enough to justify a distinct discussion. The num- 

 ber of auroras occurring in different seasons of the year has been 

 computed by the following formula : — 



N = A + Ci sin. 2 n (t + c a ) -f C 2 sin. 4 n (t + c,) + C 3 sin. 6 n (t + c 3 ) ; 



and the result compared with the observations. The mean probable 

 error has been obtained by the usual rule, applied to the differences be- 

 tween the number of observed and computed auroras. The formula 

 just mentioned is the same as I employed in 1845 in discussing the 

 daily changes of temperature and magnetic declination at Cambridge, 

 Mass.* In 1843, Eklof published f at Helsingfors, Russia, a mathe- 

 matical investigation of the yearly march of auroral phenomena, in 

 which he employed the same periodic function as I have adopted. 

 Copies, however, of the Scientific Transactions, in which Eklof pub- 

 lished his labors, are very rare in this country. I only know of the 

 single one which I had recently an opportunity to examine, in the 

 Astor Library of New York. As Eklof confined his inquiry to a few 



* 



* Memoirs of the American Academy of Arts and Sciences. III. 44. 

 t Acta Soc. Sci. Fennic, etc. II. 302. 



