22 THE TIDAL PROBLEM. 



by the great explosion of Krakatoa on August 27, 1883, as set forth by 

 Lieutenant-General Strachey in the monograph of the Royal Society on the 

 "Eruption of Krakatoa and subsequent phenomena." He says: 



The observed facts clearly establish that the successive repetitions of the disturbance 

 at the numerous stations, after varying intervals of time, were caused by the passage 

 over them of an atmospheric wave or oscillation, propagated over the surface of the globe 

 from Krakatoa as a center, and thence expanding in a circular form, till it became a great 

 circle at a distance of 90° from its origin, after which it advanced, gradually contracting 

 again, to a node at the antipodes of Krakatoa; whence it was reflected or reproduced, 

 traveling backwards again to Krakatoa, from which it once more returned in its original 

 direction; and in this manner its repetition was observed not fewer than seven times at 

 many of the stations, four passages having been those of the wave traveling from Kra- 

 katoa, and three those of the wave traveling from its antipodes, subsequently to which 

 its traces were lost (p. 63). 



The velocities of propagation of these waves were found to vary from 

 674 to 726 miles per hour — somewhat below the normal rate of sound at the 

 surface of the earth, which is 757 miles per hour at 10° C. and 780 miles at 

 22° C. The average temperature of the air at its base is 15° C. to 17° C, 

 from which the temperature declines with ascent, as does also the density. 



The mean time occupied by the Krakatoan waves in making a first 

 circuit of the earth, for the computation of which 27 stations were avail- 

 able, was 36 hours and 24 minutes, the angular rate being 9.89° per hour; 

 the mean of the second circuit, for which 18 stations were available, was 

 36 hours and 30 minutes, the angular rate being 9.86° per hour; the mean 

 of the last observed circuit, for which 10 stations were available, was 37 

 hours and 50 minutes, the angular rate being 9.77° per hour. 



Now if the forced tidal wave be analyzed into instantaneous impulses 

 and these be regarded as discontinuous, they may each be treated as though 

 they gave rise to free waves similar to those derived from the volcanic 

 impulses of Krakatoa. If we compare the intermediate rate determined 

 for the free Krakatoan waves with the angular rate of the forced lunar tide, 

 it will appear that the latter would outrun the former at the rate of about 

 4.6° per hour. The free wave would therefore soon begin to flatten the 

 surface configuration of the forced tide by extending its amphtude, and in 

 less than ten hours its influence would begin to be antagonistic to the 

 forced tide. This antagonistic influence would reach its maximum about 

 ten hours later, but would continue with declining force for nearly another 

 ten hours, beyond which, because of the relatively high viscosity of the air, 

 it may be regarded as negHgible. It appears therefore that the periods of 

 the free atmospheric waves are not such as to effectively reinforce the 

 forced waves and hence they do not rise to appreciable value. 



In addition to this there seems reason to suspect that the compressi- 

 biUty and the relatively high viscosity of the air may combine to cause a 

 portion of the atmospheric tide to take the form of an elastic wave rather 

 than of a fluidal movement; that is, the tidal force may produce alternate 

 expansion and compression of the air such as would not be possible in 

 water because of its incompressibility. Such expansional and compressional 

 states of the atmosphere would be reheved by a prompt return to the un- 

 strained condition as fast as the tidal forces were in any measure withdrawn 



