310 Intelligence and Miscellaneous Articles. 



investigation all the more interesting and keep them for a con- 

 siderable time in the borderland of theory and experiment from 

 drifting into the clutches of pure theory. It would be very 

 interesting to verify the rough calculation that molecular mag- 

 netism ceases to respond to magnetic forces alternating more 

 rapidly than at the rate of about 10 9 per second. In the depart- 

 ment of irreversible actions it would be interesting to investigate 

 what is meant by " tapping." What amount and kind of vibration 

 enables the molecules to set themselves ? Moving a body gently 

 has no appreciable effect. What is the meaning of a " jar " ? 

 There is probably no hard and fast line to be drawn, but these 

 and other borderlands claim investigation by properly qualified 

 experts. GL F. F.GK 



XXX. Intelligence and Miscellaneous Articles. 



on the annual and semi-annual seismic periods. by 

 charles davison, m.a., mathematical master at king 

 edward's high school, Birmingham. 



METHOD of Investigation. — The method adopted is similar to 

 that employed by Dr. 0. Gr. Knott in his paper on "Earth- 

 quake Frequency." 



If f(6) be a periodic function of 6, then 



/W = «o + a i cos C + a i) + a 2 cos ( 2G + a 2 ) + . . . a n cos (nd + a M ) + . . . , 

 from which it follows that 



1 f 0+7J-/2 9/y O n 



7T 0— 7i72 7r 07T 



' 3 cos(30 + a 3 ) + ... 



n-K 



2a n sin — 



H —cos (nd + a n ) + 



nir 



The latter expression gives the mean value of f(d) through an 

 interval tt/2 on either side of 0. 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 num- 

 bers 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 mean corresponding to the end of January. 

 Six-monthly means are calculated in this way for the end of each 

 month; each mean is divided by the average of all twelve, and 

 the difference between each quotient and unity is multiplied by 



