time appears the first dawn of conscience. And so, with their regularly alternating analysis and synthesis, Rosmini would have gone on sketching for us the characteristics of the succeeding orders. But here, to our misfortune, the treatise terminates, and we have nothing but rough notes and hints as to what would have followed. We must not, however, forget the warning which Rosmini gives us, more than once, concerning his stages of cognition. He only gives us the order in which they commence; but, when once commenced, they go on through all the other periods, increasing in power and widening in application. Moreover, the acts of the understanding are always excited by some stimulus external to themselves, and depend on this stimulus; and hence, when particular stimuli come late, we shall find the corresponding cognitions belonging to earlier orders coming into being alongside of cognitions belonging to the later orders. But what of the practical application of all this? some of our readers may ask. Well, Rosmini himself answers, "I am a thinker, a psychologist. You good people of practice and experience must make the practical application of my principles for yourselves." But being human, as well as a psychologist, he cannot altogether refrain: he gives us some of his own practical applications; and of these, some are very striking and suggestive, and some of-well, very moderate utility. "The object of instruction," Rosmini tells us, "is to bring the young to know, and it may therefore be called the art of properly directing the attention of the youthful mind." "There are always three distinct parts of instruction," he tells us elsewhere: "(a) that which serves to increase in the mind of the pupil the number of cognitions he has gained in the preceding order, and to make them more perfect; (b) that which enables the pupil to pass from the order of cognition in which he is, to the next higher order; and (c) that which serves to exercise and perfect the pupil in the knowledge belonging to the order he has just reached." He adds that it is evident that the language and style of the teacher should vary according to the order of cognition attained by the child. All language that goes beyond that order is wasted; or, worse still, it will produce confusion. In treating of the first order of cognition, he points out that nature has placed perception as the foundation of the whole immense pyramid of human knowledge, and that perception therefore should be the foundation of all human education. "Nature herself leads the child to observe every thing, and to experiment on every thing; but all these experiments and perceptions are unconnected and desultory. The earliest office of the educator, therefore, consists in regulating the child's observations and experiments, so as to lead him to perceive and to perfect his perceptions." The application of this is little more than hinted at, but enough is given to show how strikingly alike Rosmini and Froebel were with regard to the earliest childhood, though each worked independently and in complete ignorance of the views of the other. Indeed, one of the chief advantages of studying Rosmini's system is the added strength and clearness and meaning which it so frequently gives to the plans of Froebel, who, as a practical teacher, stands a head and shoulders taller than his Italian contemporary. Nor is Rosmini's psychology always equal to Froebel's. He has, for instance, some strange views on language, which, but for Prof. Max Müller's championship of very similar ones, would come upon us not only as novel, but also as startling. Rosmini holds that "by language we form our ideas," and that man could not have invented that part of language which expresses abstractions." But, what is far more disconcerting to a teacher, is to find him stating that "one of the fundamental principles which should govern the instruction given, from first to last, is to consider language as the universal instrument provided by nature for the intellectual development of man," and to see, in the application, that this means that education is to be mainly a training in the use of words. Still, undoubtedly many of the practical hints he gives for the teaching of reading and writing will be found valuable, though they are applied somewhat prematurely; and much that he says on the use of music, and on pictureteaching, is highly suggestive. On the whole, however, we are inclined to think that teachers will be most struck with, and set most value on, the exposition given of the gradual development of the moral sentiment, "based as upon a rock, on the great fact, that, rooted in the depths of the child's nature, there is a primary necessity of growing respect and love to whatsoever intelligent being he comes to know," and with this, step by step, the corresponding gradual training. We have met with nothing elsewhere so soundly reasoned, so clearly expressed, and so practically suggestive; though here, again, the general line pursued is the same as that pursued by Froebel. For the present we will say no more. But we hope we have said enough to prove to teachers that The Ruling Principle of Method' is a book to be studied with pleasure and profit. And, though some of us may be inclined to pronounce the system as rather logical than psychological, we shall all of us gain by coming in contact with a mind so eminently clear and reasonable, and so full of human kindliness. T. Macci Plauti Captivi. With Introduction and Notes. By FROM the Clarendon Press comes a very neat little edition of the Captivi' of Plautus, by Mr. W. M. Lindsay, intended as a companion to the Trinnummus' of Messrs. Freeman & Sloman of the Westminster School, where the plays of Plautus have been frequently exhibited by the scholars with much dramatic and archæological success. The only fault to be found with those exhibitions, however, is their practice of ignoring the musical element, that must undoubtedly have been an important feature in the original production of the Plautine plays. In fact, the ancient divisions of the comedies were effected solely by the musical passages, or 'Cantica;' and in the manuscript the name of the musical performer at the first exhibition of the play is often given in the title, or, rather, after it. In the present edition of the Captivi,' Mr. Lindsay has very properly called attention to this fact, which even careful students of the Roman drama are too apt to overlook; and his remarks, although unduly brief, will be instructive to the young student, for whom this little book is intended. Within the limits which the editor has marked for himself in the preface, he has done very excellent work, availing himself of the most recent German research, and giving notes, that, while useful to the schoolboy, are often very suggestive to the more mature scholar. Mr. Lindsay properly regards the Plautus lecture as affording “the best opportunity for teaching the etymology and structure of Latin words," and he has therefore given this side of the subject particular attention in the notes. The book may be unreservedly commended as being precisely what it professes to be, — an edition of the Captivi' that will "enable boys of the higher forms to read with intelligence and interest a play which, more than any other of Plautus, may suitably be put into a school-boy's hands." The reading of Greek and Latin at sight is deservedly becoming an important part of the preparatory training for college, both in England and our own country. The advantages of an ability to read an ordinary classical author without the aid of a dictionary are so obvious as to need no comment, and, as they impress themselves more and more upon our instructors, a much-needed reform will gradually come about. One may hope to see the day when collegeexaminations will test not only the memory, but the genuine knowledge, of the student, and when the object will be to discover not merely how much he knows of some particular author, or portion of an author, but of the language as a whole. Already sight-reading of easy Greek and Latin has become a part of the required entranceexaminations at Yale and Harvard, it has for some time held a prominent place in the classical instruction at Columbia, and the time is not far distant when it will form one of the important tests of all our leading colleges. Mr. C. S. Jerram of Trinity College, Oxford, already well known as the author of several useful publications, has just sent forth a volume of extracts for sight-reading, bearing the imprint of the Clarendon Press, and entitled Anglice Reddenda.' It supplements a much simpler work issued some years ago, and is intended for students who may reasonably be supposed to have acquired a somewhat extensive vocabulary. The extracts are about equally divided between Greek and Roman authors, and are admirably selected so as to interest and entertain as well as to instruct. It may be doubted, however, whether such excerpts as odes from the first book of Horace, fragments of the fourth Æneid, passages from the Metamorphoses and Fasti of Ovid, and the first eclogue of Vergil, will possess the requisite novelty to the class of students for whom this book is professedly intended. Common Sense Science. By GRANT ALLEN. Boston, Lothrop, 12°. Studies in Life and Sense. By ANDREW WILSON. London. If the question, What is the ideal method of popularizing science?' were raised at any of our large scientific meetings, about as many minds as men would probably be heard. Everybody admits the importance of the topic; everybody recognizes that science is all along getting popularized and gradually rendered digestible by the average man: but there is much difference as to the relative value of the several agencies by which this result is being produced, and the direction which these efforts should take in the future. There is a great deal of false popular science, a class of writing in which the difficult points are always skipped, and the light and temporarily interesting ones unduly magnified; in which the interest is attracted towards certain minor points, and the whole doctrine set forth in a perverted perspective. One can dress up the facts of science in as attractive a garb as one likes; but the aim must be to bring home the fact, and not the study of the costume. The spirit of accuracy by which science is differentiated from uncritical knowing is the sine qua non of a real interest in scientific work. Into what category of popular-science' writing one will put this work of Grant Allen's will depend largely on one's conception of the purposes of such literature. The geniality and attractiveness of his style are well known. They are important factors in the success of his works. The present series of essays exhibit the strength and the weakness of this class of writing. Its strength consists in its power to bring home simple truths in a way that suggests their real significance to the average mind; its weakness, in the fact that so much of it is not 'common-sense' science, but common-place' science: it says very little for the amount of words. A striking feature of this and other recent general works is the great rôle which psychological subjects are now playing in science. Of the twenty-eight essays here printed, ten are distinctly psychological, and many others partly so. The main reason of this increased interest in the scientific study of mental phenomena is the recognition of their intimate relation with education. We are beginning to appreciate that the requisite for rationally educating the mind is to accurately know it. It is only just to Mr. Allen to give a sample of some of the essays. A very typical one is that on self-consciousness, the tone of which will be readily gathered from the following sentences: "A philanthropist who had it in his power to abolish, if he chose, with a single wave of his hand, either small-pox or self-consciousness, would probably do more in the end to diminish human suffering and to increase human happiness if he elected to get rid, by an heroic choice, of the less obtrusive but more insidious and all-pervading disease; for small-pox, at the worst, attacks only a very insignificant fraction of the whole community; while every second person that one meets in society, especially below the age of fifty years, is a confirmed sufferer from the pangs of self-consciousness." The essay on memory sets forth in apt illustrations the complexity of human knowledge; that on the balance of nature, the inter-relation between the various classes of organic life. Under the title ‘Big and Little,' is a lesson on the relativity of knowledge. The 'Origin of Bowing traces the gradual refinement of a savage's slavish obeisance into the modern gentlemanly courtesy. The Pride of Ignorance' teaches an admirable lesson, as also does the essay on home-life. Other sufficiently suggestive titles are 'Holly and Mistletoe,' 'Sleep,'' Amusements,' Evening Flowers,' 'Genius and Talent,' and so on. Like all his works, this collection of papers will doubtless find a large and appreciative public. To those who do not already know the facts which it contains, it will offer an attractive method of acquiring them. The spirit of Dr. Wilson's book is quite a different one. There are many who will listen to Mr. Allen who would not listen to Dr. Wilson; but those who choose the latter will not be sorry for their choice. There is in these essays an unusual amount of information, well and attractively put together. It needs to be read attentively, but leaves the reader with the same feeling of satisfaction that one experiences when rising from a good and substantial meal. There will follow a process of healthy digestion, and the food will contribute some little to the making of its partaker. Dr. Wilson is a biologist, and the sixteen careful studies contained in this volume touch portions of the entire field, from the Inner Life of Plants' and The Past and Present of the Cuttlefishes,' to the Body and Mind.' In each topic the author writes as one perfectly at home; avoiding the fault of attempting to tell too much, as well as of having too little to tell. It is popular-science writing, a very good type indeed. Like the former book, this, too, is characterized by a preponderance of psychological subjects. Seven of the essays treat entirely or mainly of mental phenomena, while several others touch upon such topics. The Old Phrenology and the New' is an unnecessarily painstaking refutation of the claims of the cranial-bump examiners,' with a brief account of the evidence for the modern doctrine of the localization of function in the cortex of the brain. The old phrenology serves as an excellent type of the shoals, on which the hasty wanderer, leaving the straight but slow path of scientific advance, is likely to be wrecked. The nature of the relation between nerve-tissue and mental phenomena is outlined in the paper on body and mind; the main point being to show by striking examples the strange effects produced by intense expectation and concentration, which furnishes the kernel of truth in the claims of the mind-cure. The Mind's Mirror' explains the development of the expression of the emotions in animals and men, while The Coinages of the Brain' is a timely account of the part played by hallucinations in such happenings as our psychic-research societies are likely to record. THE American committee of the International Congress of Geologists—a committee appointed by the American Association will present a report at the meeting of the American Association in August concerning the positions to be taken by the representatives of American geologists at the next session of the congress in London (1888), upon the more important questions of nomenclature, classification, and coloring, which will there be discussed. It requests that Section E set apart a day for the purpose of considering these questions to be submitted by the committee, and of aiding that body to ascertain the direction of American opinion thereon. In order the better to accomplish this object, it requests Section E to issue an invitation to all American geologists (whether members of the American Association or not) to attend this session and participate in the work. The American committee also request that members of the association be informed of the opportunity offered for obtaining the great geological map of Europe, now preparing by a special committee of the International Congress. This map will be issued in 49 sheets, which, combined, will cover a space about 11 by 12 feet. The price is $20 a copy, with additional charges of duty and expenses amounting to about $6. Incorporated scientific institutions are of course exempt from duty-charges. For further information address Dr. Persifor Frazer, secretary of the American Committee, 201 South Fifth Street, Philadelphia, Penn. Brooklyn Entomological Society has appointed a committee to welcome the members of the club, and to assist in making the meetings interesting, as well as to give such information regarding matters of special interest to entomologists as may be desired. The same society will arrange for one or more field-excursions in the vicinity of New York, and a reception will be arranged for. Members of the club intending to contribute papers will please communicate the same to the president, Prof. J. H. Comstock, Ithaca, N.Y., or to the secretary, Mr. E. Baynes Reed, London, Ontario. -The Botanical Club of the American Association will hold its meetings, as usual, during the week of the association. For particulars address Mrs. E. L. Britton, secretary of the club, Columbia College, New York. The Society for the Promotion of Agricultural Science will hold its eighth annual meeting in New York, beginning on Monday evening, Aug. 8, at Columbia College, and continuing on Tuesday. For further information address Prof. W. R. Lazenby, secretary, Ohio State University, Columbus, O. The aggregate production of shad for distribution the present season by the United States Fish Commission has been enormous. The number produced has been increasing from season to season, owing to the perfection of the methods in use. A summary of the distribution for the present season, arranged by river-basins, is as follows: Penobscot River...... the hop-vine. In the autumn a counter-migration from the hop-vine to the plum-tree occurs, the winter eggs are deposited, and the cycle of life goes on in the same way. It is a notable fact that in regions where the cultivation of hop-vines is a new industry, the growers have had complete immunity for a while from the pest. In California to-day they are not troubled by it. Professor Riley believes that the Phorodon humili has been brought to this country from Europe on plum-stock; and there is reason to believe that the Phylloxera, the dreaded grape-pest, was carried from this country to Europe on grape-vine cuttings. Therefore California hopgrowers are warned to beware of importing plum-stock from eastern hop-regions. These discoveries render it possible to check the ravages of the hop-louse either by the use of insecticides in the springtime, before the insect has reached the winged state, or by the destruction of the sheltering plum-trees. The experiments will be continued with a view to protecting the hop-vines after they have become infected with the hop-louse. - The project of holding a summer school of physics at Harvard College this season has been abandoned; but on July 19 and 20 apparatus designed for use in the 'forty-experiment course,' preparatory for admission to Harvard College, will be shown to teachers or others at the Jefferson Physical Laboratory, and questions relating to the experiments will be answered. The same thing will be done for the sixty-experiment course' on the second day, July 20. Kennebec River...... Tributaries of Narragansett Bay. Hudson River and tributaries.. Tributaries of Delaware Bay.. Tributaries of Chesapeake Bay..... Tributaries of Albemarle Sound.. Tributaries of Gulf of Mexico.. Total....... 1,169,000 800,000 1,275,000 1,979,000 5,099,000 68,149,000 5,322,000 3,566,000 7,048,000 1,014,000 95,421,000 It will thus be seen that over 68,000,000 young shad-fry have been returned to the waters of Chesapeake Bay. The entire production of the fisheries of the Chesapeake for the present season was about 2,000,000 young shad. It is therefore evident, that, for every mature shad taken from the waters of the Chesapeake, thirty-four young, healthy, and vigorous shad have been returned to those waters. Experiments already made by the commission indicate, that, up to the close of their river-life (the young shad migrating in October), twenty per cent of the fry placed in our rivers will survive, and attain a size of from two to three inches in length. Arrangements have been made by the commission to secure complete statistics of the shad-catch all along the entire coast for the present year, similar statistics having already been collected in 1885 and 1886. Information already in the hands of the commissioner makes it certain that the aggregate production of shad on the coast has been larger the present season than at any time in the last twenty years, but it will be impossible to give the measure of increase. For the Potomac River it is already assured that the increase of 1887 is fully 100,000 shad over that of 1886, and the increase of 1886 over that of 1885 exceeded 100,000. In the Potomac fisheries alone in the last two seasons the increase in shad has been over 250,000; the increase representing a much larger number than the entire catch of 1879, in which year the fisheries of the Potomac reached their lowest ebb. - Professor Riley, the entomologist of the Department of Agriculture, has made public the result of an exhaustive personal investigation into the habits of the Phorodon humili, or hop-louse. His discoveries are expected to prove of great value to hop-growers, as he has succeeded in learning the habitation of this plant-pest during the winter months, and tracing it through the varying stages of insect-life. Before the investigation, it was not known how or where the insect survived the winter. As a result of his inquiries, Professor Riley has satisfied himself that the eggs laid by the female at the close of the summer are deposited in plum-trees, where the insect hatches in the spring, and resides until the third generation. This third brood, unlike its predecessors, is winged, and immediately after development abandons the plum-tree and attacks LETTERS TO THE EDITOR. **The attention of scientific men is called to the advantages of the correspondence columns of SCIENCE for placing promptly on record brief preliminary notices of their investigations. Twenty copies of the number containing his communication will be furnished free to any correspondent on request. The editor will be glad to publish any queries consonant with the character of the journal. Correspondents are requested to be as brief as possible. The writer's name is in all cases required as proof of good faith. Theoretical Meteorology. A REVIEW of Professor Ferrel's recent work on this subject in Science for June 3 furnishes an opportunity to present a few points on this subject. Professor Laughton, ex-president of the Royal Meteorological Society, once said that there was hardly a theory in meteorology that was well established. If this be so, it seems to me there is great danger of putting too much reliance upon mere theory, which does not have a sufficient groundwork of facts. There is special danger of this in meteorology, where the mathematical discussions of gaseous movements and vortices are hedged about with so much difficulty and complication. I am well aware that the views here advanced are opposed to those of many most advanced thinkers in this field, and I only ask an unbiassed hearing. To my mind there are at least two fundamental errors in this subject, but these are intimately interwoven throughout its warp and woof. These are, first, that there is friction only between the air and the earth, or at least that friction between contiguous air strata may be neglected; second, that conditions and changes of pressure, temperature, and moisture in the atmosphere, are the only causes acting in producing either its general motions or storms. The objections to the first theory are briefly as follows. At a height of 100 feet, or at the most 200 feet, in a level country, there is no longer friction between the air and earth, but rather between air and air. This is especially the case on the ocean; and here, surely, we would have no waves, if it were not for the friction between air and air. If there were no friction, all storms would take place in a virtual vacuum, and into a vacuum air would tend to flow with about the velocity of sound. Professor Ferrel thinks, that, according to laws of gaseous motion, the earth's atmosphere would leave the poles and heap itself at the equator, but this is prevented by friction with the earth's surface; but, as we have just seen, we need consider only friction of air on air at 100 feet elevation. The objections to the second theory cannot be set forth as easily as the above. When we are gravely told that the sun heats up a certain portion of the earth's surface, and that in consequence vertical currents are set up which finally bring about a wind of 100 miles an hour, we can but be credulous. As a matter of fact, the sun does not heat up a limited portion of the earth. Its rays shine with equal intensity over 1,000 miles from east to west. It has also been shown that this heating of the surface does not ascend more than a few inches in the air. One of the strongholds of the theorists is unstable equilibrium; but right here we find two seemingly contradictory statements. On p. 51 of Professor Ferrel's book, Recent Advances in Meteorology,' there is a suggestion that this state (unstable equilibrium) is brought about whenever there is a less diminution of temperature with height in an ascending column than in neighboring portions of air. On p. 328 of the same volume, however, the idea is given that this same state may be produced if there is an abnormally great diminution of temperature with height. It would seem as if in both these instances, even if there were a tendency to this state, air would flow in at all times from surrounding regions, and instantly relieve the condition. This relief would be afforded the more rapidly, the less the friction. However, the error here is farther back. We cannot suppose that the atmosphere is either quiescent or flowing in a current having a uniform velocity in all its layers, to the height, say, of 15,000 feet. The fact is admitted that there is a uniform acceleration in the different strata as we arise; so that, even if an upward movement should begin, a few hundred feet would destroy all vertical tendency. As a matter of fact, when we consider the actual conditions under which solar radiation acts at a storm-centre, we see that this unstable state could not be formed. At a storm-centre clouds cover the earth's surface, and prevent all abnormal conditions from great heat. Balloon-ascents have shown uniform temperatures up to the top of the clouds. The theoretical computations of the velocity of the upper air strata do not correspond with the actual movements recorded. On p. 259 Professor Ferrel gives the velocity of the current at the height of 16,000 feet as 26 miles per hour in the middle latitudes of the United States. On Mount Washington, 6,300 feet in height, the velocity when a low area passes is 53 miles per hour, and when a high area passes it is 21. The velocity of the low areas near Mount Washington is 34 miles per hour. This would indicate that the power of the storm must be below 6,300 feet, since it is admitted that its progressive motion is due to the movement of the strata where it exists. It may be safely said that a height of less than 6,000 feet for the centre of disturbance would be fatal to a great many of the present theories of storm-generation. Formerly it was said, that, owing to friction with the earth's surface, the upper part of the storm must be in advance of the lower; but it is certain that such a state of things could continue only a few minutes, for the upper portion of the storm would be rapidly separated from the lower. Professor Ferrel, on p. 260 of the present volume, explains this difficulty by suggesting that the upper part of the storm is continually re-forming itself, and that there is no actual transferrence of air. I hardly think that this suggestion will be accepted. It seems to me our storms would behave differently if it were true, and certainly our synoptic charts do not give any clew to such re-formations of the upper part of the storm. It seems to me this later theory destroys the continuity of the ascending current and the essential features of unstable equilibrium. One of the most difficult phenomena to explain is the fall of rain at a distance of 300 and more miles from the storm-centre. If we suppose the ascending currents are at the centre of the storm, then rain should fall at that point. Professor Ferrel, at p. 266, advances the novel idea that the rain is formed in or carried to the upper currents, and, as these are more rapid than the storm, it must fall in advance of the storm. I do not think this theory takes sufficient account of the facts. Let us, suppose the raindrop carried to a height of 7,200 feet observations in balloons show that rain very rarely occurs above that height, and that the 'power' of the storm is at 5,000 feet. We may consider the velocity of the current at 7,200 feet 15 miles per hour greater than at 5,000 feet: the drop would fall at about 10 feet per second, or would reach the earth in 12 minutes; and hence, if it had been carried in the upper current during this time, it would have fallen 3 miles in front of the centre, instead of 300 or more. As a matter of fact, since the currents below 5,000 feet are very much slower than above that height, any acceleration would be entirely overcome, and from these principles the drop would actually fall back of the centre. On the continent of Europe the bulk of the rain falls at the rear of the storm. To my mind, however, theoretical meteorology most signally fails in its attempts to explain our more violent storms and tornadoes. That the sun's heat could start a vertical current which, with the condensation of moisture in the upper air, would give rise to winds of 200 or 300 miles per hour, seems incredible. The attempt to meet the difficulties by suggesting'great contrasts of temperature,' 'meeting of warm southerly with cold northerly winds,' cool air overrunning warm,' 'warm air overrunning cool,' etc., does not seem at all satisfactory. As long as it was supposed that tornadoes occurred at the centre of a low area where it was thought there was an ascending current, the theory seemed plausible; but when it was clearly shown, in March, 1884, that tornadoes do not occur at a low centre, but 400 or 500 miles to the south-east, it became necessary to explain this. It seems to me that all attempts to elucidate this subject have merely served to lighten the darkness without removing it. There is no space left for minutely examining the great superstructure built on what seem weak foundations. It seems as though the first and most important step is to remove the slur cast upon this science by those who are qualified to know its weakness. Let our theorists bend every energy to establish some fundamental proposition, either by actual experiment in the laboratory or by investigation in nature's laboratory at the spot where the 'power' of the storm manifests itself. It seems to me the recent attempts of Weyher in France to demonstrate the existence of this power,' by means of a rapidly revolving fan at some distance above water or grain, show the great need of further proof. These experiments show what might be if only there were an enormous fan in the upper air, but where is the fan? Must we not conclude that the true explanation is now farther off than before, and certainly much farther from the present theories. H. ALLEN HAZEN. Washington, July 1. Determination of the Depth of Earthquakes. THE report of Captain Dutton and Everett Hayden on the Charleston earthquake (Science, ix. p. 489) is undoubtedly a very valuable addition to earthquake literature. There are two or three points, however, to which I wish to draw scientific attention, in the hope that investigation hereafter may clear them up. Perhaps the most interesting and important point in the report is their method of determining the depth of earthquakes. The authors first review rapidly other methods. Mallet's method — by protracting the lines of emergence back to their meeting-point — they dismiss as too uncertain. Seebach's method used in the earthquake of Central Germany in 1872, which depends on the law of decreasing velocity of the emergent wave- they also dismiss, because the times of arrival at different points cannot be determined with sufficient accuracy, on account of the different velocities of the two different kinds of waves, normal and transverse. In place of these methods they propose what they claim to be a wholly new one, founded on the law of decrease of intensity; i.e., of decrease of the shock-motion or motion of the earth-particle, or, in other words, the wave-height or amplitude. They show by mathematical discussion that the place of the maximum rate of decrease of intensity bears a fixed relation to the depth of the focus; viz., as I to 3. Upon this basis they estimate the depth of the focus to be about twelve miles. In Fig. 1, which we reproduce from their report, the fall of the double-curved line represents the decreasing intensity. The place of most rapid fall, i.e., where the curve changes from convexity to concavity, is the place of most rapid decrease of intensity. This place was quite distinctly marked. It was about seven miles from the epicentrum. We wish now to draw attention to the fact that this method does not differ very greatly from, and perhaps is not an improvement upon, another method suggested by Mallet in his Report to the British Association, 1858,' p. 102, though not used in his discussion of the Neapolitan earthquake of 1857; viz., by means of what may be called the circle of principal disturbance.' This method is mentioned and explained in my Elements of Geology,' p. 117. The authors seem to have overlooked it. 1 With constant wave-length, intensity a amplitude. The destruction about the epicentrum of an earthquake depends mainly, perhaps, upon the amount of motion, but partly also upon the direction of motion; horizontal motion being far more destructive than vertical. Now, the whole amount of motion is assumed to decrease as the square of the radius of the agitated sphere increases (x); but the horizontal element of the motion increases as the cosine of the angle of emergence. Under these two conditions, there will be a certain distance all about the epicentrum, bearing a fixed relation to the depth of the focus, where the horizontal element will be a maximum. This is at dd' (Fig. 2), where the angle of emergence is 54° 44′. In other words, the 'circle of principal disturbance' is the base of a cone whose apex is at the focus, and whose apical angle is 70° 32'. The distance ad of this circle from the epicentrum is to the depth of focus ax as I to vz. Now, it is evident that in violent earthquakes the destruction over the whole area of this circle might be nearly the same; for in the central parts the whole motion would be greater, and on the margins the sideways motion would be greater. But beyond this circle the destructiveness would very rapidly decrease, because the whole motion and the sideways element are both decreasing: in other words, if we used the graphic method, the curve of destructiveness would be like the curve of intensity (Fig. 1), except pose the spherical wave were cut off, not on one side only, but on both sides; in other words, suppose a shock generating normal circular elastic waves of compression to occur in the centre of a thin plate: is it not evident that the intensity of these would vary simply inversely as the radius (II)? Or, if the plane be reduced to a bar, such waves would be substantially constant in intensity. But we are not left to general reasonings on the subject. If the intensity or wave-height follow the law of inverse squares, it is impossible to understand how the waves should carry so far as we actually find. In the Charleston earthquake the motion at the distance of six hundred miles was still sufficient to create alarm and to produce seasickness. Now, the amount of motion at the epicentrum was not more than ten or twelve inches. Let us take twelve inches as the greatest motion, and the epicentrum as ten miles from the focus. At the distance of six hundred miles, according to the usually assumed law of decrease, the amount of motion or wave-height would be only a three-hundredth of an inch; but if the spherical wave is reflected back from the surface, and combines with the advancing wave, it is probable that its decrease is only as the increase of the radius. In that case, at six hundred miles the motion would still be a fifth of an inch, which is a very sensible motion. that it would be flatter on the top, and the descent more abrupt at a certain distance from the epicentrum. The decrease of destructiveness is more rapid at a certain point than is the decrease of intensity. Now, since the intensity is estimated largely, if not wholly, by destructiveness, and since destructiveness depends largely upon the sideways motion, is it not possible, is it not even probable, that the supposed place of maximum decrease of intensity is really the place of maximum decrease of destructiveness; i.e., the circle of principal disturbance? If so, then the depth of the focus would be about ten miles instead of twelve miles. We have assumed all along that the intensity or excursion of the earth-particle, or the height or amplitude of the wave, varies inversely as the square of the radius of the agitated sphere (1x). The authors as well as all other writers assume this law. But is there not good reason to doubt its accuracy? The law is probably true so long as the wave is spherical; i.e., until it emerges on the surface. But when it emerges, what becomes of the energy which would have continued the wave if it had not been cut off by emergence? Some of it is doubtless consumed in more violent motion, and perhaps rupture, at the surface; but is not much of it reflected back into the earth to combine with the advancing waves? All other elastic waves, whether light-waves or sound-waves, coming out of a denser medium into a rarer (or vice versa), are largely reflected from the surface: why not earthquake-waves also? Sup FIG. 1. It is very important that investigations should be undertaken to determine the law of decrease of wave-motion of earthquakes. This, however, cannot be done without seismographs. While on this subject, it may be well to say something about Seebach's method of determining the depth of the focus. The method by the circle of principal disturbance, and that by maximum decrease of intensity, are based on the law of inverse squares, and 54°4 35°16' FIG. 2. therefore fail if this law be untrue. Seebach's method, on the contrary, is based on the law of decrease of velocity of the surface wave; supposing, of course, a constant velocity of the spherical wave. I have been in the habit of representing Seebach's method as follows: on the co-ordinate axes A, B, C, D (cd being the earth surface), of the earth, let equal times be taken on AB, and spaces passed over in equal times on CD. The one represents the |