Bibliography. Traité des propriétés des figures, par le General PONCELET. 2d edition, 2 vols. in 4°, avec planches.-This work, which is a complete exposé of this important subject, contains also the principal discoveries which the illustrious general has made in this department of inquiry. He has been engaged on the work since 1812, and was occupied with it when taken prisoner of war in Russia on the retreat from Moscow. The second edition, besides many improvements, contains the general theory of the centers of harmonic means; polar reciprocity; analysis of transversals, and their principal application to the projective properties of curves and geometric surfaces. Cours d'algébre superieure, par SERRET, Membre de l'Institut, Prof. au College de France, et à la Faculté des Sciences des Paris. 3d edit., 2 vols. in 8vo.-The first two editions of this work were disposed of with great rapidity. The third contains many improvements by the author. While this learned man does not pretend that the work is a complete treatise upon higher algebra, it contains notwithstanding a body of doctrine which will be of great use to those geometricians who are engaged in this important branch of mathematical analysis. Traité d'Astronomie pour les genes du monde. 2 vols. in 12mo, avec 2 planches and 162 figs. dans le texte.-This work contains a resumé of the lectures which Mr. PETIT has given during the last 27 years at the Observatory of Toulouse, of which he was director. The treatise is elementary, but calculations are not excluded. There are besides, in the form of notes, details and anecdotes in respect to important discoveries as well as distinguished astronomers. Eléments de Mécanique, par Mr. VIEILLE. In 8vo, de 256 pages avec figures.Vieille is Inspector General of the University of France. This work of his is designed for the use of the various colleges, and is fully adapted to that purpose. Le Chimiste: a Journal of Chemistry applied to Arts and to Agriculture; published by HENRY BERGÉ, Professor of Chemistry at the Museé de l'Industrie at Brussels. This journal appears semi-monthly, costs but 8 francs per year, and, according to its title, contains the novelties in the department of chemistry applied to the arts. Each part consists of 16 pages 8vo. ART. XIV. On the supposed Tadpole nests, or imprints made by the Batrachoides nidificans (Hitchcock), in the red shale of the New Red Sandstone of South Hadley, Mass.; by CHARLES UPHAM SHEPARD. * No impressions belonging to this or any other geological formation surpass if they equal these in their extreme delicacy of surface and sharpness of outline, rivaling as they do in these respects the most perfect metallic castings. Dr. Hitchcock, by whom they were first described, has well observed concerning them, that even viewed by the side of the splendid specimens of foot-prints, rain-drops and other rock-markings displayed in the Ichnological cabinet of this college (Amherst), "they are the most attractive of all." Dr. Hitchcock was led to conceive of and adopt the theory of their origin first suggested and made public by Prof. Silliman, Jr., and the late Capt. N. S. Manross, viz., that they proceeded from the gyratory movements of tadpoles; though he very cau * Several excellent photographic representations accompanied this paper, which are omitted, as it was impossible to do them justice on wood. tiously observes, "in concluding that the impressions were made by batrachians similar to those now living, I am by no means free from doubts as to the identity of the phenomena. The single figure he has given † (Pl. L, fig. 1) of these markings, if taken by itself does certainly favor the hypothesis adopted; though it fails in its uninterruptedly smooth and continuous surfaces as compared with the rough and broken sides of the recent tadpole cavities,-not to mention the rounded borders to the edges of the latter, when contrasted with the hexagonal outline of the corresponding part in these specimens. The cavities made by tadpoles morever are without any order in respect to each other, and vary somewhat among themselves in size and depth. Occasionally also, unoccupied spaces are seen between the holes, whereas in the shale nothing is more striking than the general uniformity among the impressions, and the very complete manner in which the entire surface is covered by them,raised lines (sometimes resembling swollen veins), being the only boundaries between contiguous cavities. The slabs of shale present three rather distinct varieties of these impressions, one of which is very accurately represented in the plate above referred to. In this the depressions are imperfectly arranged in rows, with a marked tendency to a concentric arrangement. The borders of the cavities are distinctly hexagonal, and the edges often equilateral. The cavities have a depth equal to about one-eighth their diameter. They are perfectly symmetrical, smooth and glossy. In a few of the specimens, the sides and bottoms are slightly pitted with ovoidal bodies of the size and shape of coarse gunpowder. The slab removed from such a surface of course exhibits upon its convexities corresponding granules in relief. As they are distributed without any order, and not generally present, they would appear to be due to seeds, as these of a larger size and spherical form are frequent in the formation. In the second variety we have little more than the strongly nerved outlines of the hexagons. The cavity is shallow, or nearly obsolete; but on its bottom, and proceeding from one and the same side relatively in each impression, is often seen a tripartite, flame-like marking, or brush, which spreads over nearly half the area. The direction of this fan-shaped brush is constant throughout the series, thus evincing an origin from a common cause, and one that acted simultaneously. The impressions moreover are occasionally traversed by raised lines proceeding from a subjacent layer, and thereby subdivided into smaller compartments; but in these instances it is always easy to trace the hexagonal boundaries of the superior layer. The depressions are obviously arranged in rows, somewhat approximating to fur* Ichnology of New England, 4to, 1858, p. 122. Boston. + Idem. rows, the parallel sides of which are more conspicuous than the transverse edges which subdivide the furrows into cells. It may here be observed that the fan-shaped brush is scarcely at all visible in the first described variety. The diameters of the cavities in both are the same, being from one to one and a half inches. The differences in the depth of the cavities in the two varieties probably grew out of the hardness of the bottom where they originated. The second kind, or shallow impressions, are constantly associated with the third variety presently to be described, being situated from one-quarter to one-third of an inch only above them. A series of singularly interrupted and overlapping wave lines, obviously the remains of the parallel or zigzag, furrowedges of the second variety above described, plainly enough show that they were produced by ripple action, through a gentle current of water setting transversely across the furrow-ridges. The third kind of impressions is considerably different from either of the foregoing, and requires a more particular description. The hexagons are disposed in long, nearly straight, parallel series, though now and then a row suddenly runs out where it abuts directly against a furrow-ridge; or in other words a ridge is seen to bifurcate, or to be replaced by a furrow. The cavities in this variety have nearly double the breadth or area of the two first varieties. In hexagons of the third variety the two opposite sides that are at right angles to the furrows have treble the length of the other two pairs, which seemingly have been shortened at their expense. The angles of the hexagon also are not equal. The four situated at the extremities of the longer sides, are less than 110°, while the two remaining (transversely opposite) ones are over 130°. The four shorter edges moreover are often flattened down into a broad band, while the long transverse ridges remain thin and sharp, though not straight at top, but gently arcuated. Indeed they are sometimes so low and faint as to become almost obsolete, thus changing the row of cells almost into a trough, whose borders are composed of the shorter zigzag sides of contiguous hexagons (under angles of 130°);-the whole seeming to have originated in a contraction of these sides, and a corresponding elongation of those at right angles to the furrow. The flattened band is not perfectly horizontal, but inclines a little toward the bottom of the trough, and constantly in one direction throughout the series,--its lower side being situated upon the upper or most shallow side of the hexagonal cell or cavity, or in other words the greatest depression in the furrow adjoins the superior edge of the band-it being kept in mind that the greatest concavity in the cells is never central but always somewhat marginal. In some of the slabs the furrow-edges are much less deeply truncated, rarely they are flatly bevelled; and in one case for a little distance, I have seen them replaced by four narrow planes. But the most singular feature of those specimens with a single broad band, consists in the presence upon it of a circular scar, which is uniformly located between the large angle of 130° and the adjoining smaller one of 110°, just in one corner of the impression, aud always in the same corner relatively, throughout the series. Its diameter is about one-fifth of an inch, and it would appear to have arisen from the presence of some adhesive matter at these points which has operated to interfere with the usually easy cleavage of the shale, whereby several layers of it have remained adhering together, producing either a depression or an elevation upon it, according as the scar is found on one side or the other of the separated shale. In addition to the foregoing, the tripartite brush is seen radiating directly from the scar, obliquely into and nearly across the bottom of the contiguous depression, pointing as it were to the scar on the contiguous band. It should further be mentioned that the repetitions of these impressions of each separate sort are very numerous, and each equally smooth, sharp and perfect, through a thickness of from one-third to half an inch, and in every instance where overlapped by a different variety, the parallelism of the rows is very obvious. The difficulties in the way of the tadpole theory early induced me to question it as explaining the above appearances; and I was led to seek other modes of accounting for the phenomena more in harmony with the facts. For a time, at the suggestion of a very eminent authority in comparative anatomy, I endeavored to find an explanation in the supposition that they proceeded from the spawn of gigantic batrachians, whose footprints at neighboring localities are so common in shale of the same formation. But such an origin, besides other incompatibilities, required an organized association of the ova into a flat tier or mat, made up of parallel rows (one egg in depth), for rods in length and many feet in width. No reptilian germs are known to be extruded in such a shape. My next conception was, that the imprints may have owed their origin to a gigantic species of alga, allied to the Hydrodictyon utriculatum, though constituting a different genus, and possibly pertaining to a different family altogether, of these fresh-water plants. A recent mineralogical visit to the granite quarries of Rockport at Cape Ann, by bringing under my inspection a very remarkable exhibition of ripple-marks upon the sea-shore, leads me to refer the South Hadley imprint to a similar cause. The recent ripple-marks occur in a very striking manner almost directly in rear of the Sandy Beach Hotel, in a somewhat sheltered place at the head of a little bay or cove, where the sand is fine and the bottom hard. A gently swelling, elongated bar, six or eight rods in length, running parallel with the shore is here found. Its breadth is about half its length, and its elevation where the highest, twelve or fifteen inches above the narrow flat creek-bottom between it and the shore. The breadth of this interval does not exceed ten or fifteen feet, the middle half of which is nearly flat, while the sides therefrom slope upward very gradually each way. The bar is left bare at about half tide. The water flows in and out of the creeklet at both ends of the bar, and when the tide is sufficiently high, flows back and forth cross-wise, to the bed of the creek. During the rising of the tide, the bed of this elongated depression is more or less covered with water for nearly an hour before the bar is wholly submerged. Throughout this period, as well as at all other times while accessible, and best of all, at low water, when the surface is left wholly bare, an almost perfect repetition of the second and third varieties of the South Hadley impressions is every where visible, though the size of the cavities is constantly from two to threefold that of the fossil specimens. With singular precision may be seen the parallelism of the furrows (corresponding with the sea-margin), the cross partitions (though generally more faint than in the shale), the zigzag margins formed by those sides of the cells which give rise to the furrow-ridges, the frequent splitting of a ridge so as to form an additional (an interpolated) furrow, the smoothing down of a ridge so far as to produce the flat band, and the almost constant occurrence of the deepest part of the trough on the down-hill side of the furrow. Other coincidences might be pointed out with the aid of drawings; but the foregoing are perhaps sufficient for our purpose. The appearances remained in full view during several days of calm weather, the pattern being only slightly interfered with, during the ebbing and flowing of the tide. At low water the configuration of the surface was invariable. The examination of these sea-shore markings led me to recur to a large sandstone slab (with a surface two feet square) procured two years ago from the Forrest-marble Oolite of Wiltshire, England, on account of its crustacean foot-prints. Here also we are presented with ripple-marks of the same regularity as on the Rockport beach. In area, the cavities are just half way between those from the sea-shore and those from the New Red Sandstone. The zigzag lines of the furrow-ridges, the position and distinctness of the transverse partitions, the greater depth of the cavities constantly toward one side rather than in the middle of the furrows, and the occasional bifurcation of the ridges, so as to embrace an additional trough are all plainly conspicuous. This specimen taken along with the Rockport seashore ripples leave no remaining doubt in my mind that the ori |