1921. j Angenheister.—A Study of Pacific Earthquakes. 211 
will give an apparent tilt or alteration of the direction of gravitational 
force. If the horizontal displacement x is harmonic, we have 
/ 27 rt \ 
£ = zsin y— + S 2 /, 
where t is the time variable, and T the periodic time of the vibration. 
The apparent tilt will be given by 
The maximum value of this apparent tilting is 
Now, the main phase of strong earthquake-waves contains vibrations 
in both the x and z directions, each equal to several millimeters, with 
periods of approximately 20 seconds. If the velocity of such waves is 
v = 3| km./sec., we have \ = vT = 70 km. Taking these values, we find 
1 = 0-09" ; [t] = 10-3". 
The apparent tilting is thus over a hundred times the true tilt, and 
in horizontal seismograph records we see that tilt is hidden by a far greater 
apparent effect. 
For near earthquakes the horizontal and vertical motions of the main 
phase are of far shorter period and of nearly the same velocity of propa¬ 
gation. The amplitudes of the x and z motions are also nearly equal, so 
that to a first approximation it will be seen that 
' i = i T= T 
[i] 2tv 2100 ; 
i.e.j the shorter the period the larger is the apparent tilt compared with 
true tilt. It thus follows that neither for near nor distant earthquakes 
can any information on tilt be obtained from ordinary seismograph 
records. 
On the other hand, the amount of tilting for near earthquakes might 
be expected to be of such a magnitude as to be capable of detection by other 
methods. The strong earthquakes of the Tonga Deep show in the main 
phase of the vibrations at Apia waves of 0-5 to 1 sec. period and up to 
5 mm. vertical displacement. This should correspond to 1-7 to 3-4 seconds 
of true tilting, and a solidly mounted telescope of medium power should 
show such tilting by observations of stars. A test of this was made at 
the Samoa Observatory in the case of the large earthquake of the 26th 
June, 1917, observations being made eight minutes after the first arrival 
of the earthquake-wave, when large vibrations were in progress due to 
the main phase. The transit instrument used has a magnification of 30. 
The micrometer eye-piece has fifteen parallel wires and two crossing- 
wires at a distance of 2-5 seconds of time apart (at Equator) or 37-5 seconds 
of arc. The cross-wires are east-west, and stars moved along a parallel 
course cross the field near one of the cross - wires. A periodic lateral 
movement of the star image of magnitude one-twentieth of the distance 
apart of the cross-wires could have been detected with certainty— i.e., 
2 seconds of arc. No tilting could be detected. The vertical movement 
