of "A General Natural History and Theory of the Heavens," Kant undertakes the discussion of no less a problem than this: "To discover the arrangement which unites the great members of the creation in all its parts, even to infinity, and to deduce, by the aid of mechanical laws, the formation of the celestial bodies and the origin of their movements from the primitive state of nature." Kant's views are stated with clearness and ingenuity, but Laplace, by means of his superior knowledge of astronomy, has made a much more definite statement of the phenomena to be explained, and his name is properly more closely connected with the nebular hypothesis than that of any one else. In the hands of Laplace this hypothesis gives a plausible explanation of the formation of the planets of our system and of their satellites; of the zodiacal light and of the singular equality observed between the angular motions of rotation and revolution of the satellites. He explains also the remarkable phenomenon presented by the first three satellites of Jupiter, and which consists in this, that the mean longitude of the first, minus three times that of the second, plus twice that of the third is always equal to two right angles. The chance is very small that such a condition should happen at random. Under this hypothesis the comets are not considered as members of any planetary system, but are regarded as small nebulosities wandering with very small motions from one solar system to another, and formed by the condensation of nebulous matter lying near the limits of a system. Their motions being possible in all directions, when they pass under the control of the attracting force of our sun the inclinations of their orbits with respect to any plane should be distributed at random, and this accords very well with the observed fact. The great excentricities of the cometary orbits also result from this hypothesis; since, if their orbits are elliptical, the major axes must be at least equal to the radius of the sphere of activity of the attracting force of our sun. But from this hypothesis cometary orbits may be hyperbolic, and hence we may observe comets with a sensible hyperbolic movement. However, among the two hundred and thirtyeight comets whose orbits have been determined up to the present time, there is not a single one having a well determined hyperbolic orbit. Several such orbits have been computed, but in every case there is a good degree of probability that the observations can be satisfied within the limits of their probable errors by parabolic orbits. From this it appears that if comets enter our solar system they must do so in such a way that the chances are very slight for giving an orbit that is sensibly hyperbolic. Laplace submitted this question to the calculus of probabilities, and found that there is six thousand to bet against one that a nebulosity that enters the sphere of activity of the sun, in such a way that it can be observed, will describe either a very elongated ellipse, or an hyperbola, which by the greatness of its axis may be taken for a parabola in the part where the comet is seen. In this solution it was assumed that the perihelion distance of the comet does not exceed twice the radius of the earth's orbit. About the beginning of this century two German students began the systematic observation of shooting stars. For many years such observations promised but little, but within ten years past the astronomical theory of shooting stars and meteors has been greatly advanced, and many interesting relations have been discovered between the orbits of shooting stars and of comets. The comet is now generally regarded as the primitive body from whose gradual dissolution is formed a stream of small particles of matter moving around the sun in orbits similar to that of the comet. When the comet's orbit is situated very near the orbit of the earth some of these particles enter the atmosphere of the earth and being ignited by their passage through it produce the phenomenon of shooting stars. One of the most striking coincidences of the orbits of comets and of meteoric streams is that of the first comet of 1866 with the November stream of meteors. It was this coincidence that drew the attention of astronomers to the theory of these streams, although thirty years before Prof. Erman had pointed out the probable cosmical origin of meteoric streams and of their motions around the sun. Several other coincidences have been noticed, among the most interesting of which is the connection of a stream of meteors with the orbit of Biela's comet. Some observers make a distinction between shooting stars and meteors, the last, it is asserted, occurring more frequently during the early hours of the night when more of the meteoric stones have been seen to fall. But this distinction does not appear to be well establishad, since in the early part of the night there are many more observers, and again, the meteors coming into our atmosphere at that time of the night would have a smaller relative velocity and would be less likely to be consumed, and therefore would have a greater chance of reaching the earth's surface as solid bodies. A few meteors have been observed which are remarkable on account of their very great velocities and their decided hyperbolic orbits. The fol lowing is a list of these so far as I have been able to collect cases well authenticated: Computer. 1. Meteor of Oct. 29, 1857.... Petit.... Excentricity 1.80, hyperbo Computer. 2. Meteor of Nov. 15, 1860.... Newton. 3. Meteor of March 4, 1863.... Heis... 4. Meteor of Jan. 30, 1868.... Galle... { No orbit computed, an hyperbola considered certain. ... Excentricity=8.74 .Excentricity=2.28 5. Meteor of Sept. 27, 1870.... Mattheissen... .... Excentricity=1.182 6. Meteor of June 17, 1873.... Niessl.. Excentricity 1.185, hyper bola doubtful. To these results there is this objection; that they depend on observations that are very difficult to make, and which may be affected by such constant errors as will entirely vitiate the results; but most of the computers think there is but little doubt of the existence of hyperbolic orbits. Assuming this to be well established, it is further assumed that bodies moving about the sun with such velocities and in such orbits must come to us from the stellar regions. It is difficult to account for such velocities without making this assumption, and yet there are obvious objections to it. In the first place the chemical analysis of meteoric stones has given very nearly the same elements, and this points to a common origin. But assuming that these stones come to us from the stellar regions, it is certain that they came from the most diverse parts, and we are thus led to a vast assumption concerning the constitution of the matter of those regions. Again, if we assume that the meteors move in hyperbolic orbits and have nothing but an accidental connection with the earth's path in space, since they are visible only when they enter our atmosphere, there must be an immense number continually entering the sun's sphere of activity; for if we suppose that a comet becomes visible when it is at a distance from the sun equal to twice the earth's distance, and take the radius of the earth's sphere equal to 4,200 miles and compare the volume of the ring generated in space by the earth in one revolution to the volume of the sphere whose radius is twice the earth's distance from the sun the chance of visibility is nearly 800,000,000 times greater for a comet than for a meteor. This view, therefore, leads to the conclusion that there is continually going on an enormous interchange of matter between stellar systems, and as these bodies move in hyperbolic orbits it leads also to the result that such orbits must be the most probable, which is contradictory to the result obtained by Laplace. The very great velocities which have been observed in the red flames forming the protuberances on the sun may lead to queries whether ejective and repelling forces may not act from the sun on certain kinds of matter connected with comets and meteors. This idea of a repulsive force acting on certain particles of a comet and thus forming the tail was proposed by Olbers and first applied by Bessel in 1836 to his observations on the tail of Halley's comet. Bessel gave a complete discussion of the problem of determining the form of the tail under this assumption, together with a numerical application to his own observations. The same method has been applied by Prof. Peirce and Dr. Pape to the observations on the tail of Donati's comet in 1858, and by Prof. Schiaparelli to the observations of the comet of 1680. This method consists in applying to the particles that form the tail of the comet the common equations of motion and determining the constant that represents the force of the sun from the observations, assuming the law of force to be the inverse square of the distance. The following are the values of this constant found by the different computers, the plus sign denoting an attractive and the minus sign a repulsive force, the unit being the sun's attractive force at the distance unity: Bessel......Halley's comet, 1835...force = — 1.812 = 5.317 secondary tail 0.000 The difference of more than two units in the results obtained by Prof. Peirce and Dr. Pape for the tail of the same comet may possibly be accounted for by the fact that in this case the force is determined from the observations with great uncertainty. However the results are not very satisfactory. If the numbers indicate anything they show that the sun acts on the particles of different comets with different forces, and also with different forces on the different tails of the same comet, or that the law of force has not been correctly assumed. While the phenomena of comet's tails indicate a repulsive force, the manner in which it acts seems to be unknown. Prof. W. A. Norton in his investigations on the tail of Donati's comet has assumed that the repulsive force varies from one particle to another, and he finds the limits of this force to be -2.73 and +0.46. His conclusion is that the repulsion exerted by the sun, and also by the nucleus, is not a property belonging to all the particles of the mass, and he thinks that it is probably a magnetic or an electric force, emanating from the surface of the body or from a portion of its mass. Leaving the preceding hypothesis of a repulsive force from the sun as having too little evidence to render it plausible under any known form, we shall find that a lunar or planetary origin of hyperbolic meteors has also but a slight probability, and it appears necessary to return to the assumption that they originate in the stellar spaces. This is the position taken by Prof. Schiaparelli in his book on the "Astronomical Theory of Shooting Stars." But first he finds it necessary to remove the objection to the frequency of hyperbolic orbits, which results from the solution given by Laplace from the calculus of probabilities. Accordingly Prof. Schiaparelli gives a new solution of this problem and obtains a result directly opposite that of Laplace, finding that hyperbolic orbits are by far the most probable. It appears to me, however, that Prof. Schiaparelli is not successful in this attempt, and that in his solution he has omitted two considerations that must be attended to in a correct solution. If S be the sun, and Pa point on the surface of the sphere of activity of the sun's attractive force, the bodies that pass through P may have all possible directions, but a direction making a small angle with PS is less probable than one making a greater angle. I cannot see that Prof. Schiaparelli has introduced this condition into his solution. Again, denoting the perihelion distance by D, the velocity by v, and the radius of the sphere of the sun's activity by r, if we suppose all values of D equally probable between zero and D, Laplace finds (Conn. des Tems 1816, p. 216,) that the probabliity that the perihelion distance of the body will be comprised between zero and Dis He then multiplies this expression by dv, integrates between given limits, and dividing the integral by the greatest value of finds the probability that will be comprised within these limits. This division by the greatest value of v is omitted by Prof. Schiaparelli. There is another point in the solution given by Laplace that may be noticed. In order to perform the integration he changes the variable from v to z by means of the equation and in finding the value of z for the limits of integration by solving this quadratic in z he chooses the negative sign before the irrational part of the root, and this choice of the root throws the quantity that is afterwards made infinite into the denominator. It appears to me, therefore, that the solution given by Laplace is correct as considered from his own |