[ 401 ] 



LII. On the Interpretation of Milne Seisniogranis, 

 By C. Coleridge Farr, D.Sc."^ 



[Plate XVI.] 



THE question whether a horizontal pendulum Seismograph 

 acts as a clinograph or whether its records must in part 

 be ascribed to horizontal movements of the Earth's surface 

 has received discussion by Milne f, OmoriJ, and by others 

 also whose arguments I have not been able to peruse. Both 

 Prof. Milne and Dr. Omori conclude that the tilts repre- 

 sented by the maximum displacement of the boom would 

 indicate earth movements too large to be admissible. 



Without attempting to give a complete theory § of the 

 movement of the boom, or denying that horizontal move- 

 ments may occur when the inertia weight will act as a steady 

 point, yet from the ordinary elementary theory of forced 

 vibrations || the equation giving the movement of a vibrating 

 body, whose " free "* frequency is nj^ir, under the action of a 

 periodic force E cos pt, is 



«=7P^p7f|y <^°« (Pf-^)- • . • (1) 



If k, the resistance due to friction, be small compared with 

 the difference of the squares of the frequencies, the resulting 

 vibration has an amplitude 



u=^^,, (2) 



whilst, as is well known, the period of the vibration takes the 

 period of the disturbing cause. 



Though an earthquake record is probably due to several 

 terms of the form E cos^^ with different coefficients of decay, 

 yet in many instances I have seen a considerable portion of the 

 record appear to consist of weaves of one wave-length, in which 

 case the above simple formula will give at least a general idea 

 of the earth movement corresponding to any diagram ; but to 

 obtain it a knowledge of " p '' as well as " n '■* is necessary, 

 for which purpose the tape must be driven sufficiently fast 



* Communicated by the Physical Society : read March 13, 1903. 



t ' Nature/ toI. Ixv. p. 202, and B. A. Eeport Seismological Committee. 



X Publications of the Earthquakes Investigation Committee, No. 5, 

 Tokyo, 1901, p. 45, et seq. 



§ The theory of the horizontal pendulum is discussed at length in 

 Co7n2Jtes Bendus des Seances de la Commission Seismiqite Permanent 1902, 

 which reached me after this paper was written. 



il Eayleigh, ' Sound/ 1st ed. vol. i. p. 38. 



PhiL Mag. S. 6. Vol. 6. No. 34. Oct. 1903. 2 D 



