96 REPORTS ON THE STATE OF SCIENCE.—1912. 
the end of seven periods of fifteen months. Thus, what would usually 
be a 7x15=105 months’ interval is reduced effectively to 104. The 
time is reckoned backwards, as it seemed best to begin with more 
modern observations. 
Total No. of | Coefficients of Deviation 
Initial Date Earthquakes Cos @ Sin @ Maximum from Mean 
June 1909 409 | — 90 +. 6°4 145° +195° 
| Oct. 1905 BSA oie V1) ect 7°8 — 34 | .— 24 +26 
Feb. 1897 809 | + 58 —60 | — 48 +49 
Feb. 1871 FIG? ee 67 i cal hee +31 
Feb. 1845 35.) 483 — =113 —63 
Feb. 1819 19 treet Te oe ee +14 
Feb. 1793 201 +12°9 — 48 — 20 +30 
Feb. 1767 386 = 78 = aa —149 —99 
Feb. 1689 262 83 == Wega aye —68 
Feb. 1611 159 + 2-4 ee hae ae +37 
Feb. 1533 161 +11'5 Sy ae ee +60 
Feb. 1455 78 Sey 44) Pee =19 
Feb. 1377 92 + 50 +11 ens +63 
| Mean | +49 — 58 — 50 
a | 
Each group extends from the initial date given in the first column 
to the next initial date. The first group is thus from June 1909 to 
October 1905, and contains three periods only: and it is directly dis- 
cordant. This anomaly is under investigation, and for the present we 
will omit the group. The mean formula is then: 
+ 4:9 cos @— 5:8 sin 6 = 7°6 cos (@ + 50°), 
the maximum occurring in December 1905, April 1897, &c., two months 
later than the initial date. 
But a simple harmonic scarcely does justice to the facts. If we 
add together the results for corresponding months for the period of best 
observations, i.¢., February 1793 to October 1905 (it will be seen how 
broken is the record in the earlier centuries), and divide by ten so as to 
get simpler numbers, we get the following sequence, counting the 
time now forwards in the usual direction. 
22 20 22 21.18 21 18 18 20 17 18 17 19 16 17 
—— = a ee —SS—— ———— ——— 
64 60 56 52 52 
The starting-point has of course been selected to bring out the main 
feature, which is an almost steady fall, followed by a very rapid rise 
when we return to the beginning. The idea suggested is that of accu- 
mulation. The outward manifestations of stress (earthquakes) fall off in 
number steadily, but this means that stress is accumulating, and ulti- 
mately there is an outburst of numerous earthquakes again. If this is 
the explanation, it may be that the inequality is only quasi-periodic, as 
in the illustration (quoted first by Dr. Johnstone Stoney) of a pot boiling 
over and damping the fire, which would tend to recur roughly after a 
