40 REPORT OF THE CALIFORNIA EARTHQUAKE COMMISSION. 
CRACKS FORMED IN THE GROUND AND THE BREAKING OF PIPES. 
We can readily determine the amount of compression and extension that takes place; 
the movement of an earth particle is given by the expression 
Leet 
—A Dh ote 
y COs ( 2) 
where A is the amplitude, P the period, > the wave-length, ¢ the time, and x the dis- 
tance, measured in the direction of propagation; the compression and extension is given 
by 
dx i 
and its maximum value is 27 A/X. For a wave whose period is a half second and whose 
velocity is 4 miles a second, ’ would be 2 miles or say 10,500 feet, and if A were 0.2 of 
a foot, the wave would cause successive compressions and expansions of short lengths of 
rock amounting to 1: 8350 of the length. If c is the compression or expansion per unit 
length and M the modulus of elasticity, which for granite with a free upper surface 
would be about 7.66 million pounds per square inch, the force exerted is cM, or, in the 
7.66 x 108 
8350 
than the force necessary to break granite by crushing (6 to 10 tons per square inch), 
but the strength of granite under tension must be less than under compression, altho 
its value is not known. 
Cast-iron, which resembles granite in its general structure, requires four or five times 
as large a force to break it by crushing as by stretching; it therefore seems possible that 
the numerous cracks observed in the region west of Point Reyes station may be due to 
the vibrations. In the case of vibrations passing thru alluvium or decomposed rock, the 
wave-length will be shorter, the amplitude greater, and the breaking strength much less 
in comparison with the modulus of elasticity ; so that we should expect in places, where 
the condition of the ground is favorable, even at a distance from the earthquake’s origin, 
that cracks would open and close at right angles to the direction of propagation; it is 
to this cause we must refer the opening of cracks and the projection of water, mud, and 
sand into the air, which has frequently been described in connection with strong earth- 
quakes. This phenomenon was seen in the neighborhood of Salinas (vol. 1, p. 245). In 
very unconsolidated deposits cracks may be left open by the compression of the inter- 
vening material and water arising in the cracks may form craterlets (vol. 1, pp. 229, 231, 
338) ; but cracks formed by slumping of the ground, altho started by the vibrations, are 
practically due to gravity. 
Pipes in the ground were subjected to similar compressions and extensions, the measure 
of the force being Hc, where H is Young’s modulus for the material of the pipe. For 
cast-iron F is about 5,000 tons to the square inch and with an extension of 1: 8,350, the 
force tending to rupture it would be about 0.6 ton to the square inch. For wrought-iron 
E is about 13,000 tons to the square inch and the force developt by the above expansion 
would be 1.6 tons; it requires from 20 to 28 tons to break wrought-iron by tension, and 
16 to 20 tons by crushing; but at the joints the pipes are weaker. On the whole, not 
many pipes in the ground were broken by the vibrations, tho the stronger vibrations in 
alluvial soil must have broken a number. A very good example is the pipe near Salinas 
(vol. 1, p. 245), which was broken in many places; in some places the ends were separated 
as much as 3 feet, in others they overlapt as much as 4 feet; and they showed that they 
had been hammered together and had not simply been pulled apart. A pipe seen near 
Alvarado had had the same experience (vol. 1, p. 305). 
case of the above wave, , or 920 pounds per square inch. This is much less 
