78 Prof. C. (t. Knott on Reflexion and Refraction of 



In the same way, calculating for the incident distortional 

 wave, we obtain 



cosec 2 <£ = -00726 cosec 9 ff. 



Hence if <j> = 90°, 6' = 4° 53' fully. Thus, whatever the 

 incidence, the refracted wave goes off in a direction never 

 more than 5° removed from the normal. 



Into a detailed calculation regarding the distribution of 

 the energy, it is not necessary to go*. The amount of 

 energy which gets into the air as a condensational wave is 

 extremely small compared to the vibratory energy existing 

 in the rock. With the constants as given above it is doubtful 

 if for any incidence as much as the thousandth part of the 

 original energy is so transmitted into the air. For most 

 incidences it is distinctly less. 



It is thus easy to see why in earthquakes which may be 

 accompanied by considerable mechanical violence, there may 

 be no audible sound phenomena. The essential condition for 

 the production of earthquake sounds is a sufficiently pronounced 

 vertical motion with a sufficiently rapid period. According 

 to Professor Sekiya's recent analysis f, vertical motion as 

 measured on the seismographs is absent from most of the 

 earthquakes that shake Japan. When vertical motion is 

 apparent, it is in the more intense shocks. We cannot 

 assume of course that the vertical motion is absent in those 

 cases in which the seismograph shows no trace of it. It is 

 always much smaller than the horizontal motion, being on 

 the average only one-sixth of it. Hence when the horizontal 

 motion is itself very small, as in the weaker shocks, the 

 vertical motion may be too small to affect the seismograph. 

 Or, as is more than likely, it may have too short a period to 

 make itself felt, even though its amplitude may be large 

 enough to be otherwise apparent. We must be careful 

 indeed not to confuse the seismograph indications with the 

 rapid elastic vibrations which, seem a necessity for the pro- 

 duction of sound phenomena. That the quick short-period 

 motions that precede the big wave as shown on our seismo- 

 graphs may co-exist along with vertical vibrations sufficiently 

 rapid to cause audible sounds is highly probable ; but in no 

 other sense can they be regarded as " connected " with those 

 sounds, as seems to be suggested by Milne. These rapid 

 sinuosities appear on all the best diagrams showing the 



* [This calculation is now given below, Part II. Case (4).] 

 t See Transactions Seism. Soc. of Japan, vol. xii. ; also the Journal 

 of the College of Science, Imperial University, vol. ii, 



