208 ON THE PERIODICITV OF THE AURORA BOREALIS. 



infinite. The yearly curves indicate the relative changes from month to month, but 

 the absolute values for one place as compared with those found elsewhere do not 

 appear, unless allowance is made for the differences of scale adopted in their con- 

 struction. 



An annual curve, drawn through only twelve points, representing the monthly 

 means, can show simply the months in which the maxima and minima occur, but not the 

 flays. To see whether the occurrence of the aurora is in any way associated with 

 shooting stars, which appear in unusual abundance on certain days of the year, or with 

 the fall of meteorites, or with any other phenomena, meteorological or cosmical, I have 

 assigned to each day of the year the number of auroras observed upon it, and placed 

 the result in table LI I. If these results are projected in a curve, presenting in its 

 Alpine summits and the corresponding valleys the principal maxima and minima 

 in the annual march of auroral displays, there is also seen represented in its uneven 

 flow and its many jagged roughnesses the influence of daylight, of weather, of climate, 

 and of a great variety of accidental disturbances. The principal maxima are reached 

 on March 16 and September 24, and the minima on January 7 and June 23. From a 

 catalogue of about 5500 auroras, compiled by Wolf, 1 he deduces the times of maxima 

 as March 20 and October 15, and the times of minima as June 22 and December 25. 

 These maxima and minima do not appear to stand in any relation to those periods of 

 the year which Biot considers as signalized by displays of meteors, viz., July 25-30, 

 August 7-12, October 24-27, November 13-16. 2 



The observations justify the assumption that the number of auroras at any particular 

 season, or the ordinate of the yearly curve of auroral frequency, is a function of the 

 tropical year. It may, therefore, like any other periodic function, be expressed by a 

 series of terms arranged according to the sines and cosines of the time and its integral 

 multiples. If it is supposed that 



< = the time expressed in parts of a year as its unit, 

 N= the ordinate of the diurnal curve for the time (t), 

 « = the ratio of the circumference to the diameter of a circle, 

 x = any integer whatever ; 



and if £ denote the sum of the terms which correspond to the different values of (z), 

 the general form of the ecpuation is 



1. N— A + S. C x sin. 2 n x (t + c x ). 

 l Vierteljahrsschrift der Naturforsch. Gescllschaft in Zurich, II. 371. 2 Pogg. Ann. der Physik und Chemie, LXVI. 476, 7. 



