10 REPORT OF THE CALIFORNIA EARTHQUAKE COMMISSION, 
but had been retarded by 6 seconds in time. ‘Two of the astronomical clocks at Mare 
Island continued going after the shock, but they lost 20 seconds, which Professor See 
ascribed to ‘‘the rubbing of the pendulum points against the index ledges, which was 
also clearly shown by the brightening of the metal of the indexes.” Altho this friction 
must have acted, it hardly seems sufficient to account for so large a loss in the minute or 
so of the strong shocks, and it is not unlikely that these clocks were stopt and started 
again. Some clocks must have been stopt at very nearly the correct time of the arrival 
of the shock, but it is impossible to distinguish them from other clocks, whose times are 
claimed to be correct, but which were evidently wrong; it is best, therefore, only to use 
times from the first four observations mentioned, which have been chosen because they 
can be relied on as very nearly correct. 
The clocks which stopt evidently too late, and those which continued going but with 
the loss of some seconds of time, call attention to an error which may be made if we 
accept the time of a stopt clock as determining the time of the heavy shock. Let us 
notice in the first place that it is scarcely possible for the time thus determined to be too 
early; for, if the pendulum is made to vibrate too rapidly for a beat or two before it is 
stopt, the time is advanced; and if the pendulum is stopt, started, and stopt again, 
the clock will mark too late a time. It is only in case the gentler motion preceding the 
heavy shock should cause the pendulums to vibrate too slowly, that the stopt clock would 
indicate too early a time; but this gentler motion is just as apt to make the pendulums 
vibrate too fast. The difference between the time of the heavy shock at Mount Hamilton, 
which does not depend upon a stopt clock, and the times recorded by the stopt clocks at 
San Rafael, Mare Island, and Berkeley, make it evident that the latter could not indicate 
a time materially too late, unless we assume a rate of propagation of the disturbance much 
too low to be permissible. It is extremely probable, however, that the clocks did indicate 
a time slightly too late, and I have therefore taken for the times of arrival of the heavy 
shock at Mare Island and Berkeley one second earlier than the clocks indicated; these 
‘ clocks were all astronomical clocks, and, with their known corrections, were practically 
correct just before the shock. The clocks at San Rafael were not astronomical clocks and 
may have been a little too fast; we can take 5" 12™ 32°, a half second earlier than their 
average, as the time of the shock at that place. The time at Mount Hamilton requires 
no modification. 
We have therefore for the times, after 5" 12™ 30%, of arrival of the heavy shock and the 
distances of the stations from the fault-line: San Rafael, ¢, = 2 seconds, d, = 16 km.; Mare 
Island, tg = 5, dg = 42; Berkeley, ¢, = 8, dj = 29; Mount Hamilton, t, = 15, d, = 33.7. 
A glance at these data show that the shock was not simultaneous along the fault-line, for 
Berkeley and Mount Hamilton, less distant from the fault-line than Mare Island, felt the 
shock later. The times, with the positions of the stations as shown in fig. 1, indicate 
that the strong shock originated in a limited area somewhere to the northwest of San 
Rafael. 
If, as in the case of the beginning of the shock, we use these four observations to deter- 
mine our four unknown quantities, we find an imaginary value for the depth of the cen- 
trum, showing that the observations are not perfectly accurate. We may then, as before, 
assume various positions for the centrum and find by the method of least squares what 
time of occurrence and what velocity of propagation will make the sum of the squares 
of the errors least. The following table shows the results of these determinations ; Yp is the 
distance from a point on the fault-line opposite San Francisco to the origin, measured 
towards the northwest; 2, is the depth of the centrum below the surface; fo, the time of 
occurrence, in seconds after 5" 12™ 308; v, the velocity of propagation in kilometers per 
second; and A’, the sum of the squares of the errors in seconds between the calculated and 
observed times. It is to be noticed that the velocity is too high except in one case. 
