Fig. 8. It remains to investigate a formula for the declination of the needle. We have already seen that the magnetic needle is every where at right angles to the line of equal molecular magnetic intensity traced upon the earth through its station; which line we have assumed to be the same as the isogeothermal line passing through the same point. We have therefore only to seek for a formula which shall make known the direction of the isogeothermal line at a given place and place the needle at right angles to this line of direction. Such a formula may be derived from Brewster's formula for the determination of the mean annual temperature of a place. This is T=(t-1)(sin"8. sin"8')+ (4.) where t is the maximum equatorial temperature, 2 the minimum temperature at each of the two poles of maximum cold, and , 8 the distances of the place from the two cold poles. Let C, fig. 8, represent the north pole of the earth, A and A' the two poles of greatest cold, B a given place, BL the direction of the isogeothermal line through B. BA=0,and BA'=8'. For the isogeothermal line, since T is constant, dT=0. Hence, if we differentiate equation (4), and put the differential equal to zero, we shall have a relation between ds and ds, the variations of 8 and 8' in passing from the point B to its consecutive point r on the isogeothermal line. Thus, putting t-i=c, we have dT=c(n sin"-18 cos d sin"8'd8+n sin"- '$ cos s' sin"8d8'). Multiplying and dividing by sin-ati 8 sin-n+18', cn cos & sin 8'd8+n cos d' sin 8d8') =0. d8 sin d cos 8 (5.) If we drop the perpendiculars rs and rt upon BA and BA produced, we have Bi=ds, and Bs=d. Put Br=k, angle rВt=a, and angle rBs=a'. If in the angle A'BD we conceive two arcs to be drawn through B respectively perpendicular to BA and BD, the isogeothermal line will lie some where between these two perpendiculars; for it is only in this situation that in passing from And, da same. COS a COS a COS a COS COS a sin u B to r it can happen that 8 will be increased and di diminished, and therefore that sin"8 sin"d', in formula (4), can remain the Now Bs =Br cos rBs, or d8=k cos a'; and Bt=Br cos ds rBt, or ds=k cos a. Hence asi cos a'; and, by equation (5), neglecting the minus sign; putting also u=angle A'BD, sin 8 cos ♡ 8 sin so cos a' cos (u - a)' or, sin 8 cos si 1 cos & sin d cos u cos a + sin u sin a cos ut sin u tan a sin 8l cos 8 - sin d cos s' cos u Whence, tan a= sin 8 cos si sin u cot & tan so or, tan a= - cot u. If we put B=ABA' u=180 -- B, and cot 8 tan s (6.) sin B This formula gives the angle DBL. Subtracting this from 90° we obtain nBA, the angle included between the direction of the needle and BA(5). The difference between this and ABC will be the declination of the needle, which will be east or west, according as one or the other of these angles is the greater. The first of the equations above gives the following, which may be used as a tentative formula in place of equation (6):tan 8 (7.) cos (u – a) tans To make use of formula (6) we must know 8, 8', and B. These may be obtained by solving the two spherical triangles ACB, A'CB. The latitude and longitude of the place B, and the latitudes and longitudes of the two poles A and A' being given, we readily find CB, AC, and A'C, and the angles ACB, ACB. The formulæ which have now been investigated, viz. (2), (3), and (6), serve for the determination of the vertical and horizontal intensities at any place, and the declination of the needle. By taking the square root of the sum of the squares of the horizontal and vertical intensities, we shall have the directive force or total magnetic intensity of the place; and by dividing the vertical by the horizontal intensity we shall have the tangent of the dip. These formulæ I have compared with a large number of observations made in various parts of the northern hemisphere, and will proceed to give an exposition of the details of the calculations, and of the results obtained. (To be continued.) COS a ART. II. — General Geological Distribution and probable Food and Climate of the Mammoth; by Prof. R. OWEN.* The remains of the Mammoth occur on the Continent, as in England, in the superficial deposits of sand, gravel, and loam, which are strewed over all parts of Europe ; and they are found in still greater abundance in the same formations of Asia, especially in the higher latitudes, where the soil which forms their matrix is perennially frozen.t Remains of the Mammoth have been found in great abundance in the cliffs of frozen mud on the east side of Behring's Straits, in Eschscholtz's Bay, in Russian America, 66° N. lat.; and they have been traced, but in scantier quantities, as far south as the states of Ohio, Kentucky, Missouri, and South Carolina. But no authentic relics of the Elephas primigenius have yet been discovered in tropical latitudes, or in any part of the southern hemisphere. It would thus appear that the primeval Elephants formerly ranged over the whole northern hemisphere of the globe, from the 40th to the 60th, and possibly to near the 70th degree of latitude. Here at least, at the mouth of the river Lena, the carcass of a Mammoth has been discovered, preserved entire, in the icy cliffs and frozen soil of that coast. To account for this extraordinary phenomenon, geologists and naturalists, biased more or less by the analogy of the existing Elephants, which are restricted to climes where the trees flourish with perennial foliage, have had recourse to the hypothesis of a change of climate in the northern hemisphere, either sudden, and due to a great geological cataclysm, $ or gradual, and brought about by progressive alterations of land and sea. || Extracted from Prof. Owen's British Fossil Mammalia, 8vo. London, 1846. | Hedenström, in his “ Survey of the Laechow Islands," on the north-eastern coast of Siberia, remarks, “ibat the first of these islands is little more than one muss of these bones; and that although the Siberian traders have been in the habit of bringing over large cargoes of them (tusks) for upwards of sixty years, yet there appears to be no sensible diminution." The fossil elephantine remains discovered in India, belong to a species more nearly allied to the Elephas indicus. Cuvier, “ Discours sur les Révolutions de la Surface du Globe." It is obvi. ous that the frozen Mammoth at the mouth of the Lena, forms one of the strongest, as well as the most striking, of the celebrated anatomist's assumed “proofs that the revolutions on the earth's surface had been sudden." Cuvier affirms that the Mammoth could not have maintained its existence in the low temperature of the region where its carcass was arrested, and that at the moment when the beast was destroyed, the land which it trod became glacial. “ Cette gelée éternelle n'oc. capait pas auparavant les lieux où ils out été saisis ; car ils n'auraient pas pu vivre sous une pareille température. C'est donc le même instant qui a fait périr les animaux, et qui a rendu glacial le pays qu'ils habitaient. Cet événement a été subis, instantané, sans aucune gradation, &c."-Ossemens Fossiles, 8vo, ed. 1834, tom. i, | Lyell, “ Principles of Geology," in which the phenomena that had been sup. posed to have banished for ever all idea of a slow and gradual revolution," first attempted to be accounted for by the gradual operation of ordinary and existing causes. Jameson's "Cuvier's Theory of the Earth,” 8vo, p. 16, 1813. P. 108. were I am far from believing that such changes in the external world were the cause of the ultimate extinction of the Elephas primigenius; but I am convinced that the peculiarities in its ascertained organization, are such as to render it quite possible for the animal to have existed as near the pole as is compatible with the growth of hardy trees or shrubs. The fact seems to have been generally overlooked, that an animal organized to gain its subsistence from the branches or woody fibre of trees, is thereby rendered independent of the seasons which regulate the development of leaves and fruit; the forest food of such a species becomes as perennial as the lichens that flourish beneath the winter snows of Lapland ; and, were such a quadruped to be clothed, like the Reindeer, with a natural garment capable of resisting the rigors of an arctic winter, its adaptation for such a climate would be complete. Had our knowledge of the Mammoth, indeed, been restricted, as in the case of almost every other extinct animal, to its bones and teeth, it would have been deemed a hazardous speculation to have conceived, a priori, that the extinct ancient Elephant, whose remains were so abundant in the frozen soil of Siberia, had been clad, like most existing quadrupeds adapted for such a climate, with a double garment of close fur and coarse hair; seeing that both the existing species of Elephants are almost naked, or, at least, scantily provided when young with scattered coarse hairs of one kind only. The wonderful and unlooked for discovery of an entire Mammoth, demonstrating the arctic character of its natural clothing, has, however, confirmed the deductions which might have been legitimately founded upon the localities of its most abundant remains, as well as upon the structure of its teeth, viz., that, like the Reindeer and Musk Ox of the present day, it was capable of existing in high northern latitudes. The circumstances of this discovery have been recorded by Mr. Adams in the Journal du Nord,' printed at Petersburg in 1807, and in the 5th volume of the "Memoirs of the Imperial Academy of Sciences at St. Petersburg,' of which an excellent English translation was published in 1819. Schumachoff, a Tungusian hunter and collector of fossil ivory, who had migrated in 1799 to the peninsula of Tamut, at the mouth of the river Lena, one day perceived amongst the blocks of ice a shapeless mass, not at all resembling the large pieces of floating wood which are commonly found there. To observe it nearer, he landed, climbed up a rock, and examined this new object on all sides, but without being able to discover what it was. The following year he perceived that the mass was more disengaged from the blocks of ice, and had two projecting parts. Towards the end of the next year, (1801,) the entire side of the animal and one its tusks were quite free from the ice. On his re turn to the borders of the Lake Oncoul, he communicated this extraordinary discovery to his wife and some of his friends, but their reception of the news filled him with grief. The old men related how they had heard their fathers say, that a similar monster had been formerly discovered on the same peninsula, and that all the family of the person who had discovered it had died soon afterwards. The Mammoth was consequently regarded as an augury of future calamity, and the Tungusian was so much alarmed that he fell seriously ill; but becoming convalescent, his first idea was the profit he might obtain by selling the tusks of the animal, which were of extraordinary size and beauty. The summer of 1802 was less warm and more stormy than usual, and the icy shroud of the Mammoth had scarcely melted at all. At length, towards the end of the fifth year, (1803,) the desires of the Tungusian were fulfilled ; for, the parts of the ice between the earth and the Mammoth having melted more rapidly than the rest, the plane of its support became inclined, and the enormous mass fell by its own weight on a bank of sand. Of this, two Tungusians who accompanied Mr. Adams were witnesses. In the month of March, 1804, Schumachoff came to his Mammoth, and having cut off the tusks, exchanged them with a merchant, called Bultunoff, for goods of the value of fifty rubles. Two years afterwards, or the seventh after the discovery of the Mammoth, Mr. Adams visited the spot, and "found the Mammoth still in the same place, but altogether mutilated. The prejudices being dissipated because the Tungusian chief had recovered his health, there was no obstacle to prevent approach to the carcass of the Mammoth; the proprietor was content with his profit from the tusks; and the Jakutski of the neighborhood had cut off the flesh, with which they fed their dogs during the scarcity. Wild beasts, such as white bears, wolves, wolverines, and foxes, also fed upon it, and the traces of their footsteps were seen around.” The skeleton, almost entirely cleared of its flesh, remained whole with the exception of one foreleg, (probably dragged off by the bears.) The spine, from the skull to the os coccygis, one scapula, the pelvis, and the three remaining extremities, were still held together by the ligaments and by parts of the skin. The head was covered with a dry skin ; one of the ears, well preserved, was furnished with a tuft of hair. The point of the lower lip had been gnawed; and the upper one, with the proboscis, having been devoured, the molar teeth could be perceived. The brain was still in the cranium, but appeared dried up: the parts least injured were one forefoot and one hindfoot: they were covered with skin, and still had the sole attached. According to the assertion of the Tungusian discoverer, the animal was so fat, that its belly hung down below the joints of the knees. This Mammoth was a male, with a long mane on the |