ME. MALLET ON THE TRANSIT-VELOCITY OF EARTHQUAKE WAVES. 673 
and for the three preceding velocities, a has the following values : — 
ft. per sec. 
1.. .V'=1089 
2.. . V'=1352 
3.. .V'=1220 
1089 1089 
V2917262~ 
1708~ 
1.852 
1352 
\/29l7262 
1708 
1220 
1220 
'v/2917262 1708 
0-637 
0-791 
0-714 
The actual velocity of wave-transmission in the slate and quartz together, therefore, 
was to the theoretic velocity due to the solid material as 
« : or 0-714 : 5-774, or 1-00 : 7-946. 
From which it results that nearly seven-eighths of the full velocity of wave-transmission 
due to the material is lost by reason of the heterogeneity and discontinuity or shattering 
of the rocky mass, as it is found piled together in nature. 
This loss would be larger with still smaller originating impulses, and vice versd, but in 
what proportion we are not at present in a position to know. 
If we may for a moment allude to final causes, we cannot but be struck with this 
beneficent result (amongst others) arising from the shattered and broken-up condition 
of all the rocky masses forming the habitable surface of our globe, — that the otherwise 
enormous transit-velocity of the wave-form in earthquake shocks is by this simple means 
so reduced. 
That this retardation is mainly effected by the multiplied subdivisions of the rock, 
and in a very minor degree by difierences in the elastic moduli of rock of different 
species, is apparent on examining the Tables IV. and V. of the previous part of this 
Report referring to the experiments at Holyhead. 
Although, therefore, we are now enabled, from what precedes, to calculate values 
for a, for the slate rocks and for the quartz of Holyhead, separately, and thus obtain 
separate values for V', for each of those rocks ; the result would probably be more or 
less delusive, as we have no possible means of deciding what is the relative amount of 
shattering and discontinuity, for equal horizontal distances, in each of these two rocks, 
nor what the relative retarding powers of planes of separation running in variable direc- 
tions, and at all possible angles across the line of wave-transit, as compared with their 
retarding powers if either all transverse to, or all in the same direction as, the wave- 
path. 
The greatest possible mean velocity of wave-propagation, m rock as perfectly solid 
and unshattered as our experimental cubes, is determinable for both slate and quartz in 
the two directions of transmission, viz. transverse and in the line of lamination, from 
equation (HI.), and the mean values of L in Nos. 9 and 10, and II and 12, Table XI., 
as follows : — 
ft. per sec. 
Mean of slate and quartz transverse to lamination . . . V= 5-674^/2917262 = 96 91 
Mean of slate and quartz in line of lamination V =5-674^/ 910914 =5415 
