action has its velocity diminished, the angle between the directions of the motions of the two bodies about the sun is increased in all cases in which that angle is at first greater than 45°. 30. Again, when w is less than 45°, and the planet before disturbance moves in a parabola so that v=v1√2, then V-v1 cos a is positive for all values of @ unless Vv1, that is, unless v+v'<2v1, in other words 2d>2v1(√2-1)=0·828v1. Therefore, when a planet overtaken by a comet, the directions of their motions differing less than 45°, has its velocity diminished, that difference of direction will be increased unless the comet comes so near to the planet as to lose by its perturbing action a part of its velocity at least equal to about ths of the planet's velocity. 31. Therefore, it is only in exceptional cases (28, 29, 30) that the shortening by a planet's action of the periodic time of a comet moving in an orbit of long period is not connected with an increase of the angle of divergence of the two motions, and a consequent tendency to increase the inclination of the two orbits. In the exceptional cases the comet overtakes the planet, passes around close to and in front of it, and is thus left behind with an absolute velocity and hence a periodic time much less than that of the planet, and with a direct motion. 32. On the other hand, for given values of vo and v1, and w>90°, the smallest value of v' corresponds to w'=180°, when v′ =vo— V1. If the comet approaches in a parabolic orbit v=v1√2, and we have for the smallest value of v', (v3+v ̧3—2vv, cos w)*—v‚= v1 { (3—21/2 cos co)1—1 }. Hence (3-1)=0·731. Therefore, when the inclination of a comet's orbit is greater than 90°, and it approaches the planet in a parabolic orbit, it leaves the vicinity of the planet with an absolute velocity greater than ths of the velocity of the planet's velocity in its orbit. We may say that the value of ', when w>90°, will be in general much greater than v1, and therefore may conclude that the comet whose inclination exceeds 90° will rarely by a planet's attraction acting during a single passage be reduced from a parabolic orbit to one whose periodic time is less than that of the planet. 33. Apply now these propositions to the questions stated above (24). If comets are from stellar space they come toward the planets at first a trifle faster than if moving in a parabola. If one of them does not lose velocity, or if passing behind a planet it gains velocity, that comet goes off into space again never to return. But if it passes in front of a large planet, within a moderate distance of it, it loses velocity enough to remain a permanent member of our system. Most observed comets have on this hypothesis thus lost velocity. What proportion have not depends upon how fast the process of disintegration of comets goes on. If this process is very slow, the new comers on our list should form a smaller proportion than if the process is rapid. But it has been seen that in the process by which they lose velocity their orbits have their inclinations in general increased. This is particularly true for the inclinations between 45° and 135°, for the corresponding comets are more likely to pass directly across in front of the planets. Hence in fig. 1 we ought to expect on Laplace's hypothesis as a result of perturbations an increase of the ordinates between 90° and 135°, at the expense of the ordinates between 45° and 90°. Again, the periodic comets form a marked group and should probably be treated separately. Now it is reasonable to suppose that a large part of the area between 0° and 20° lying below the shaded area is due also to comets of short periods. Of the twenty-six comets in the table whose inclinations are less than 20°, nine are noted as periodic and furnish the shaded area near A. Of seven of the remainder, viz: 1743 I, 1678, 1585, 1766 II, 1819 IV, 1867 I and 1847 V, the orbits computed are ellipses, mostly short ones, but the comets have not been certainly detected at any return. Of the other ten about half were not well enough observed to enable us to say whether their periods were short or long. It is probably safe to assume that the area between the curve of sines and the shaded area belongs, up to 20°, to comets of short period. These return so frequently that their number in a list of observed comets is out of all proportion to their number among existing comets. Whatever theory of the origin of this group we may assume they should, because of the comparative ease of their being detected, not count for much in studying the original distribution of the inclinations. Čorrect then the curve in fig. 1 by striking off the surplus area below 20°, bringing back some of the area from the second into the first quadrant to counteract the effect of perturbation, and the result corresponds well with the theoretical curve of sines, especially if this curve is slightly reduced in amplitude, as it should be, because of the removal of the periodic comets. We therefore conclude, that the curve of fact does agree well with that required by the hypothesis of Laplace if we first make reasonable allowance for known perturbations, and for the comets of short periods. 34. Can the facts of the distribution of inclinations be explained with reasonable suppositions on Kant's hypothesis? I think not. If the comets are from matter at a very great distance from the sun the line AB should represent the theory, and the decided turn of the curve downward towards 180° seems inexplicable. The same is true for the downward turn of the curve near A when the comets of short period are thrown out, wholly, or in part. The effect of perturbation should be to push the area forward towards B. But if the comets come from matter somewhat nearer to the sun, the line of theory should start above A and run out below B. The perturbations should then increase some inclinations and decrease others, with a slight tendency, in the mean, to increase them. For the comets whose times are decreased, and, therefore, whose inclinations are increased, would return more frequently and so be more likely to appear in our list, while some of those whose inclinations are diminished would go off altogether. But the perturbations would not easily remove the excess of area from near A in the figure. We therefore conclude that the curve of fact is not made to agree with the hypothesis of Kant by simple and reasonable allowances for perturbations. 35. The separate group of comets of short period may, for aught that appears in this discussion, have come either from material of the solar nebula, or from outside. In the former case they would seem to be merely asteroids turned out of the region between Mars and Jupiter, usually occupied by those bodies. If they came from outside there is a reason for their direct motion in the fact that only comets leaving the neighborhood of Jupiter's orbit with a small velocity can move in these short periods, and only comets overtaking Jupiter can have their velocities so much diminished in a single approach to the planet. It is to be considered, however, that a comet leaving the neighborhood of a large planet has peculiar tendency to come again under its influence in subsequent revolutions. A slower velocity of approach changes much the problem at the second passage near the planet. 36. How the comets first became solid is a question of great interest. That they are solid seems evident from the solid nature of the fragments broken off from the comets since they entered the solar system, i. e., the meteorites and meteoroids. The character of these fragments corresponds more with that of the deeper rocks than with those on the surface of the earth. It seems very improbable that iron masses whose like in the earth is found only in the igneous trap rocks, especially in the Greenland traps, should have become consolidated in the cold of space in small parcels. The internal structure of the comet fragments are records of an interesting early history. To decipher the legends belongs rather to the mineralogist and the physicist than to the astronomer. My effort has been to find where they were written. ART. XVI.—On the Animal of Millepora alcicornis; by THE attention of zoologists was called to the relations of Millepora by the announcement of Agassiz in 1858 that "Millepora is not an Actinoid Polyp, but a genuine Hydroid, allied to Hydractinia."* Professor Agassiz figured the animals as seen by him, in his Contributions to the Natural History of the United States, vol. iii, p. 61. On the evidence afforded by a single observation of Millepora, he proposed to transfer to the Acalephæ not only that genus, but all the Madreporaria Tabulata of Milne-Edwards. Professor Verrill has shownt that the latter inference cannot be accepted, and that the Madreporaria Tabulata form an artificial and quite heterogeneous assemblage. There has been much difference of opinion as to the soundness of Agassiz's conclusion in regard to Millepora itself, and the extreme shyness of the animals has rendered it impossible to accumulate numerous observations. A paper by General Nelson and P. Martin Duncan,‡ contains figures of the animals of Millepora alcicornis, as observed by the former author while stationed at Bermuda many years ago. The figures differ from those of Agassiz in arranging the tentacles regularly in whorls of four, and the authors conclude that Millepora is probably an Alcyonarian. The arrangement of tentacles is certainly quite unusual in the Alcyonaria, admitting the correctness of General Nelson's figures. In November, 1875, a paper by Mr. Moseley of the Challenger expedition was read before the Royal Society, in which the author reported observations on Millepora at Bermuda and elsewhere. The observations seem to have been quite unsatisfactory, and the author at that time ventured no conclusion from them. He was, however, more fortunate at Tahiti; and his paper read before the Royal Society in April, 1876, gives the results of a more complete and satisfactory series of observations on the genus in question than has been made by any other author. His conclusions agree substantially with those of Agassiz. In the winter of 1876-7, the writer spent some weeks in Bermuda, residing for a part of the time at Flats Village, on the shore of Harrington Sound. The abundance of Millepora in the shallow water of that beautiful lagoon afforded excellent opportunity for an investigation of the animals. In this work, *This Journal, II, xxvi, 140. + Ibid, III, iii, 187. Ann. and Mag. Nat. Hist., xvii, 354. Philosophical Transactions, clxvi, 91; abstract in Ann. and Mag. Nat. Hist., xvii, 147. | Phil. Trans., clxvii, 117; abstract in Ann. and Mag. Nat. Hist., xviii, 178. the writer was favored with the kind assistance of Mr. G. Brown Goode, of the Smithsonian Institution. Our experience enabled us to appreciate the difficulty which observers have always found in the extreme shyness of the animals. Great care was taken in collecting the animals to avoid subjecting them to any more of a shock than was necessary. In accordance with a suggestion of Professor Verrill, we were careful not to have the specimens out of water for an instant either in collecting them or in the subsequent manipulation. Specimens were collected at various hours of the day, and examined at about all hours of the day and night. Only once were we favored with a sight of the zooids in expansion. Though that observation was far from being as satisfactory as could be desired, the writer has thought it might be worth while to give an account of it; for, on a subject so important and presenting such difficulties to every observer, every scrap of observation is probably worth saving. The zooids which we saw in expansion showed generally a pretty regular whorl of tentacles at the summit. There seemed to be indications of a tendency to a grouping of the tentacles in one or more whorls below the one at the summit. But these lower whorls were not at all regularly developed, and in some cases the tentacles were scattered singly without any recognizable arrangement in successive whorls. Where an approximation to a whorled arrangement could be recognized, the number of tentacles in a whorl was generally four, but appeared to be sometimes three. As regards the arrangement of the tentacles, our observation is therefore substantially in agreement with those of Agassiz and Moseley. We feel very confident that the tentacles are not in uniform and regular whorls of four, as figured by Nelson and Duncan. 1. 2. 3. 4. 5. The accompanying figures, 1 to 20, represent the outlines of several zooids in the various positions in which they chanced to present themselves. The drawings were made hastily while the specimens were under examination. It is needless to remark that they make no pretension to any artistic character. Whatever value they may have arises from the fact of a conscientious endeavor to draw exactly the outlines which were seen, not a line being added hypothetically or inferentially. Figures AM. JOUR. SCI.-THIRD SERIES, VOL. XVI, No. 93.-SEPT, 1878. |