82 Mr. C. Davison. On the [June 15, 



in any order, and are all such as might be expected in experimental 

 results of this nature. Some of the greatest variations were obtained 

 in exactly similar experiments performed at different times. 



The mean of all the values of the polarisation in this table is 

 2'09 volts. 



The rate of fall of the polarisation depends on the time the current 

 has been electrolysing the solution, and also on its intensity, but in 

 every case the fall is very rapid at first, being in some cases as much 

 in the first minute as it is in the next five minutes, and the fall in 

 the first minute is never less than one-fourth of the polarisation. 



IV. "On the Annual and Semi-annual Seismic Periods." By 

 CHARLES DAVISON, M.A., Mathematical Master at King 

 Edward's High School, Birmingham. Communicated by 

 Professor J. H. PoyNTiNG, F.R.S. Received June 13, 1893. 



(Abstract.) 



Method of Investigation. The method adopted is similar to that 

 employed by Dr. C. GL Knott in his paper on " Earthquake 

 Frequency." 



If /(#) be a periodic function of 0, then 



from which it follows that 

 1 C0+TT/2 2 a 



* 



. mr 

 2 a n sin 



Q 



-4 --- cos (nO + an) + ..... 



mr 



This latter expression gives the mean value of /(0) through an 

 interval ?r/2 on either side of 6. From it, all terms involving even 

 multiples of are eliminated, and the coefficients of all terms after 

 the second are diminished to a greater extent than that of the 

 second. 



A definition of the unit earthquake having been adopted, the 

 earthquakes of different districts are classified in half-monthly groups, 

 the first half of February containing fourteen days, and of all the 

 other months fifteen days ; and the numbers so obtained are reduced 

 to intervals of equal length (fifteen days). The numbers for the two 

 halves of each month are added together. The mean of the numbers 

 for the six months from November to April gives the six-monthly 



