mo 
}*IR. ('. DAVISON ON THK ANNUAL 
3. If the third and succeeding terms in the expression for S — may be 
neglected in comparison with the first and second, it is evident that S — T/v/2 will 
be a maximum when the second term (which determines the six-monthly period) is a 
"minimum, and vice versct. By a slight oversight. Dr. Knott has reversed the sign of 
this term, and consequently the epochs which he obtains for the maxima of the six- 
monthly period are in reality those of the minima, and vice versd. 
4. Method adopted in this Paper .—I have described in some detail the method 
employed by Dr. Knott, for, in principle, it is the same as that adopted in this Paper. 
The chief differences are that I have used the same method in investigating both the 
annual and semi-annual periods,* and have also taken into account the variable length 
of the month. 
Whenever possible I have grouped the earthquakes in half-monthly, instead of in 
monthly intervals, the first half of February containing fourteen days, and of all other 
months fifteen days. The numbers so obtained are then reduced to equal half-monthly 
intervals of fifteen days. 
In investigating the annual period, the reduced figures for the halves of each month 
are added together, giving the numbers of earthquakes corresponding to equal monthly 
intervals of thirty days. Six-monthly means are then taken of these numbers, as in 
Dr. Knott’s method, and the mean thus obtained for the end of each month is divided 
by the average of all twelve means. 
For the semi-annual period, the reduced figures for the first half of January and the 
first half of July are added together, and so on. Six-half-monthly means are then 
taken of these numbers, and the mean thus obtained for the end of each half-month 
is divided by the average of all twelve means. 
5. Seismologists generally group earthquakes in monthly intervals, and in some 
cases I have only been able to make use of such tables. In a few others, also, for 
reasons which will be obvious, I have used them though having access to the catalogues 
on which they were founded. The results obtained in this way are not of equal value 
for purposes of comparison, as they probably depend on different definitions of the unit 
earthquake. 
In all these cases the monthly numbers are first reduced to equal intervals of thirty 
days. The discussion for the annual period is then continued as before. 
For the semi-annual period the numbers for January and July are added together, 
and so on. Three-monthly means are then taken of these six numbers, and the mean 
thus obtained for the middle of each month is divided by the average of all six means. 
The method, of course, chiefly differs from the preceding in giving fewer points upon 
the curve. 
6 . Again, in taking six-monthly means for the annual period, and dividing each by 
the average of all twelve, it is evident, from the expression for S in § 2, that every 
* In investigating the semi-annnal period by this method, it is obvious that the annual period is 
eliminated (see § 10). 
