6 REPORT OF THE CALIFORNIA EARTHQUAKE COMMISSION. 
to awaken him, and therefore that the time of the arrival was 5h 12™ 178. This time is 
far less accurate than the others but is certainly not more than a few seconds wrong and is 
important in estimating the origin of the shock on account 
ot | of the location of Ukiah with respect to the other stations. 
U This will be readily seen on referring to map No. 23 and 
to fig. 1, in which the long vertical line represents the 
fault, and the positions of stations with respect to it are 
shown. 
There are, then, only four observations which should be 
taken into account in estimating the position of the cen- 
trum, which, we may assume, lies somewhere in the 
apparently vertical plane of the fault. The question 
arises whether the slip took place at various parts of 
the fault simultaneously, or, whether it occurred first over 
a limited area, and the stress, being relieved here, in- 
creased at other places, and thus the rupture spread along 
the fault, in both directions, at a rate probably somewhat 
less than that of the propagation of elastic waves of com- 
pression. In the first case the movement would have 
been propagated at right angles to the fault, and would 
have arrived at the various stations after intervals of 
time proportional to their distances from the fault-line. 
Taking our origin of time at 5" 12™ 00° we have the 
following data (where the ?s are the times of arrival 
after 55 12™ 008, and the a’s are the distances from the 
fault-line): San Francisco, ¢; = 0 seconds, d, = 12 km.; 
Berkeley, t, = 6, d, = 29; Mount Hamilton, t, = 12, d; = 
33.7, Ukiah, t, = 17, d, = 42.6. (These distances are 
determined from the maps and are not taken from fig. 1, 
where the fault is represented as perfectly straight.) 
If we attempt from these data to determine the most 
probable value of the velocity and of the time of occur- 
rence by the method of least squares, we find a velocity 
of 1.8 km./sec. and a time of 5° 11™ 52.5°, with errors 
of —0.9, + 2.5, -0.8, —1.0 seconds for the stations in the 
order given above; the sum of the squares of the errors 
is 8.6; the positive sign indicates that the observed times 
were too early, and vice versa. The small velocity caleu- 
lated is quite inadmissible; and we therefore try the other 
alternative to see if it does not yield better results. We 
may consider that we have four unknown quantities to 
be determined: the time of the shock, the distance of the 
centrum measured along the fault-line from a given point 
ey of reference, its depth below the surface, and the rate of 
propagation. Four observations are sufficient to deter- 
160 

140 
120 
60 
-20 
-40 
-60 
-80 
: ) 
Ukiah «2 2 7 884 + >: 8h8 mine these four quantities, but the observations we have 
M Tsland cea vel a's 4215:6) yea cs 1 1 = 
San Francisco ont ey em lead to impossible results, which may be seen by a general 
Berkeley vuiltea. . Jae... gag comparison of the positions of the stations and the times 
observed at them. For evidently there is no point on 
the fault-line so situated that the difference of the distances from it of Berkeley and 
San Francisco is half the difference of the distances from it of Mount Hamilton and 
