THE TIME AND ORIGIN OF THE SHOCK. 7 
San Francisco, and one-third the difference of the distances of Ukiah and San Francisco; 
which shows that the observations are not accurate enough to make an exact determina- 
tion of the unknown quantities possible. We are led therefore to assume a rate of prop- 
agation, and by trial to find the place on the fault-plane which will accord best with 
the observations; that is, which will make the sum of the squares of the errors least. 
In the neighborhood of an earthquake origin, the preliminary tremors, the second phase, 
and the long waves (which will be described further on) are not separately distinguish- 
able; and there are very few and unsatisfactory observations regarding the rate at 
which the disturbance is propagated. 
Professor Imamura ' calculates the velocity as 7.5 km./sec. from observations at Tokyo 
of earthquakes originating at an average distance of 679 km., the greatest distance being 
less than 1,300 km. Corresponding observations at Osaka give a velocity of 7.9 km./sec. 
for an average distance of 792 km., but they are rendered unreliable on account of the 
poor clock at that station. By the difference method, that is, by dividing the difference 
of the distance from the origin of two stations by the difference of time of arrival at 
them, he finds an average velocity of 12.1 km./sec., the stations ranging in distance 
between 284 and 1,285 km. from the origin. From observations at Tokyo and Mizusawa 
he finds by a similar method an average velocity of 9.6 km./sec. for an average distance 
of 522 km. from the origin, and 12.4 km./sec. for an average of 984 km. 
Professor Omori?’ finds for the velocity of two earthquakes between Taichu, near 
their origin in Formosa, and Tokyo, a distance of 1,620 km., 6.13 km./sec. and 6.75 
km./sec., respectively. Tokyo is 1,710 km. from the origin and Taichu 90 km. In the 
first case the time at Taichu was determined by a chronometer watch, in the second 
from the seismogram ; in both cases the Tokyo time was determined from the seismograms. 
Professor Credner * finds by the difference in time of arrival at Leipzig and Gottingen 
of two small earthquakes whose origins were about 100 km. south of Leipzig, a velocity 
of 5.9 km./sec. G6ttingen is about 200 km. from the origin. 
Professor Rizzo * from observations of the Calabrian earthquake of 1905 at two sta- 
tions, Messina and Catania, distant 84 and 174 km., respectively, from the epicentrum, 
finds a surface velocity of 6.9 km./sec.; this supposes the centrum at the surface; a 
deeper centrum would give a slightly smaller velocity. ‘The tendency is always to obtain 
too low a value for the velocity. The strongest disturbance does not usually occur at the 
very beginning of the shock, but somewhat later; the earlier and lighter part is felt near 
the origin, but at a distance only the stronger part is observed ; this is also true of seismo- 
graph records. The velocities calculated from such observations are evidently too small. 
Professor Wiechert in a communication to the International Seismological Associa- 
tion in September, 1907, accepted 7.2 km./sec. as a fair value of the velocity near the 
surface of the earth; which is the same as the velocity near the origin. I have taken this 
value, 7.2 km./sec., as being probably as near the truth as we can come at present. With 
this velocity we find by the method of least squares that the most probable position of 
the centrum is at a point lying about 10 km. north of the point on the fault-line opposite 
San Francisco, and at a depth of 20 km. below the surface; the time of occurrence of 
the shock is 5" 11™ 57.6%; and the errors in seconds are: San Francisco, +1.1; Berkeley, 
— 3.4; Mount Hamilton, — 0.2; Ukiah, + 2.4; the sum of the squares of the errors is 
18.6 seconds. The objection to this determination is the error at Berkeley which is 


1 Publications of the Earthquake Investigation Commission in Foreign Languages, No. 18, p. 102. 
2 Note on the Transit Velocity of the ee en Earthquakes of April 14, 1906. Bull. Imperial 
Earthquake Investigation Commission, vol. 1, No. alos 
5 DieiVogtlandische Erdbebenschwarm von 13 eb? bis zum 18 Mai, 1903. Abh. math.-phys. Kl. K. 
Sachs. Gesells. d. Wissen. 1904, Bd. xxvimt, p. 153. 
4Sulla Velocita di Propagazione delli Ondi Sismiche nel Terremoto della Calabria. Accad. R. delli 
Scienze di Torino, 1905-1906, p. 312. 
