_d._ By measurements of the horizontal and vertical distances of overthrow or of projection, to infer either the _velocity_ of projection, or _angle of emergence_. Fractures by shock present their planes always nearly in directions transverse to the wave path. Projections or overthrow take place (unless secondarily disturbed) in the line of the wave path, or in the vertical plane passing through it: but the direction of fall or overthrow may be either in the same direction as the wave transit (_i.e._, as the motion of the wave particle in the first semiphase), or contrary to it. It is thus obvious that the principal phenomena presented by the effects of earthquake shock upon the objects usually occurring upon the surface of the inhabited parts of the earth, resolve themselves into problems of three orders, and are all amenable to mechanical treatment, viz.: 1. Problems relating to the direction and amount of velocity producing fracture or fissures. 2. Problems relating to the single or multiplied oscillations of bodies, considered as compound pendulums. 3. Problems referable to the theory of projectiles. These three may combine in several cases, and on the part of the observer must combine with measurements, angular and linear, and with geodetic operations to be conducted in the shaken country. The methods of application in detail are described fully, as well as their actual application and results, in my work published in 1862 (2 vols.), entitled "The First Principles of Observational Seismology, as developed in the Report to the Royal Society of London of the Expedition made by Command of the Society into the Interior of the Kingdom of Naples, to investigate the Circumstances of the Great Earthquake of December, 1857," to the many illustrations of which the pecuniary grant, in aid, of £300 was most liberally made to the publishers (Messrs. Chapman and Hall) by the Society.