26 THE TIDAL PROBLEM. 



oscillation which assumed the form of a harmonic spheroid of the second 

 order to be 78 minutes. A series of other oscillations of lesser lengths 

 would be developed. He found that the compressibility of the matter is 

 not a vital factor, for if t be the time required by a wave of distortion to 

 traverse the earth's diameter, and if P be the period of oscillation of shape, 

 then P = t 0.848 if the material is incompressible, and P = t 0.840 if 

 the material preserves uniconstancy. Bromwich,^ bringing into the com- 

 putation the efifect of gravity, found that the gravest free period of a sphe- 

 roid of the size, mass, and gravity of the earth, with a rigidity about that 

 of steel, is 55 minutes. The corresponding period, if the effect of gravity 

 be neglected, is 66 minutes. If the rigidity be about that of glass, the 

 period is 78.5 minutes if the effect of gravity be included, and 120 minutes 

 if gravity be neglected. 



Nagaoka == has made a study of the pulsations connected with the Kra- 

 katoan eruptions of August 26 and 27, 1883, as recorded by the gasometer 

 at Batavia, 94 miles from Krakatoa, on the supposition that these pulsa- 

 tions were derived directly from the volcanic explosions and thus registered 

 their relative times. He reached the conclusion that the series of eruptions 

 were rhythmical with a unit-period of 67 minutes and a tendency toward 

 the grouping of these shorter periods into larger ones of about 200 minutes. 

 The former he interprets as an expression of the fundamental period of 

 oscillation of the earth as a spheroid. Referring to the results of Brom- 

 wich, he cites the coincidence of the Krakatoan periods so deduced with 

 the computed periods when the assumption is made that the rigidity of 

 the earth lies between that of steel and that of glass. Nagaoka also cites 

 the apparent relationship of this period to seismic phenomena, and the 

 apparent connection of certain of these phenomena with the Chandlerian 

 nutation of the pole. 



The correspondences may be carried appreciably further. While exact 

 determinations of the velocities of seismic tremors recorded at a distance 

 from an earthquake are not yet available, the time required by the fore- 

 most waves to traverse the earth's diameter may be taken provisionally 

 at 22.5 minutes. These vibrations are generally interpreted by European 

 and American seismologists as compressional waves and as passing through 

 the earth along chords, or along curves of adaptation departing slightly 

 from chords. The second set of tremors, generally interpreted as distor- 

 tional, require about 50 per cent longer for chords up to 140°, and perhaps 

 up to 180°, which would make their diametrical period about 33.75 min- 

 utes. For the chords between 140° and 160°, and perhaps up to 180°, 

 Oldham inferred a longer period from the available observations, which 

 are, however, thus far not sufficiently numerous for positive conclusions. 

 These problematical vibrations may be directly transmitted or may be 

 reflections. The period deduced for them is approximately double that of 

 the compressional waves. The foremost large seismic waves, which have 

 approximately a uniform velocity and which are interpreted as following 



» On the influence of gravity on elastic waves, and in particular on the vibrations of 

 an elastic globe, by T. J. A. Bromwich. <Proc. Lond. Math. Soc, XXX, 1899. 

 2 Nature, May 25, 1907, pp. 89-91. 



