90 



NA TURE 



[May 23, 1907 



rhythmic character. Another remarkable fact is the 

 recurrence of explosions at intervals of about 3h. 20m. 

 Recent investigations in surface seismic waves show that 

 the principal phase of world-shaking earthquakes travels 

 once round the earth in about 3h. igni., which almost 

 coincides with the recurrence intervals in the several 

 explosions of Krakatoa. Thus the outburst of the volcano 

 after the explosion of sh. 20m. p.m. happened after the 

 surface wave had made two complete revolutions round 

 the earth. In the absence of the seismograph records at 

 that time, we are quite ignorant of the existence of seismic 

 waves during those explosions, but the magnetograph 

 records at Batavia show distinct evidence of the vibrations 

 of the ground. The repetition of explosions at regular 

 intervals of time, which has such significance in the pro- 

 pagation of seismic waves, does not seem to be a mere 

 chance coincidence. The surface seismic wave requires 

 nearly the same time in traversing the different major 

 arcs of the earth, so that they will meet at the antipodal 

 point almost simultaneously, and in returning will again 

 coalesce at the centre of excitation, in the same manner 

 as the Krakatoa air waves. The disturbance at the origin 

 must therefore re-accumulate at the interval of about 

 3h. 20m., and tend to call forth a new explosion, if the 

 preceding explosion has already excited the seismic waves. 

 This will probably account for the repeated occurrence at 

 such stated intervals. Without laying too much stress on 

 the effect of the seismic waves, which may have been 

 associated with the spasmodic activity of the volcano, we 

 have another reason to believe that the ground vibrated 

 with the period of about 67m. 



In spite of the numerous theories which may be advanced 

 as to the cause of the Krakatoa sea waves, a simple 

 hypothesis of the existence of vibrations with a period of 

 about 67m. both before and after the explosion removes 

 most of the difliculties that will be felt in accounting for 

 the definite periods observed in tide-gauges scattered in 

 different parts of the world. The activity of Krakatoa 

 continuing from May to August 27, 1883, the exciting 

 causes would naturally have been numerous during that 

 interval of time to start sympathetic vibration of the 

 earth. Whether the movement of the ground was con- 

 fined to the region in the immediate neighbourhood of 

 the volcano or extended round the whole earth could 

 not be easily answered, and whether the period coincided 

 accidentally with the natural mode of vibration of the 

 earth or not is a matter of doubt, but the various data 

 hitherto accumulated as to the rigidity of the earth from 

 various phenomena connected with it tend to show that 

 such supposition is efficacious as a working hypothesis. 



The examination of mareograms in different parts of the 

 world shows that the times of arrival of the Krakatoa waves 

 are by no means definite, and the diagrams are sometimes 

 markedly different from each other. In some the waves 

 are blended together with the proper oscillations of the 

 bay in which the instrument was placed, while in others 

 they appear as regular secondary oscillations. In all 

 cases they present long-continued disturbances ; the more 

 conspicuous waves are, with the exception of that at 

 Batavia, preceded by minor oscillations, which sometimes 

 merge insensibly into the higher waves, so that it is 

 difficult to decide where the disturbance begins. Accord- 

 ing to the recent investigations by Messrs. Honda, Terada, 

 and Yoshida, the secondary oscillations in numerous bays 

 on the Pacific coast of Japan can be looked upon as 

 forced oscillations by the waves of the same periods, which 

 already exist in the surrounding ocean. During the 

 Krakatoa eruptions the waves made their way into the 

 surrounding seas and ocean, and the regular succession 

 of waves in bays is to be attributed to the effect of forced 

 vibrations. 



The periods of Krakatoa waves recorded on mareograms 

 are : — in Batavia, 122m. ; Port Blair, 63m. ; Negapatam, 

 68m. ; Madras, 8i-2m. ; Dublat, 65m. ; Beypore, s8m. ; 

 Karachi, 6qm. ; Aden, 67m. ; Port Alfred, 64m. ; Port 

 Elizabeth, 70m. ; Table Bay, 62m. ; Port Moltke, 6im. ; 

 Colon, 70m. The average period of this wave series, 

 with the exception of Batavia and Madras, is about fifim., 

 which almost coincides with the mean period of explosions 

 from oh. qm. to ith. 15m. on gasometer records. This 



NO. i960. VOL. 76] 



remarkable coincidence can be corroborated with simple 

 physical experiments in the following manner. 



When a pendulum with a magnet attached to it is set 

 in vibration by intermittent current acting underneath, the 

 period is double that of the exciting current, or when the 

 pendulum support vibrates in a vertical path, the frequency 

 is half that of the vertical motion. The well-known ex- 

 periment of Melde, by which a string is set in sympathetic 

 vibration by a tuning-fork of double frequency, and the 

 crispation produced by the vertical vibration of the sup- 

 port, as observed by Faraday, are examples of forced 

 vibrations with period double that of the exciting force. 

 In the application to the Krakatoa eruption, we notice that 

 the motion of the st-a-bed near the place of eruption was 

 nearly vertical ; consequently, if the sea vibrates in an 

 analogous manner as a pendulum, the period of the excited 

 wave would be double that of the exciting body. The tide 

 gauge at Batavia shows a big wave of 132m. ( = 2x66m.) 

 after the great eruption, and the mean period of the 

 successive fourteen waves is 122m., which is nearly double 

 the mean period of previous explosions. It is quite re- 

 markable that if the rigidity of the earth lies between 

 that of steel and that of glass, the mean fundamental period 

 of spheroidal oscillation is about 67m. 



According to Lord Kelvin, the tidal effective rigidity of 

 the earth is about the same as that of steel. I have also 

 lately shown that the prolongation of the Eulerian period 

 to the Chandler period of about 430 days is closely con- 

 nected with the velocity of seismic waves, and tends to 

 point to the same conclusion as regards the rigidity of the 

 earth. According to Bromwich (Proc. London Math. Soc, 

 XXX., 1899), the periods of fundamental spheroidal vibration 

 of an incompressible clastic solid sphere of the size of the 

 earth are S5m. and 7Sm., when the rigidity is equal to that 

 of steel and of glass respectively. In the above calculation 

 the effect of gravity is also taken into account, which is to 

 reduce the period by a considerable amount ; with the 

 rigidity of steel, the period is 66m. without gravity. The 

 period of 67m. is the mean value when the rigidity lies 

 between that of steel and of glass. 



The prevalence of waves of the said period in the tide 

 gauges scattered over the different parts of the earth's 

 surface is a striking coincidence, and may be explained 

 by assuming that the source of the waves was excited by 

 vibrations corresponding to the fundamental mode of 

 oscillation of the elastic gravity waves propagating round 

 the earth. That most of the mareograms show continued 

 disturbance before the appearance of big undulations 

 suggests the probable existence of previous vibrations. 

 Sincfe such vibrations are radial and tangential, the waves 

 appearing in bays at some distance from the e.xciting 

 source would have mostly the same period as the source, 

 while those observed in the neighbourhood of the eruption, 

 as Batavia, would be double. Some doubts may be ex- 

 pressed as to whether the observed period is not peculiar 

 to these bays, so that whatever may be the period of the 

 exciting source, such undulations should invariably appear. 

 With the exception of .\den and Colon, the proper period 

 of the above-mentioned bays generally differs from that of 

 the Krakatoa wave. 



The above considerations favour the view that the 

 vibration of the ground near Krakatoa was extremely 

 slow, and had a period of about 67m. Whether this 

 vibration extended all over the earth, or was confined to 

 the vicinities of the volcano, is a question still to be 

 solved. If the said period is really due to the spheroidal 

 vibration of our planet, we shall have opportunities of deter- 

 mining more exactly the period of vibration when volcanic 

 eruptions of the same character as those of Krakatoa take 

 place, or sometimes even with world-shaking earthquakes. 

 It will be worth examining seismograms, if great earth- 

 quakes do not give signs of the existence of vibrations of 

 very long period by enhanced disturbances at regular 

 intervals corresponding to the period of vibration of the 

 earth. Another means of detecting the presence of such 

 vibrations would be to examine the mareograms in bays 

 with the proper period of about 67m. Long-continued 

 observation in such bays will probably reveal the nature 

 of the spheroidal pulsation of the earth, if such really 

 exists. H. Nagaoka. 



