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.

It is not my intention here, nor would space allow, of my going into the details of observation, nor of the deductions and conclusions I have recorded in those volumes. I have referred to their contents as marking the advent of a new method. I have ventured to call it a new organon in the investigation of Earthquakes, and, through them, of the deep interior of our earth; and will only add that the method, on this its very first trial, proved fertile and successful. The depth of focus for this shock of December, 1857, was about seven to eight geographical miles below sea level, roughly stated. It gives me great pleasure to add that my friend, Dr. Oldham, Director-General of the Geological Survey of India, has since applied these same methods to the phenomena of the great Cachar Earthquake of the 10th January, 1869, and with success. The pressure of official duties has, he informs me, as yet prevented his fully working out his results, but they appear so far to indicate, as we should expect, a depth of focus or origin considerably greater than in the European case of 1857. Some account of Dr. Oldham's results were this year communicated to the Geological Society of London through myself, they are of great interest and importance.

Such, briefly and imperfectly sketched, is the existing state of Seismology. As a branch of exact science it is, as it were, an affair of yesterday. It is with reluctance that I have been compelled, in this review, to refer to my own work so prominently. The harvest has been and still is plenteous, but in this field of intellectual work the labourers are few. This must continue to be so as long as Geology shall continue to be viewed in public estimation (in England at least) as a fashionable toy, that everyone who has been to school is supposed capable of handling; and until all who profess to be geologists shall have learnt that, to make sound progress, they must first become mathematicians, physicists and chemists.

It is to the general imperfect knowledge of these sciences amongst geologists that speculative errors show such vitality, and that Geology makes such poor progress towards becoming the interpretation of the world as a machine (Erdkunde).

It is for the same reason that Seismology and Vulcanology make little progress; the first cannot be pursued beyond its present boundaries, nor can even its present position be understood or explained by anyone unfamiliar with the laws of wave motion, of all classes of waves; and it would be easy to show, by quoting from various British or foreign text-books on Geology, how extremely imperfect is the grasp of some of the authors upon the subject of earthquake-wave motion, even such as they admit and endeavour to explain and apply: in fact, many geologists appear never to have framed to themselves any clear idea of what is a wave of any sort, liquid or elastic. The general silence as to seismic theory of French geological writers is remarkable, to whatever cause attributable. It has been said that French philosophers show themselves little disposed to acknowledge or to follow the lead of their foreign compeers in any branch of science. If this be true, or in so far as it may be so, it is unworthy of French science, which has such boundless claims upon our homage. I am disposed to attribute the fact in this case to other circumstances; and, amongst these, to the small extent to which our language is known amongst French scientific men.

Germany has shown more desire to cultivate this branch of science. Although, as yet, the distinct enunciation of its fundamental principles has but sparsely found its way into her text-books, several able monographs, such as those of Schmidt and of Höttinger, prove how completely some of her philosophers have mastered and how well applied them. The men of science of Northern Italy, amongst whom so many glorious names are to be found on the roll of discovery, have shown themselves quite alive to the importance of Seismology; and I know of no more clear, exact and popular exposition of its principles and application, and of its cosmical relations, than is to be found in a small volume by Professor Gerolamo Boccardo, published at Genoa in 1869, entitled Sismopirologia Terremoti, Vulcani e lente oscillazione del suolo, saggio di una teoria di Geographia Fisica.

My object, so far, has been to mark the progress of ascertained theoretic notions as to Seismology. I have, therefore, passed without notice many speculative monographs, and the treatment upon Earthquakes, whether speculative or historical, and however able, that constitutes a prominent feature of nearly all systematic works on Geology.

That which may be at present viewed as achieved and certainly ascertained in theoretic Seismology is the clear conception of the nature of earthquake motion; the relations to it of great sea or other water wave commotions; the relations to it of sound waves—as to which, however, more remains to be known; and the relations of all these to secondary effects, tending in various ways to modify more or less the topographic and other conditions of the land or sea bottom. And in descriptive Seismology the present distribution of the earthquake bands or regions of greatest seismic prevalence and activity are tolerably ascertained, and their connection with volcanic lines and those of elevation rendered more evident. Viewed alone, nothing can yet be said to be absolutely ascertained as to the immediately antecedent cause or causes of the impulse. The function of Earthquake, as part of the cosmical machine, has become more clear, as the distinctive boundaries between Earthquake and permanent elevation of the earth have been made evident; and it has been seen that Earthquake, however contemporaneous occasionally with permanent elevation, is not the cause, though it may be one of the consequences of the same forces which produce elevation; and thus, that an infinite number of Earthquakes, however violent, and acting through however prolonged a time, can never act as an agent of permanent elevation, unless, indeed, on that minute scale in which surface elevation may arise from secondary effects, like that of the Ullah Bund.

Much remains to be done, and much may be expected even from the continuation, if done in a systematic and organised manner, of the statistic record of Earthquakes in connection with those other branches of cosmical statistics, Climatology, Meteorology, Terrestrial Magnetism, etc., the