DEDUCTIONS FROM THE TIDES. 27 



the surface of the earth, pass from the point of origin around to the anti- 

 podal point in about 112 to 115 minutes. The largest and strongest group 

 of these large waves takes about 135 minutes. Comparing these with one 

 another, it appears that the period of the maximum group of the large waves 

 is six times that of the compressional waves, the former, however, travers- 

 ing a semicircumference and the latter a diameter. The period of the second 

 set of short vibrations for most chords is one-half more than that of the 

 first set, while that of the problematic set is approximately twice that of 

 the first set. Three times the period of the compressional waves, twice 

 that of the best recorded distortional waves, one and a half times that of 

 the problematic waves, and half that of the maximum long waves are 

 each approximately 67.5 minutes, or essentially the same as Nagaoka's 

 unit-period for the Krakatoan pulsations. The gasometer record of the 

 Krakatoan eruptions is rather coarse and can not be read with exactness, 

 but, taking Nagaoka's readings, the discrepancies between the recorded 

 times of the twelve eruptions of August 27 and the periodic times on the 

 67.5 minute basis are as follows in minutes: (starting-point, first erup- 

 tion on August 27); -29 ( = -33.5, the half period, + 4.5); +14; -1.5; 

 + 2; -t- 16; -3.5 (strong); + 3 (strong); +23.5 ( = 22.5, one-third period, 

 + 1); +33.5 (half period); -1.5 (the great eruption); -9 (the final erup- 

 tion, strong). In the interpretation it is assumed that the eruption of 

 August 26 at 5^ 20™ p.m. started a series of oscillations in the lithosphere 

 which, at the end of the sixth period of 67.5 minutes, with a lag of 4 min- 

 utes, had developed sympathetic relations with the volcanic forces and 

 stimulated the first of the twelve eruptions that followed. These have the 

 degree of correspondence to the assumed period just shown. Each erup- 

 tion falling at or near the critical stage of the pulsation previously developed 

 may be supposed to have strengthened the succeeding oscillations until 

 the series reached a first double maximum at the seventh and eighth erup- 

 tions, and a second and greatest maximum at the eleventh and twelfth. 

 If this interpretation be justified, it may mean that the vibrations which 

 arose from the earthquake developed into the form and periodicity of the 

 fundamental vibrations of the earth-spheroid. The inadequacy of the 

 data, quantitatively and qualitatively, to estabhsh this positively is obvi- 

 ous, and it may not be safe to rest much upon it; but the following are 

 curiously related to it. 



The moon's synodical period, 1,490.5 minutes, is 22 times 67.75. The 

 solar period, 1,440 minutes, is about 21.25 times 67.75. If 67.75 minutes 

 be taken as the normal period of spheroidal oscillation, 22 of these con- 

 stitute a lunar day, 314 approximately the average fortnightly excursion 

 of the moon north and south of the equator, and 628 the lunar month. 

 If a represent the northerly fortnightly excursion, and a' the southerly, 

 each of these equahng 314 earth-pulsation periods, they will obviously 

 have close commensurate relations at the periods represented by aa', 

 a (a-\-a'), and (a + a'y, whose numerical values are 218, 436, and 870 days, 

 respectively. Now, 436 days is the recent estimate of Kimura * for the 



» Physico-Math. Soc. Tokyo, Pt. II, 24, pp. 357-364, 1905; Sci. Obs., July 25, 1906. 

 Pop. Astr., Oct. 1906, p. 469. 



