416 Transactioiis. — Chemistry and Physics. 



arguments I have not been able to peruse. But Professor 

 Milne and Dr. Omori conclude that the tilts represented by 

 the maximum displacement of the boom are too large to be 

 admissible as tilts ; and Omori discusses the accelerations of 

 the earth-particles of four earthquakes which would result 

 from the assumption that the maximum boom-movement was 

 due to a series of waves of vertical displacement passing under 

 the pillar of the instrument. 



The following considerations do not appear to me to have 

 been sufficiently realised : — 



The differential equation representing the motion of a 



body capable of free vibration of frequency n, but acted upon 



by a periodic force E cos pt, as 



d 2 u Tr du „ _. 



dF + K <¥ + 7rw = Ecos ^ 



where K is the constant of delay in the free vibration. 



The solution cf this is 



~w 



u = V(^W+KV COS {PI ~ C) 

 pK 



\v 



here tan C = 



n 



2 _ 



p* 



This equation applies to seismograph of the Milne type 

 and bodies also, as well as to other vibrating bodies. 



The result shows (1) that the vibrating body, in this case 

 the boom of a seismograph, no longer vibrates in its natural 



period — , but takes the frequency of the disturbing force p; 



(2) that if friction be small compared with the difference of 

 the squares of the frequencies, the resulting vibration has an 



amplitude - 2 _ 2 ; (3) the phenomenon of beats may occur 



between the forced vibration and the free period of the boom. 



Considering the second conclusion first, it is evident that 

 the maximum amplitude of swing of the boom gives no in- 

 formation whatever of the amplitude of the disturbing cause, 

 without also a knowledge of the periods of the free and forced 

 vibrations. It does not follow, as appears to be supposed, 

 that the maximum amplitude of swing of the boom is associ- 

 ated with the maximum amplitude of the disturbing cause. 

 Of waves of equal amplitude but different wave-lengths 

 those nearest in period to the free period will give the 

 largest trace, and if p and n become equal the only thing 

 which prevents the swinging of the boom from eventually 

 becoming infinite is the term K' 2 p 2 , which in this case must 

 be considered, though it is very often small enough to be neg- 



* Rayleigh's " Sound," p. 38, 1st ed. 



