The door was closed, and the choir was learning a new hymn. Bathsheba was stirred by emotions which latterly she had assumed to be altogether dead within her. The little attenuated voices of the children brought to her ear in distinct utterance the words they sang without thought or comprehension:

Lead, kindly Light, amid the encircling gloom

Bathsheba's feeling was always to some extent dependent upon her whim, as is the case with many other women. Something big came into her throat and an uprising to her eyes as she thought that she would allow the imminent tears to flow if they wished. They did flow and plenteously, and one fell upon the stone bench beside her. Once that she had begun to cry for she hardly knew what, she could not leave off for crowding thoughts she knew too well. She would have given anything in the world to be, as those children were, unconcerned at the meaning of their words, because too innocent to feel the necessity for any such expression. All the impassioned scenes of her brief experience seemed to revive with added emotion at that moment, and those scenes which had been without emotion during enactment had emotion then. Yet grief came to her rather as a luxury than as the scourge of former times.

99.66

From The Popular Science Review. ture, would be much more satisfactory CLASSIFICATION OF COMETS. than the arrangement of comets into vaBY RICHARD A. PROCTOR, B.A., CAMBRIDGE, rious orders differing only in size. One of the most interesting questions, then, AUTHOR OF "SATURN," THE SUN," ETC. in the cometic astronomy of a few years SOME of the facts of science are stran- ago was this - Are the peculiarities just ger than any fictions which even the liveli- referred to — the absence or presence of est imagination could devise. So strange a nucleus, or of a tail- really characterare they that even the student of science (istic, or do they correspond to mere difwho has been engaged in the work of ferences of development? I say that mastering them is scarcely willing to ad- this question belonged to cometic asmit them in their full significance, or to tronomy of a few years ago, though even accept all the inferences which are di- then there were reasons for regarding rectly or indirectly deducible from them. the various forms of structure observed This, true in all departments of science, in comets as depending only on developis especially noteworthy in astronomy; ment. Of course comets which, during and perhaps there is no branch of astron- the whole time of their visibility, showed omy in which it is more strikingly seen neither tail nor well-defined nucleus, than in that which relates to comets. could afford no means of answering the During the last quarter of a century dis- question. But a comet like Donati'scoveries of the most surprising nature the glorious plumed comet of 1858 have been made respecting these myste- which appeared as a mere globular haze rious bodies; relations have been re- of light, and gradually during its apvealed which bring them into association proach to the sun assumed one form with other objects once regarded as of a after another of cometic adornment totally different nature, and the path the nucleus, the fan-shaped expansion, seems opened towards results yet more the long curved tail, striations within the amazing, by which, more than by any tail and envelopes outside the fan, while others which even astronomy has dis- finally even subsidiary tails made their closed, we seem brought into the pres- appearance — teaches us unmistakably ence of infinite space and infinite time. that these features depend merely on deThe earth on which we live - nay, our velopment. We might as reasonably solar system itself - -seems reduced to place the chicken in another class than the utter insignificance compared with the full-grown fowl because it has neither tremendous dimensions of comet-trav-comb nor coloured tail-feathers, as set a ersed space; while all the eras of history, small comet in another order than that and even those which measure our earth's to which Donati's belongs because the existence, seem as mere seconds com-small one shows neither tail nor coma. pared with the awful time-intervals to The gradual loss of these appendages by which we are introduced by the study of Donati's comet, during its retreat into cometic phenomena. outer space, of course strengthens this One of the most interesting points view. But perhaps the most remarkable suggested by the recent cometic discov-proof ever afforded of the variety of aperies is the question, how comets are to pearance which the same comet may be classified. That they are not all of present, was that given by Halley's comet the same order is manifest, whether we at its return in 1835-36; for on that occaconsider their size, or the shape and ex-sion, after showing a fine coma and tail tent of their orbits. But precisely as in during its approach towards the sun, it zoological classification mere size or de- was seen in the southern hemisphere by velopment is considered a much less Herschel and Maclear, not only without important point than some really charac-tail, but even without coma, appearing teristic difference of structure, or even in fact precisely like a star of the second than a difference of distribution, so in magnitude. After this that is to say, classifying comets it would be unsatis- during its retreat it gradually resumed factory in the extreme could we have no its coma, and even seemed to be throwmore characteristic difference to deal ing out a new tail, but no complete tail with than that of dimensions. Suppos- was formed while the comet remained ing, for instance, that we could separate visible. comets into those with or without a nucleus, or those with or without a tail; such a classification, if it was found to correspond with a real difference of na

Indeed the difference between the appearance presented by the same comet before and after its nearest approach to the sun is not only remarkable in itself,

but subject to remarkable variations. |not here enter into any special consider"What is very remarkable," says Siration of the results of spectroscopic John Herschel on the first point, "the analysis as applied to this comet, because shape and size are usually totally differ- to say truth our spectroscopists have not ent after the comet's reappearance (on met with any noteworthy success; and the other side of the sun) from what they we must wait till the spectroscopists of were before its disappearance. Some," the southern hemisphere have sent in he remarks on the second point, "like their statements before we can determine those which appeared in 1858 and 1861, whether any special accession has been without altogether disappearing as if made to our knowledge. It may, however, swallowed up by the sun, after attaining a be assumed from what has been observed certain maximum or climax of splendour here, that the characteristic spectrum of and size, die away, and at the same time comets, large and small, is that threemove southward, and are seen in the band spectrum which was first recogsouthern hemisphere, the faded rem-nized during the spectroscopic investinants of a brighter and more glorious ex-gation of Tempel's small comet in the istence of which we here witnessed the year 1866.

spects the distinctions on which it depends, but exceedingly suggestive (as, in fact, every just mode of classification may be expected to be).

I would divide comets into three classes, according to the nature of their paths.

grandest display; and on the other hand Comets, then, must be classified in we here receive as it were many comets some other way. It is not difficult to from the southern sky, whose greatest select the proper mode of classification display the inhabitants of the southern - a method not only satisfactory as reparts of the earth only have witnessed. It also very often happens that a comet, which before its disappearance in the sun's rays was but a feeble and insignificant object, reappears magnified and glorified, throwing out an immense tail, and exhibiting every symptom of violent excitement, as if set on fire by a near ap- First, there are the comets which have proach to the source of light and heat. paths so moderate in extent that their Such was the case with the great comet periods of revolution belong to the same of 1680, and that of 1843, both of which, order as the periods in which the planets as I shall presently take occasion to ex-revolve around the sun. This class inplain, really did approach extremely near cludes all the comets which have been to the body of the sun, and must have described as Jupiter's comet-family, and undergone a very violent heat. Other all those similarly related to Saturn, to comets, furnished with beautiful and Uranus, and to Neptune. Other comets conspicuous tails before their immersion of somewhat greater period than Nepin the sun's rays, at their reappearance tune's comet-family may perhaps be reare seen stripped of that appendage, and garded as associated with as yet undisaltogether so very different, that but for covered planets revolving outside the a knowledge of their courses it would be path of Neptune, and therefore as belongquite impossible to identify them as the ing to the same family. I would not, same bodies. Some, on the other hand, however, attempt to define very narrowly which have escaped notice altogether in the boundary of the various classes into their approach to the sun, burst upon us which comets may be divided, and in at once in the plenitude of their splen- what follows I shall limit my remarks to dour, quite unexpectedly, as did that of comets which are clearly members of one the year 1861." or other class, leaving out of consideration those respecting which (for want, perhaps, of more complete information than we at present possess) we may feel doubtful.

It was clear, then, long since, that comets cannot be classified either according to their size or their development. But this has been even more conclusively shown by the spectroscopic analysis of large and small comets. For certain bright bands seen in the spectra of the small comets which had been examined before the present year, are found also to characterize the spectrum of the comet which adorned our northern skies last June and July, and to be shown not only by the coma, but also by the tail. I do

Secondly, there are comets of long periods, but which yet show unmistakably, by their motions, that they are in reality members of the solar system — such, for instance, as Donati's comet, which may be expected to return to the sun's neighbourhood in the course of about two thousand years.

Lastly, there are the comets whose

from the comets of long period, because perturbations excited within the solar system might change an elongated elliptic orbit into a hyperbolic one. The point at issue is thus seen to resolve itself into the question whether we can assert that there are comets which from the earliest times (the youth of the solar system) have belonged to it (i.) with short periods and (ii.) with long periods, while (iii.) other comets have visited it from other systems. We find in fact that the attempt to classify leads in this case, as it has led in so many others (as perhaps it inevitably must lead, if properly conducted), to the question of origin.

motions indicate a path not re-entering | some at least of those which travel on into itself. These are of two orders: elliptic paths of great eccentricity are in those which retreat from the sun on a reality to be classified apart from the hypath tending with continual increase of perbolic comets, as having had a different distance to become more and more nearly origin and a different history. We might, parallel to the path by which they had indeed, reverse the argument just adapproached him; and those whose reduced, and reason that the hyperbolic treating path carries them divergingly comets ought not to be classified apart away so that they retreat towards a different part of the heavens than that from which they arrived. Technically, the two orders are those of comets pursuing (i.) parabolic and (ii.) hyperbolic paths. In reality, however, we may dismiss the parabolic path as never actually followed by any comet, any more than a truly circular path is ever actually followed by any planet. We may take it for granted that any comet which seems to follow a parabolic path really follows either an enormously elongated oval path, and so belongs to our second class; or a path carrying it forever away into outer space, and nearly in the direction from which it had arrived, but not exactly. A comet's And here perhaps the question will path could only have the true parabolic arise, may we not cut the Gordian knot form by a perfect marvel of coincidence; by denying that even the comets of short and in point of fact if a comet could by period can be separated from the hypersome amazing chance approach our sun bolic comets which visit our system from on such a path, the very least of the mul-interstellar space? I am aware that the titudinous disturbing attractions to which theory of comets and meteors which the comet would be exposed would suf- Schiaparelli has advanced, and which fice to change the path either to the ellip-many in this country have viewed with tic or the hyperbolic form.

considerable favour, points to this conAnd here we may pause to inquire how clusion. For according to that theory far the second of the three classes into meteor-systems are groups of discrete which comets have thus been divided can bodies which have been drawn towards be regarded as a class apart. Does the our solar system, gradually lengthening mere fact that a comet has a re-entering out as the process of indraught continued, path- so that, unless perturbations af-and have then been compelled by the fect it, the comet will travel in continual perturbations to which they have been dependence on our sun-afford a suffi- subjected within our system, to become cient reason for distinguishing the comet members of it; and as comets and mefrom others which travel on a hyperbolic teor-systems have been found to be assopath? It appears to me that this ques-ciated together in some mysterious way, tion admits of being answered in two this theory of the introduction of meteorways. When we remember that a comet systems is in reality a theory of comets. approaching our system on a slightly Now since some certainly among the hyperbolic path might have that path meteor-systems have periods of moderate changed into an elliptic figure by the length, this theory of Schiaparelli's would perturbations to which the comet would regard the short-period comets as drawn be subjected during its visit, we may out of the interstellar depths, while manireasonably decide that the mere fact of a festly it would be absurd not to extend comet pursuing an elliptic path ought Schiaparelli's theory to hyperbolic comnot to be considered a valid reason for ets. In fact, we know that he himself distinguishing it from one of the hyper-regards his theory as requiring the occabolic comets. But when we consider, on the other hand, that there are comets like those of Jupiter's family, which are quite distinctly separated by the nature of their paths from the hyperbolic comets, we may not unreasonably infer that

sional appearance of meteors of hyperbolic path, and therefore as not merely consistent with the phenomena of hyperbolic comets, but accounting for them. Adopting his theory, then, to its fullest extent, we should regard all comets and

meteors as bodies coming from the inter- velocity at given distances from the sun. stellar depth: for it is not easy to see Thus, when at the distance of Neptune how any comet or meteor-system could its velocity would be 47 miles per secbe so far distinguished from its fellows ond; at the distance of Uranus, 5'9 as to be regarded as originally a member miles per second; of Saturn, 83 miles; of the solar system. of Jupiter, 113 miles; of the asteroids, from 15 to 16 miles per second; and the velocity in crossing the distances of Mars, the Earth, Venus, and Mercury, would be 208 miles, 259, 303, and 414 miles per second respectively. Now we know that the greatest velocity which any given planet can communicate to a body approaching it under its sole influence from interstellar space is very much less than the velocity which such planet can communicate to a body approaching it under the sun's influence in addition to its own, for the communication of velocity to a moving body is a process requiring time, and in the latter of the two cases just considered the body is for a much smaller time under the influence of the planet. And the velocity which

But for reasons which appear to me incontrovertible, I find it impossible to give in my adhesion to Schiaparelli's views, in the form in which he presented them. A line ought to be carefully drawn between what has been proved and what has not been proved respecting the opinions which Schiaparelli has advanced. His most happy conception, that meteors would be found to travel in the paths of comets, has been realized, and no possible question can be raised as to the completeness of the demonstration; but it is quite otherwise with his supposition respecting the manner in which meteoric systems or comets have been introduced into the solar system. It not only has not been proved that comets have been compelled by the perturbations of the planets to become permanent members of the solar system, but

cause we only require to consider the ratio in what follows. Then we have —

grave doubts rest on the bare possibility 183 √ √

of such an event occurring.

=

I- = 25'9

2a

&c.

}

= 25'9,

terms,

Let it be remembered that the conditions of the problem are purely dynamical. We know that a comet's head obeys the laws of gravity, and whatever peculiarites may affect the motions of the matter of comets' tails are not by any means such as would help to render easier the captures conceived by Schiapa-infinity would have a velocity of about 25'9 miles per relli. Confining ourselves then to gravity, we can determine readily in what way a comet might be captured. Take the case of a particle travelling towards our solar system from out the interstellar depths under the influence of the sun's attraction. Such a particle may be regarded as practically approaching the sun from an infinite distance, and we know its

if a is made infinite. But if a be taken equal to half
the distance of Alpha Centauri, say = 100,000, we have
= 25°9 — 0′00006475 — 0*000000000809375 — smaller
all the terms after the first being together manifestly
less than 0'00007, or about 4 1-2 inches. In other
words, whereas a body approaching the sun from
second, a body approaching the sun from the distance
of Alpha Centauri, so that its mean distance may be
regarded as half the distance of that star, would have a
velocity less by 4 1-2 inches per second, a difference so
small that it may be regarded as evanescent.
such differences are when we are merely comparing
curious consideration, however, that minute though
velocities, yet distances due to such differences in the
enormous time-intervals which the study of comets in-
troduces to our consideration, are to be measured by
thousands of miles.

It is a

The comparison is easily made in any given case. Take, for instance, the planet Jupiter, supposing it at rest, and a particle drawn towards it from an infinite distance under the combined influence of the sun and planet (the particle lying originally on the side away from the sun). We readily obtain for the velocity V of the particle just as it is reaching the surface of Jupiter the equation