AND SEMI-ANNUAL SEISMIC PERIODS. 
1113 
December, the number of shocks felt during the six winter months is 3357, the 
number during the six summer months 2142, and the ratio of one to the other 1'57. 
The amplitude of the annual period is '35, and the value of the ratio 1 + 2a/7r : 
1 — ^ajiT is 1’56. 
10. Duration of the Seismic Record .—It has been assumed in the preceding j)ara- 
graphs that the curve obtained by plotting the number of eai'thquakes felt in each 
month is not affected by periods of longer duration than one year, or by periods which, 
are not exact fractions of a year. The assumption may be tested by considering a 
period of 12m + n months, where m is either zero or a positive integer. The number 
of earthquakes (F,.) belonging to this period felt during the month of each year 
may then be represented by 
a cos a. -{• a cos (a + 12yS) + . . . + a cos [a + (\- l).12^], 
where /3 = 27rj{l2m + n), and X is the number of years over which the seismic record 
extends. Then 
F,. = a cos [a + (X — 1). 6^] sin 6X^/sin G/3 ; 
and the value of F,. is zero whatever be the value of a if 6X/3 = /ctt, where k is an 
integer, i.e., when X = ^-(I2m + 7^)/12. Hence, F,. is zero for all values of r, and 
consequently our method of investigation is not affected by the period considered, 
provided the interval over which the seismic record extends includes an exact number 
of these periods. 
But whatever be the number of such periods included in the seismic record, the 
absolute error introduced by a given uneliminated portion of a period will be 
constant, and, therefore, the relative error will be the less the greater the interval 
over which the record extends. 
On another account, also, it is desirable that this interval should be as long as 
possible. For, owing chiefly to orogenic causes, there are often series of frequently 
recurring shocks, lasting for one or more months, which, if the record be a short one 
or imperfect, would unduly increase the numbers felt during those months. The 
record should therefore be an extensive one in order to eliminate the effects of 
occasional variability in the rate of orogenic action and to bring into special pro¬ 
minence those of a periodic character. 
MDCCCXCin.—A. 7 c 
