which he called attention to the Notes on Earthquakes addressed to him of late years by the learned Professor of Dijon, and he has often mentioned at our meetings the relations indicated between the frequency of earthquakes and the age of the moon. The cause of the interest connected with these relations is easily understood. If, as is now generally supposed, the interior of the earth is in a liquid or pasty state through heat, and if the globe has for its solid part only a crust comparatively very thin, the interior liquid mass must tend to yield like the surface waters to the attractive forces exerted by the sun and moon, and there must be a tendency to expansion in the direction of the radius vectors of these two bodies; but this tendency encounters resistance in the rigidity of the crust, which is the occasion of fractures and shocks. The intensity of this cause varies, like that for the tides of the ocean, with the relative position of the sun and moon, and consequently with the age of the moon: and it should also be noted, that as the ocean's tides rise and fall twice in a lunar day, at periods dependent on the moon's passing the meridian, so in the internal fluid of the globe, there should be two changes in a day, the time varying with the same cause. Without entering now into more details, it will be easily conceived, that if the mobility of the internal mass of the globe plays a part in the production of earthquakes, there must be some dependance, admitting of study, between the occurrence of an earthquake, and the circumstances which influence the action of the moon on the whole globe or on any place or portion of it, that is, the angular distance with the sun, its actual distance from the earth, and its distance from the meridian of the place, or in other terms, the age of the moon, the time of perihelion, and the hour of the lunar day. These considerations which have not escaped M. Alexis Perrey, have beyond doubt inspired the idea of the two-fold work which we have been charged to examine; and they have obtained for the views, the interested attention of M. Arago and many other men of science. They have involved on the part of the author the determination of the precise date, and period of the moon, for each earthquake on record and even for each shock of which earthquakes may consist--a work of vast labor; the researches have been now continued for several years and are still in progress. ** In the memoir of the 21st of March, 1853, on the relations between the frequency of earthquakes and the age of the moon, the author devotes the first chapter to the tabulation and the numerical transformation of the results of observation. He has conceived four modes of tabulating the facts. In the first method, followed in his memoir presented to the Academy on the 5th of May, 1847, the author reckons as a day of earthquake each of those on which the earth has been shaken, whether it has happened only in one country or on the same identical or different hours in two or several countries, separated by intervals not participating in the movement. Noting then, after the Connaissance des Temps, to what day of the lunation, each day of earthquake corresponded, he brings together in one column all the days which pertain to the first day of a lunation; in a second, all pertaining to the second day of a lunation, and so on. Thus he forms a table consisting of 30 columns, each column giving the number of days of earthquake corresponding to the successive days of the moon. The numbers vary, and the law of variation is the same in his first table comprising a register of 2735 days of earthquakes between 1801 and 1845, as in his later one embracing 5388 days between 1801 and 1850. In both tables, the number of earthquakes during days near the syzygies is a little larger than in days near the quadratures. ་ In his second method, the author regards as distinet, the earthquakes in different regions separated by an undisturbed region, and each day of earthquake is counted 1, 2, 3, &c., according as the earthquakes of this day were experienced in 1, 2, 3, &c. separate regions. By this new mode of tabulating, the number 2735 is increased to 3041, and that of 5388 to 6596. The same law is observed in these new tables as in the first set: and similar also is the result obtained by dividing the half century into two quarter centuries. In the third method of arrangement, M. Perrey takes as a distinct phenomenon each of the shocks of which a single earthquake is composed, and registers it separately. But he has not the documents for completing this work, as the number of shocks often is not stated. The author has contented himself by considering by this method 931 shocks felt in Ceutral America and mostly at Arequipa, as published by M. de Castelnau in the 5th volume of his "Voyage dans les parties Centrales de l'Amerique du Sud." This table, without giving identical results with the preceding, leads to the fundamental relation already mentioned. Finally, in the fourth method of arrangement, the application of which is difficult and has not yet been made by M. Perrey, the collection of shocks in a country, preceded and followed by a period of tranquillity is regarded as a single phenomenon. To the nine tables formed by one or the other of the first three methods of tabulating, the author has added a tenth, formed by the first mode: it embraces four years, from 1841 to 1845, and only 422 days of earthquakes. Although this number is small the numbers lead to the same general conclusion-that is, the greater frequency of earthquakes at the syzygies than at the quadratures. SECOND SERIES, Vol. XIX, No. 55.- Jan., 1855. 8 This general law, although distinctly observable in the series of results, is however obscured by many anomalies. In order to eliminate these anomalies as far as possible, Prof. Perrey divides the 29.531 days of a lunar month into twelfths, sixteenths and eighths, and obtains, by proportional calculations applied to the number of the different tables constructed according to the solar days, the numbers which correspond to each fraction of lunation. In his new tables thus constructed, excepting some minor anomalies, the law above stated is more fully confirmed, that for a half century earthquakes have been more frequent at the syzygies than at the quadratures. M. Alexis Perrey has also enquired whether a relation exists between the frequency of earthquakes and the distances, at the time, of the moon from the earth. For this purpose he has tabulated according to the different methods of tabulation pointed out, the number of times the earth has been shaken, on the day of the perigee and apogee of the moon, the day before, night before, the following day, and the next following; he has hence ascertained, by the groups of numbers thus formed, the total corresponding to the perigee, and also to the apogee. In order to facilitate a comparison of the results, he has taken the difference of the totals thus obtained and divided by their sum, whence he has found the quotients 1 1 1 1 1 1 1 which are all, above, and the last nearly equals. It appears therefore that the unequal attractions of the moon on the earth at its greatest and least distance from the earth, has a sensible influence on the production of earthquakes. In the Note of Jan. 2, On the frequency of earthquakes as related to the passage of the moon over the meridian, the author aims to discover whether the repetition of the shocks of earthquakes during a lunar day, has, like the tides, a relation to the moon's passing the meridian. He has submitted to this investigation, 824 shocks observed at Arequipa, registered by M. Castelnau, after calculating the hour of each, with reference to the moon. He has thus made ont a table, which he afterwards divided into 16 equal parts, and then grouped these by twos into 8 parts, using the mean lunar day of 24 hours 50 minutes. In this way, notwithstanding some large anomalies which cannot fail to be presented in so small a number of cases, the number obtained by each mode of grouping, gave evidence of the existence in the course of the lunar day, of two epochs of maximum number of shocks and two of minimum, the former at the times of the moon's passing the meridian-the superior and inferior-and the latter at intermediate intervals. M. Alexis Perrey, by discussing the catalogues which he had formed, thus shows by three ways independent of one another, the influence of the course of the moon on the production of earthquakes. 1. That the frequency augments in the syzygies. 2. That the frequency augments in the vicinity of the moon's perigee, and diminishes towards the apogee. 3. That the shocks of earthquakes are more numerous when the moon is near the meridian than when 90 degrees from it. The tables still present more anomalies, and the author has omitted nothing which should remove them, so as to bring out the law in all its purity. He at first thought of representing the frequency by diagrams. like those for barometrical observation, a process by which the general march of phenomena is perceived amid the anomalies. which tend to mask it. We regret that this has not been done, as it speaks at once to the eye. M. Alexis Perrey has endeavored to obtain his results by calculation, and has devoted to this subject the second chapter of his principal memoir, and the second part of his Note of Jan. 2, 1854. Without attempting to follow the author in these analytical discussions, we simply state here that, in order to represent the results of observation, he employs a formula of interpolation of the form, 4m+A sin (t+a)+B sin (2t+)+C sin (31+7)+... in which m, A, B, C, &c., are constant coefficients of the same nature with ; «, 8, 7, &c., are constant angles; and t a variable augle dependent on the lunar motion, which is equal to 0 degree for the new moon, 90 degrees for the first quarter, and 180 degrees for full moon, &c. He then adapts the formula by known methods to each of his tables deduced from observation, by determining the constants which it includes. By means of the formulas thus obtained, the author has been able to form tables corresponding to those made simply from observations in which the law of the phenomena is presented, free from the principal anomalies which tend to conceal it in the first tables. The numbers contained in these new tables have been constructed with care and have led to regular curves in which the law is expressed fully and clearly. All the curves have a marked resemblance, although not wholly similar-an identity could not be, for the results are only approximative aud take a special impress from the groups of numbers which they represent. The resemblance in the curves leads to two principal maxima, corresponding to the syzygies, and two minima for the quadratures; and sustains the general deduction, that for half a century earthquakes have been most frequent at the syzygies. The Academy will perceive the importance of this conclusion, and may judge at the same time from the preceding, of the care with which the author has pursued the subject, he having brought together for the half century 7000 observations. This number is however still small for the solution of a problem of this kind, and it is important to increase it both by adding the facts of successive years, and also by going back to past centuries, which the author has already commenced.* * ART. XI.-On the Periodical Rise and Fall of the Lakes; by MAJOR LACHLAN, Montreal.† FEW countries can boast of objects of more imposing natural grandeur or deeper philosophical interest, than are presented in Canada, in the vast extent and other striking peculiarities of its magnificent inland fresh water seas, and their noble connect ng rivers and unrivalled cataracts, coupled with the singularly anomalous nature of its climate and seasons compared with European countries in the same parallel of latitude: and an additional geographical interest may be considered as attaching to it, in the magnetic meridian passing through it-the line of "No variation" curving through part of its mediterranean waters.‡ The investigation of the causes and effects of these great physical phenomena might well engage the attention of a whole life of patient observation and study; and such, doubtless, will at no distant day, be the case; but in the present state of things, in so young a country, all that can be expected is the occasional contribution of the unpretending philosophical gleaner; and, as such, I now venture to lay before the Canadian Institute the following desultory observations on the periodical rise and fall of our great Lakes, in the hope of strengthening the arguments adduced by me in the paper which I had lately the honor of submitting to it, in advocacy of the establishment of a system of simultaneous meteorological and tidal observations throughout British America-as not only a great philosophical desideratum, but also likely to prove of substantial service to the country, were it only to make us better acquainted with the great benefits de This Report closes with a recommendation to the Academy that an appropriation should be made to enable M. Alexis Perrey to complete his valuable researches -especially for books, travelling, and transportation of documents, &c., and in accordance with it a considerable sum was placed at his disposal. + Read before the Canadian Institute, March 18th, 1854; Canadian Journal, July, 1854. To do justice to the subject treated of in this paper, a good map of British America should be at hand to be refered to, and, above all others, that graphic "Map of the Valley of the St. Lawrence," constructed by T. C. Keefer, Esq., in which the striking connection of the whole system of Lakes is so well portrayed. |