672 ME. MALLET ON THE TEANSIT-VELOCITY OE EAETHQTJAKE VAYES. 
To apply the results thus obtained to those of experimental wave-transmission at 
Holyhead. 
Poisson has shown* that the velocity of wave-transmission (sound) in longitudinal 
vibrations of elastic prisms is 
y2_^ 
P ' 
(I-) 
When g has its usual relation to gravity, I and^ are the length and weight of the 
prism, and ^'=^5 ^ being a weight that is capable of elongating the prism by an 
amount —ll, or extending it to the length 
/(l-fS). 
Substituting, we have 
pi ’ 
but 
W being the weight capable of doubling the length of the prism. Therefore 
or 
V=v/yL, 
(II,) 
So that L being the modulus of elasticity of the solid, expressed in feet, the velocity of 
wave-transmission through it, if absolutely homogeneous and unbroken, is 
V=:5-674^/L (III.) 
Where, owing to want of homogeneity, or to shattering, or other such condition, as 
found in natural rock, the experimental value of V ditfers from the above theoretic one, 
we may still express the former by the same general form of equation — 
r=as/U (IV.) 
in which the coefficient a expresses the ratio to \/ g that the actual or experimental 
bears to the theoretic (or maximum possible) velocity of wave-transmission. 
In the slate- and quartz-rocks of Holyhead, I ascertained the mean lowest velocity of 
wave-transmission (for small explosions or impulses) to be 1089 feet per second (omitting 
decimals), the mean highest velocity 1352 feet per second, and the general mean velocity 
from all, 1220 feet per second. 
Applying equation (IV.) to these numbers, and adopting the values of L given in 
Table XI. (mean of Nos. 9 and 10), we obtain 
V' . . 
“=■ 71 ’ 
* Traite de Mecanique, vol. ii. p. 319. 
