_ ON THE FACTS AND THEORY OF EARTHQUAKE PHENOMENA. 97 
Corol. 2. Independently of any diminution in the absolute velocity of the 
ae earth-wave, the apparent horizontal velocity will diminish rapidly, 
approaching indefinitely the limit V. This is evident from the 
geometrical considerations arising from the fact that PX is 
always equal to QY. 
It is obvious, then, that by the establishment of these very simple and in- 
expensive seismometers, and connecting them galvanically (as respects their 
registration) by methods now become both familiar and simple, we may get 
good first approximations to one of the most important questions of the 
physics of our glube—a knowledge of the depth from which earthquake 
impulses arrive. 
Simple and inexpensive, however, as the apparatus recommended is, its 
establishment in the only way in which it can be of much real use, namely 
by connected distant stations, involves the choice of seismic areas fitted for 
the purpose, and the support and aid of governments, if not for outfit, at 
least for appointment of observers, and police protection of stations and wires. 
It is to be hoped that even these may not be withheld as the advancing know- 
ledge of the importance to physical geology of seismic research becomes better 
understood and diffused. Meanwhile a still simpler form of rough seismo- 
meter, suited to the resources of distant and isolated observers, may be with 
advantage, perhaps, pointed out,—and also an indirect method, by which the 
depth of earthquake origin may be approximated, without the use of seismo- 
meters of any sort. The form of seismometer about to be deseribed is most 
applicable to seismic districts where the angle of wave-emergence is not 
steep, 2. e. where the shocks are usually nearly horizontal. 
If any homogeneous, parallelopiped, or rectangular prism, standing on 
end, upon a level surface, be upset by its own inertia, the supporting sur- 
face being suddenly moved beneath it, in the direction of its own plane (as 
by the horizontal component of an earthquake shock), it may be shown 
that the velocity of the surface must be 
A s—=—~., (1—cos 0 
Vis go V FB Ex ( cos’@. ) 
where a is the altitude of the solid, d its diameter of base, and @ the angle 
formed by the side and a line drawn through the centre of gravity to the 
extremity of the base, and V?=2gh. 
_ This velocity is independent of the density or material of the solid, 
because the oversetting force, being its own inertia, is always proportionate 
to the density. With a given velocity V, therefore, it is possible to as- 
‘sign the dimensions a and b such, that it shall be just overset; and with 
this velocity another solid, having @ greater, shall remain unmoved,—as- 
suming always that friction upon the supporting surface gives sufficient 
adhesion to cause the solid to upset, and not to slide (partly or wholly) 
without upsetting. 
_ If in place of a square prism like a wall, the solid be a right cylinder, such 
as a pillar, the diameter of whose base, as before, is &; then 
156°4-16a2 
tm 
br 12a2 
and from this very simple expression for the horizontal velocity, for which I 
“am indebted to my friend Professor Haughton, it is easy to construct a seis- 
Mometer of the greatest simplicity, that (in the absence of better means) 
hall give, within a narrow limit, the actual velocity of shock. 
1858 H 
xg Va? +01 —cos 0); 
