1108 
MR. C. DAVISON ON THE ANNUAL 
compared with the others “almost suggests,” says Dr. Knott, “ that this semi-annual 
characteristic is almost accidental, and that with a sufficient number of observations it 
might vanish altogether ” ; “ and yet,” he adds, “ it seems too general to be accidental.” 
It appears to me, therefore, desirable to examine the seismic records of other 
countries besides those which were at the disposal of Dr. Knott in 1884, and this I 
shall endeavour to do in the present paper. The relation of seismic periodicity to 
intensity will also be considered, though the materials are somewhat inadequate for 
the purpose. In the closing paragraphs, a summary is given of the principal 
conclusions arrived at, and an attempt is made to show that the annual variation in 
barometric pressure may be the cause of the annual seismic period. 
With regard to the origin of the semi-annual period, I regret that I am unable to 
offer any definite suggestion. 
Method of Investigation. 
2 . Dr. Knott’s Method .—If f{6) be a periodic function of a variable we may 
write 
f[d) = ag + (^1 cos {6 + ctj -f cos (29 + a?) + • • • "T ««cos (/i 0 otn) , 
from which it follows that 
, cusm2(h , X , , a„sin?z</) / , x , 
”1“ m cos (29 fi- tto) -j- . . . -j- y cos (n9 -j- a,;) fi- . . .; 
2(f) 
n(f) 
the latter equation giving the mean value of f (9) through an interval ^ on either 
side of 9. 
Let T and S be the values of the last series when (/> is put equal to tt/I and 7r/2 
respectively, then 
T = (Xg -f " cos (9 -fi ad ^ cos (29 -j- a.,) -j- . . . 
•K TT ' 
, 4rt„sinJ7i7r / ^ ^ , 
+ -^ — COS (n9 + a„) -i- . . . , 
nir ' 
+ 
TT 
sin |?i7r 
S Ug -f — COS (9 + “i) — ^ COS ( 3 ^ ttg) + . . . 
OTT 
niT 
cos (n9 +««)+..., 
