The chief features of this document are a digest of Mr. Hopkins's previously published "Mathematical Papers" on the formations of fissures, etc., by elevations and depressions, and those on the thickness of the earth's crust, based on precession, etc., which he discusses in some relations to volcanic action.
This extends to forty-one pages, the remaining eighteen pages of the Report being devoted to "Vibratory Motions of the Earth's Crust produced by Subterranean Forces--Earthquakes."
The latter consists mainly of a _résumé_ of the acknowledged laws, as delivered principally by Poisson, of formation and propagation of elastic waves and of liquid waves, by Webers, S. Russel and others--the original matter in this Report is small--and as respects the latter portion consists mainly in some problems for finding analytically the position or depth of the centre of disturbance when certain elements of the wave of shock are given, or have been supposed registered by seismometric instruments, such as that described by myself, and above referred to.[D] At the time my original Paper "On the Dynamics of Earthquakes" was published, there was little or no _experimental_ knowledge as to the actual velocity of transit of waves--analogous to those of sound, but of greater amplitude--through elastic solids. The velocity as deduced from theory, the solid being assumed quite _homogeneous_ and _continuous_, was very great, and might be taken for some of the harder and denser rock formations at 11,000 or 12,000 feet per second. That these enormous velocities of wave transit would be something near those of actual earthquake shock seemed probable to me, and was so accepted by Hopkins.
Thus, he says (Report, p. 88): "The velocity of the sea-wave, for any probable depth of the sea, will be so small as compared with that of the vibratory wave, that we may consider the time of the arrival of the latter at the place of observation as coincident with that of the departure of the sea-wave from the centre of divergence."
In my original Paper (Dynamic, &c.), I had suggested, as an important object, to ascertain by actual experiment what might be the wave's transit rate in various rocky and incoherent formations; and having proposed this in my first "Report upon the Facts of Earthquake" to the British Association, I was enabled by its liberality to commence those experiments, in which I was ably assisted by my eldest son, then quite a lad--Dr. Jno. William Mallet, now Professor of Chemistry at the University of Virginia, U.S.; and to give account of the results, in my second Report ("Report, British Association for 1851") to that body.