ranged in a pyramidal form; often the vertex being a piece considerably larger than any of the others; the basal pieces of the pyramid are in most cases thinner and longer than any of the others; these, as well as the remainder of the pieces of this species, are turgid and massive, and like those of the calyx, are destitute of ornament.

On the side of the vault, above the anal field, is a considerable ovoid intumescence, composed of nearly thirty small pieces, whose surfaces are quite plain and level in contrast to the other pieces of the vault; they are arranged in nearly parallel rows, as follows, commencing with the lowest: 1-3-4-5; on the fifth row (which nearly completes this field-there are but two more rows) supervenes an ovoid opening, about one line in length, without a proboscis. This is the only opening upon the vault.

We have named this elegant species after Mr. O. W. Corey, to whom we are much indebted for many favors.

Geological Position and Locality.-Rare in sub-carboniferous limestone near the top of the knob stone bed, Hardin and Allen counties, Ky., and same geological horizon, Washington county, Indiana.

GENUS ONYCHOCRINUS, nov. gen. Lyon & Casseday.

1 to 3 X5

5 pairs.

Generic description.-This genus, in the shape of some of the pieces and in its general form, resembles more closely Forbesiocrinus than any other; yet they are so widely different in other respects that it will require no great perception to distinguish between them. The column near the calyx is cylindrical, large, composed of very thin articulations similar in size to each other; perforation small.

The radials are large, and form, together with the brachials, a continuous line: the arms are quite robust, furnished with strong pinnulæ.

Interradial fields, triangular in general shape; an anomalous one on the anal side. Anal field-long and narrow: one to three small interaxillary pieces on each ray.

Basal pieces small, subradials large, pentangular, alternating with the radials.

Onychocrimus exculptus, n. s.

Calyx vasiform, spreading rapidly to the base of the free arms, together with the arms resembles much the talons of a bird, whence its generic name; surface ornamented with minute granules.

Basal pieces, three; their under surfaces concave, forming a saucershaped depression, which was wholly filled by the column; they are low, rather thick, upper surfaces prolonged into an obtuse angle; the column facet marked by small short striæ on the outer margin.

Subradials, five; large, four are pentagonal, two of which are larger than the remaining two; their upper articulating surfaces form quite sharp angles; the fifth is hexagonal, its superior surface parallel to the inferior, smaller than the remaining pieces.

Radials, generally five in each ray; the first row are very large, heptagonal, except in the postero-lateral rays, where they are hexagonal, having but one facet on the side next the first anal piece instead of two; their lower surfaces rest on the retreating angles formed by the subradials, with which they alternate; their superior margins are horizontal, on which are imposed the second row of radial pieces; these are smaller than the first, hexagonal, nearly twice as wide as high. The third and fourth rows are similar in form, but become gradually smaller; the fifth rows are heptagonal, axillary, and support on each beveled edge a row of two or three brachials, which are smaller than the radials, obscurely hexagonal, bounded by wave-like lines; near the center of their inferior borders they are prolonged into minute uvulæ, or little tongue-like projections, similar to those found in some species of Forbesiocrinus, (and described by Hall as patelloid pieces,) which fit into corresponding depressions in the adjoining pieces.

Upon the last brachial pieces rest two arms; they are as long as the body, robust, composed of exceedingly stout pieces, grooved by a deep sinus, decreasing gradually in size to their outer extension; they are similar in form to the brachials described above; from either side of these arms, alternately disposed, are stout, short pinnulæ, composed of thick · pieces stretching in a direction outwards and upwards, without tentaculæ. Commencing with the first two pieces of the arms, they come off in two pairs, then on the next two pieces come off again two pairs, but on the alternate side from the first two; this arrangement is continued throughout their whole length, the pinnule becoming smaller and more closely crowded together toward the termination of the arms.

Interradials.-These vary from twenty to twenty-five, according to the age of the individual. The first is large, septagonal, situated between the first two radials of each row, followed by three pieces about half the size of the first; the middle piece of the three is an elongated pentagon, smaller than the other two, which are hexagonal, upon the outer upper facet of each of which, and lying against the radials, are one or two smaller pentagonal pieces; then follow (in the specimen we have before us) fifteen yet smaller pentagonal pieces; they are arranged in the form of a hemispherical arch, depressed towards the disc of the stomach, the sides of the arch being extended up along the radials and brachials as far as the commencement of the free arms.*

* See also under description of Vault.

Interaxillaries. In a line with the radial, and between the two opposite arm pieces, is one to three quite small pentagonal interaxillary pieces; sometimes two yet smaller pieces occur.

Anal pieces, one; small, quadrangular; one is superimposed on the subradial, followed by three pieces of like form and size, and similarly disposed.

Vault. The vault of this remarkable crinoid resembles so much some of the asteriada that we may consider it as one of the connecting links between the crinoidea and the star-fishes. The specimens in our possession do not show distinctly the whole of the vault, so that a description must necessarily be imperfect until better examples are found. The plates which we have described above as interradials, form the greatest portion of the perimeter of this upper surface; the remainder of the perimeter is formed of a row of pieces lying on the anal side; their relative position is as follows: viewing it from the anal side, in the position in which the animal grew, we sce a row of small pieces (interradials?) which extend up along the radials and brachials of the left ray, fitting into the serrated depressions existing at the junctures of any two pieces. This is found only on the left ray, the pieces forming the right being squarely truncated and without other pieces attached in any way to them.

The general surface of the vault is depressed, the edges being raised and curved inwards. From the centre, and in the direction of the arms, extend five rays, composed of two rows of large granular pieces, one row alternating with the other. We cannot discover pores in any of these pieces, which are most probably analagous to the ambulacra of the asteriada.

The interstitial pieces lying in the fields bounded by the five rays of larger ones are very small, granulose, and arranged without any apparent order.

It is impossible, from the fragmentary portions in our cabinets, to trace the farther similarity between this genus and the star-fish, as the central - portions of all are so concealed that we cannot make them out clearly.

Geological Position and Locality.-Found at Clear Creek, Hardin county, Ky., in sub-carboniferous rocks near the upper part of the sandy mud-beds of the knobstone. In beds of similar age in Montgomery county, Ind. Good specimens are rare. Louisville, Ky., Nov. 1, 1859.

ART. X.-Theoretical Determination of the Dimensions of Donati's Comet; by Prof. W. A. NORTON.

I HAVE recently undertaken to bring the theory developed in a previous number of this Journal,* in an article entitled "Dy. namical Condition of the Head of a Comet," to the test of numer ical computations, by determining, by calculation, the theoretical dimensions of the great Comet of 1858. The more important results may be briefly stated; the complete discussion is reserved for a subsequent number of the Journal.

* Vol. xxvii, [2], 86.

It appears from the investigation that, confining our attention. to the outer bright envelope, the process of ejection of nebulous matter from the nucleus was mostly confined to a certain portion of its illuminated side lying nearest to the sun, and that the limiting angle of inclination of the jets to the line connecting the centre of the nucleus with the sun, was 25°. From this circumstance it resulted that the envelope had nearly a circular form. The lateral dispersion of these luminous jets, as they were flowing away into space, under the influence of the sun's repulsion, or, in other words, the breadth of the tail, was partially due to the directions, more or less inclined to the radius vector, in which they originally issued from the nucleus; but another and highly efficient cause coöperated to produce that result. If, as we conceive, certain portions of the cometic matter, at the surface of the nucleus, were brought by some action of the sun into the condition to be repelled by both the nucleus and sun, we may make two suppositions with regard to the forces of repulsion thus developed that the force exerted by either body was of the same intensity for all the particles acted upon, or that it varied from one particle to another. It is not easy to decide, upon à priori grounds, which of the two suppositions is the most probable. The latter is certainly no less so than the former. If we adopt this as a fundamental hypothesis, we have an efficient cause in operation adequate, in connection with that already mentioned, to the development of the tail of the comet, in all its vast proportions; and which may incidentally have produced the special phenomena observed, as the supernumerary tails, and the alternate bright and dark bands seen to traverse a certain portion of the principal tail. The ejected particles that are unequally repelled, by both the nucleus and sun, do not part company in consequence, while they are in the vicinity of the nucleus, nor materially while within the limits of the envelope, for the reason that the ratio of the repulsive forces of the two bodies remains constantly the same; but as soon as they pass out of the sphere of influence of the nucleus they are analyzed by the solar repulsion, and driven off by it into space, in separate and diverging paths. The various susceptibilities to repulsion possessed by the particles have accordingly no sensible effect upon the dimensions or form of the envelope, but may give rise to a wide lateral dispersion of the flowing streams that make up the tail of the comet. The particles that are most energetically repelled go to make up the preceding or convex side of the tail.

I have made the calculations, regarding the solar repulsion as varying between certain prescribed limits. The determinations of the breadth of the tail, at various points of its length, accord with the results of observation; at the same time that the tail is found to have the form and positions actually observed.

The supernumerary tails observed were but lines of receding

particles subject to much greater forces of repulsion than the other particles ejected from the nucleus. All such collections. of matter would, of necessity, be in advance of the principal tail, and lie in a curve that would approach more nearly to a straight line. Their position makes known the intensities of the repulsive forces to which they owe their separate existence.

An interesting result of the investigation is that the alternate bright and dark bands so distinctly seen to traverse a certain portion of the tail of Donati's comet, in nearly parallel directions, on the evening of Oct. 10th, had each the position of a line connecting particles which started from the region of the nucleus at a certain previous date, and at the same instant of time. They accordingly find their natural explanation in corresponding alternations in the quantity of nebulous matter given off simultaneously from the nucleus. The most probable cause for such alternations of discharge that can be conjectured is that the nucleus turns about an axis, and so presented periodically different sides to the sun, which were unequally influenced by his inciting action. If this be the true explanation of the phenomenon, we have in the observed distance between contiguous bright bands, the means of determining the period of rotation; or, at least, the shortest interval of time in which the rotation can be completed. If we take this distance at 1°, the period of rotation comes out about 24 hours.

There was a special cause of lateral dispersion at work in the case of the cometary particles that, on their return, came very near the nucleus. Such streams of particles must have been repelled off obliquely, and may very well have presented the appearance of luminous jets issuing from the sides of the nucleus, and have formed curved terminations to the inner envelope. From the dispersion thus produced resulted an absence of matter, or a dark space, behind the nucleus, whose varying boundary was determined by the intersections of lines of particles unequally repelled by the sun.

The indications are, that the formation and gradual expansion of one envelope after another, may have arisen from the process of ejection beginning in all instances high up in the photosphere surrounding the nucleus, and gradually extending downward to the vicinity of the solid surface. It appears, upon investigation, that if this descending action were to proceed according to a certain uniform law, the outline of the envelope would recede from the nucleus at a uniform rate. This process of evolution of cometary matter, in whatever it may consist, is probably auroral in its origin and character, and has its counterpart on both the earth and sun.*

New Haven, Nov. 30, 1859.

To render the investigation more complete, I have considered the case of the cometary matter being projected from the nucleus, without experiencing any repulsion from its mass.

SECOND SERIES, Vol. XXIX, No. 85.-JAN., 1860.