ON SEISMOLOGICAL INVESTIGATIONS, 67 
mere glance at the figures shows that the number of recorded earth- 
quakes steadily increases; in the first 50 years (1790-1839) there are 
471, and in the last 50 years (1850-1899) there are 1555. The number 
of eruptions also increases, though not so markedly: in the first 
50 years there are 465, and in the last 50 years 601. Now it seems 
probable that these increases are chiefly due to increased facilities for 
newsgathering; at any rate, a real secular change of this kind would 
require independent evidence. Further, it is clear that if the two 
series of numbers are both steadily increasing there will be a tendency 
for small numbers in one series to be associated with small numbers 
in the other, and large with large—that is to say, we shall get a 
spurious correlation (or rather, a spurious increase in the correlation) 
due to this cause. 
‘Hence a further computation was undertaken in which the secular 
effects were eliminated in the following manner :— 
‘Taking 10 yearly sums, the numbers and their logs are :— 
j | ] j | 
No. of No. of 
Years Erup- | Log. | Cale. O—C || Earth- | Log. | Cale. 0-C 
tions | quakes 
1790-9 . r 84 1°92 | 1°71 | +21 74 1°87 | 1°67 | +-20 
1800-9 . : 61 1:78 | 1:84 | —-06 74 1°87 | 1°81 | +°06 
1810-9 . 5 65 181 | 1°94 | —'13 89 1:95 | 1:95 00 
1820-9 . A 142 2715 | 2°01 | —-06 121 2°08 | 2°07} +°01 
1830-9 . : 113 2°05 | 2:07 | —-02 113 2°05 | 2716; —'ll 
1840-9 . 4 127 2°10 | 2°10 00 183 2°26 | 2°26 00 
|1850-9 . ; 160 2°20 | 2°11 | +09 299 2°48 | 2°34 | +:14 
—|1860-9 . é 107 2°03 | 2°09 | —-06 337 2°53 | 2-41 | +:°12 
-|1870-9 . : 144 | 2°16 | 2:06} +°10 || 290 2°46 | 247) —-Ol 
1880-9 . 5 113 | 2°05} 2°00 | +°05 | 374 2°57 | 2°51 +:06 
{1890-9 . 77 | 1:89} 1:91 | —:02 | 255 2°51 | 2°55 |) —‘14 
‘The ‘‘ calculated ’’ columns are from the formule 
Eruptions 210+nx0020-n*x0°0114, 
Harthquakes 2'26+n x 0°087 — n? x 0'0060, 
where n is the number of the term, counting from the middle term 
(1840-9). Part of these assumed secular terms may, of course, be 
real; but we have no means of testing the point, and for the present 
we shall assume that they are spurious and therefore to be eliminated. 
“When these formule are suitably modified and applied to the 
individual years and the correlation again calculated it is found to 
be 
4 r=0°39 + 0°05. 
x 
This is still quite comparable with the former value, and the conclusion 
seems justifiable that earthquakes and eruptions are affected by the 
same cause.” | 
; XIV. Report on an Improved Seismograph. 
Experiments are being made by Mr. J. J. Shaw, of West Bromwich, 
with a view to increase the efficiency and economy of the Milne-type 
seismograph. 
B2 
