Analysis of Microseismogrums. 469 



increase, in good agreement with the value for 1 obtained 

 from the equation for the periods, namely 119°'2. A leasi 

 square solution from the values obtained for </> l increases the 

 value of 6 1 by a degree, making it 120 c '2. This value 

 indicates an oscillation whose period is three of the units 

 of t or 6^ seconds. But the values of Cj show a rise from a 

 value which is nearly zero to one of 25 followed by a fall. 

 On plotting these values against the time, it is seen that they 

 can be well represented by the expresion 22 sin (6°£ - 12°) ; 

 and since the unit of time is 2*14 seconds, this indicates 

 a complete fluctuation of amplitude in 2 14 minutes. 

 - The phase when £ = of the angle <£ A may be taken 

 without sensible error to be zero ; hence the complete 

 expression for the first periodic term becomes 



22-sin(6°£-12 o )sinl20°-2£. . . . (17) 



8. The values of (f} 2 exhibit much greater irregularities 

 than those of cj? 1 , particularly in the neighbourhood of £ = 10, 

 where' the amplitudes are nearly zero. If, however, we 

 assume that there is a change of phase at this point of 180°, 

 we can remove the most serious discrepancies. The mean of 

 the first 9 values of (/> 2 gives 323° as the argument at £=6, 

 and the mean of the last 9 values gives 44° as the argument 

 at £ = 24. Increasing 323° by 180° we obtain for the in- 

 crement of $2 per unit of £, 134 0, 5, which is in good agree- 

 ment with the value 136°* 5 previously obtained. 



Plotting the values of c 2 against t, taking those before 

 £ = 11 to be negative on account of the change of phase by 

 180°, we find that the points are satisfactorily represented 

 by 20 sin (5°£ — 70°j, and the complete expression for the 

 second periodic term is 



20 sin (5° £-70°) sin (134°-5 £ + 56°). . . (18) 



It is to be noted that no great degree of accuracy is 

 claimed for the coefficients 6° and 5° of £ in the factors 

 sin (6°£ — 12 c ) and sin (5° £ — 70°), the data analysed being 

 too restricted in extent for a closer determination, but they 

 are probably correct to within 10 per cent. 



9. An obvious interpretation of the results here obtained 

 is that the microseismic motion was due to two groups of 

 waves of periods of 6-§- and 5| seconds respectively. The 

 group velocities were slightly different, but were of such an 

 order that on the average each group attained a maximum 

 within an interval of two minutes. Since the maximum 

 amplitudes were nearly equal, the combination of the two 



