Thus passed two weary weeks. We pored over dry statistics, hunted up every scrap of weather record, and annoyed everybody with questions about cloud and wind; but to little purpose.

The crew of the Ascension is a changing one, three years being the usual term of service, so that no one was able to give us the benefit of long experience of Ascension weather. The answers to our questions were contradictory and distracting in the extreme, being based on casual observation or general impression. The only thing that everybody seemed to agree about was, that “such cloudy weather had not been known within the memory of the oldest inhabitant; it was altogether exceptional, and by-and-by there would be as clear skies as even we could desire.” Yes, “by-and-by” perhaps; but meantime Mars would not wait, and the present was threatening our expedition with disaster.

Oh! those weary weeks. Fearful of losing a single hour of star-light during the night, we watched alternately for moments of break in the cloud, sometimes with partial success, but more frequently with no result but utter disappointment, and the mental and physical strain, increasing every night, grew almost beyond our strength. What was to be done? There was the Observatory complete, the instruments faultless, and the astronomer idle, for there too was the cloud.

Ever since our arrival on the island, we had been much interested about the water supply, and now that we were at the source, we hoped to be able to learn the parentage and history of our one gallon per day.

We had already seen, peeping aboveground here and there, the pipe which we knew conveyed the water to Garrison, there to be stored for the use of man and beast; but we had seen no spring, and I was delighted at a proposal to visit the “Wells” under guidance of Captain Phillimore, who made himself so thoroughly acquainted with the all-important system of our water supply.

Starting from Garden Cottage, we again passed through the tunnel I have already mentioned; this time with lanthorns, which showed it to be worked out of compact beds of cinders and ashes, and occasionally of clay and trachyte, to which clung green moss and lichens. Along one side, just aboveground, an iron pipe ran the length of the tunnel, and we did not lose sight of it until we found sun-light once more in Breakneck Valley. Here we found the two circular wells that contributed so largely to our daily gallon of water. These are known as the “Brandreth Wells,” named after Lieutenant Brandreth, R.E., who came out here in 1830 to assist Captain Bates in his anxious search for water.

Meantime the 5th of September has come. I could write no diary, and have not the slightest recollection of how I spent the day—unprofitably, I fear, in watching and waiting; finally bringing on a violent headache towards evening, which was less painful, however, than the excessive nervous excitement I was endeavouring to repress. To-night Mars will be nearer to us—his ruddy glare brighter than ever again for a hundred years, and what if we should not see him?

The sun had shone all day in a cloudless sky, but before sunset some ugly clouds rolled up from wind-ward, and made me feel quite feverish. I could not rest, but kept wandering about from tent to tent like an unquiet spirit; inwardly resenting David's exceeding calm, as a tacit reproof to my perturbation. There he sat, quietly tying up photographs, softly whistling to himself, as if nothing were going to happen, and then he actually smoked a very long pipe, with even longer and slower whiffs than usual. Of course it was affectation! But I wondered how he managed to keep up the deception, and for the first time fully believed what he had told me of having enjoyed his breakfast on the morning of the Transit of Venus, notwithstanding that it rained.

Do all comets belong to tile solar system?–Orbits -which are clearly hyperbolic– Opinion of Laplace with regard to the rarity of hyperbolic comets–Are there any comets which really describe parabolas?–First glance at the origin of comets.

Do all the comets which have been observed up to the present time belong to the solar system? Or, as we have already suggested, are there comets which visit the sun but once, and which before penetrating to the sphere of his activity and submitting to the influence of his attraction were altogether strangers to our system?

Theoretically speaking the reply is not doubtful. A celestial body, describing under the influence of gravitation an orbit of which the sun is the focus, may move in a parabola, an ellipse, or an hyperbola. All depends upon its velocity at any one given point of its course, that is, upon the relation existing between the velocity and the intensity of gravitation at that point. The better to explain this let us take a point whose distance from the sun is equal to the mean distance of the earth, and let us suppose the body to have arrived at this point.

Discovery of the comet and of its periodicity by D'Arrest–Return predicted by M. Yvon Villarceau for 1857 ; verification to within half a day–Importance of the perturbations caused by Jupiter–Research of MM. Yvon Villarceau and Leveau –Return of the comet in September 1870.

Here, again, we have a periodical comet whose periodicity has been determined by calculation, and whose returns have been predicted and observed without the help of any comparison with previous comets. It bears the name of the astronomer who discovered it in 1851, and who recognised the periodicity of its orbit. M. Yvon Villarceau had drawn the same conclusion, and calculated the ephemeris for its next return to perihelion, which he announced for the end of 1857, a prediction verified to within twelve hours. The new comet was seen again at the Cape of Good Hope by Sir Thomas Maclear. On its following return, which took place in 1864, astronomers were less fortunate, and were unable to perceive the comet, whose position in the heavens and distance from the earth were very unfavourable. In 1870 the perihelion passage of the comet took place on September 23; it was observed three weeks before by M. Winnecke, thanks to the ephemeris calculated by MM. Yvon Villarceau and Leveau.

‘Of all the comets which have not failed to return to us,’ says M. Yvon Villarceau, ‘ the comet of D'Arrest is perhaps the most interesting in regard to its perturbations. T do not thinkthat any other comet has been so closely followed by Jupiter.’

How to discover the periodicity of an observed Comet and predict its return –First method: comparison of the elements of the orbit with those of comets that have been catalogued –Resemblance or identity of these elements; presumed period deduced from it–Second method: direct calculation of elliptic elements – Third method.

There are, however, a certain number of comets of whose return astronomers are certain, and the time of whose apparition they can calculate. The prediction of the probable epoch at which these comets will be situated in regions of the heavens where they will be visible from the earth, and the determination of their perihelion passage, can be effected more or less accurately. These are the comets whose orbits, when calculated from a sufficient number of observations, prove to be neither parabolas nor hyperbolas, but, on the contrary, are closed and elliptic, and such that the comet thenceforth continues to describe them in regular periods; in a word, they are periodical comets Newton treated the orbits of comets as parabolic, merely in order to so represent the arc, always very short, described in the neighbourhood of the perihelion, when the comparatively small distance of the comet from the sun renders observations possible. In his opinion comets were bodies of regular periods, and which described ellipses, certainly very elongated, but in all respects similar to the planetary orbits.

Comets which have or seem, to have a common origin–Double comets–Systems of comets according to M. Hoek–Distribution of aphelia over the celestial vault; region of the heavens particularly rich in aphelia.

When, in accordance with the actual facts of science, we endeavour to form an idea of the constitution of the visible universe, we see that the celestial bodies which compose this whole are everywhere distributed into groups and associations united by the common bond of universal gravitation.

There are the planetary systems. In the centre of each group is a star or central sun, whose preponderating mass retains near him, circulating in regular orbits, other stars or planets, to which this central sun distributes heat and light. Our planetary system is the type of associations of this kind.

There are the stellar systems, groups of two, three, or more suns gravitating about one another, probably in accordance with the same laws. These systems are themselves the elements of greater associations, which, like the resolvable nebulas known under the name of stellar masses, are composed of myriads of suns. The Milky Way is one of the most splendid examples of these immense agglomerations.

In certain regions of the heavens the nebulae are themselves to all appearance grouped into systems, so that the general plan of the universe is one vast synthesis of associations of different orders encompassing each other without end.

Differences of inclination, eccentricity, and direction of motion.

If, then, periodical comets, calculated as such, and known to be periodical by their return, are governed by the same laws as the planets, why is a distinction made between these two kinds of celestial bodies? This is a question of high importance, and one which we cannot completely answer at the present moment. A full reply would necessitate some definite knowledge concerning the origin of the bodies which compose the solar world. It would be necessary to have studied and compared the physical constitution of comets with that of planets. Both in origin and constitution we shall see farther on that they appear to be essentially different. Surveying the question, however, from a single point of view, regarding it as a question of movement only, we can already show differences which separate these two classes of celestial bodies, and justify the double denomination by which they are distinguished.

Comets, as we have already seen, appear in any quarter of the heavens, instead of moving, like the planets, in the narrow zone of the zodiac. This difference arises from the inclinations of their orbits to the plane of the ecliptic Among the principal planets Mercury alone has an inclination as great as 7 degrees; and among 115 telescopic planets 29 only have an inclination greater than 10 degrees, and very few exceed 30 degrees; but we see, on the contrary, the planes of cometary orbits admit of all inclinations.

Calculation of the elliptic elements of the second comet of 1867, discovered by Tempel–Perturbations due to Jupiter, and corsequent delay in the return of the comet to its perihelion in 1873–Remarkable agreement of observation and calculation.

The second comet of 1867, discovered by M. Tempel, was found by several astronomers to have elliptic elements. It passed its perihelion on May 23, 1867, and its period had been calculated at 2,064 days. But Dr. Söllinger, taking into account the perturbations its passage in the vicinity of Jupiter would produce in the elements of its orbit, assigned a retardation of 117 days in the date of its return to perihelion in 1873. It was, in fact, seen again in the course of that year, and its perihelion passage took place on May 9, which gives for the duration of the revolution performed in the interval between the two apparitions a value of very nearly six years, or 2,178 days, three days less than the number determined by calculation.

Tempel's comet of short period is, therefore, the ninth periodical comet whose return has been verified by observation; that is to say, which really forms an integral part of our solar system. Observed in May 1873, at Greenwich, by Messrs. Christie and Carpenter, it appeared in the telescope like an elongated nebulosity, about 40″ in diameter, with a central nucleus, which shone like a star of the twelfth or thirteenth magnitude.

Had the Egyptians and Chaldeans any positive knowledge concerning cornets?– Apollonius of Myndus; the Pythagoreans considered comets to be true stars– According to Aristotle they are transient meteors ; fatal influence of the authority of this great philosopher upon the development of Cometary Astronomy.

Such is a very brief history of the errors into which the human mind–we should rather say the human imagination–. has fallen with respect to comets. We have now to show how little by little, and by very slow degrees, truth disengaged itself from error, and to supplement the history of superstitions and prejudices by that of science. Both are instructive and throw light upon each other at all stages of their mutual velopment. Thus, for example, we may readily conceive that the irregular movements of comets, their sudden and unforeseen apparition, to say nothing of the singularity of their aspect, for a long time precluded the idea of their being true stars, subjected to fixed laws, like the planets. Centuries of work, observation, and research were required for the discovery of the true system of the world as far as the sun, the planets, and the earth were concerned; but a difficulty of another kind stood in the way of the discovery of the true movements and nature of comets, since no trouble was taken to make exact and continuous observations of them.

Direction of the tail opposite to the sun; discovered by Apian; the Chinese astronomers were acquainted with this law–Deviations in some comets–Variable aspect of the tail according to the relative positions of the comet, the earth, and the sun.

In respect to the direction of cometary tails let us call attention to an important point–to a general phenomenon which was remarked by the ancients, in the very earliest times. Seneca refers to it in the following line:–

The comæ of comets fly the ray a of the sun. According to Edward Biot the Chinese astronomers had observed, since the year 837. this constant direction of cometary tails from the sun. ‘ In Europe, ’ says Lalande, ‘ Apian was the first to perceive that the tails of comets were always opposite to the sun; this rule was afterwards confirmed by Gemma Frisius, Cornelius Gemma, Fracastoro. and Cardan. Nevertheless, Tycho Brahe did not believe it to be very general or well demonstrated; but the fact itself is beyond a doubt. ’

Pingré observes with truth that the direction of the tail is not always strictly opposite to the sun. He instances the comet of 1577, whose tail was deflected as much as 21° towards the south, and the great comet of 1680, when the deflection was about 4 ½°. On both these occasions, however, the comet and the earth occupied the same relative positions in the heavens.

Periodicity of the meteor-swarms; radiant points; number of swarms recognised at the present day–Periodical maxima and minima in certain meteoric currents; thirty years period of the November swarm–Parabolic velocity of shooting stars ; the swarms of shooting stars come from the sidereal depths.

These considerations bring us to the theory recently elaborated by the learned Italian astronomer M. G. V. Schiaparelli, Director of the Observatory of Brera, at Milan.

According to this theory there exists between comets and shooting stars a connexion and community of origin, which henceforth we may regard as certain, as it is supported both by logical deduction and observation. We shall now explain by what train of ideas this assimilation between phenomena which at first sight appear so foreign to each other has passed from the phase of simple hypothesis into that of a theory which observations of great value permit us at the present time to consider demonstrated.

Let us first of all pass in review the facts upon which the theory is based.

The shooting stars which may be observed on any clear night throughout the year are notably more numerous at certain times, the dates of which are nearly fixed, as, for example, August 10, November 13 or 14, and April 20.

Three observations are necessary for the calculation of a parabolic orbit – Cometary ephemerides; what is meant by an ephemeris; control afforded by the ulterior observations –Elements of an elliptic orbit – Can the apparition or return of a comet be predicted?– State of the question – Refutation by Arago of a current prejudice

Three observations of a comet–that is to say, three different positions (in right ascension and declination) of the nucleus of a comet, or, in a word, three points of its trajectory or apparent orbit sufficiently distant from each other–are required, as we have said, for the calculation of the parabolic elements of the true orbit.

In the last century this determination was not only a long and laborious operation, but involved much tentative and uncertain work. Before engaging in the difficult calculation of the elements of an orbit, astronomers made trial graphically and even mechanically of different parabolas, and only began the calculation after satisfying themselves that one of these curves nearly represented the positions furnished by observation. Great improvements were introduced into these methods during the last century by Lalande, Laplace, and Gauss. But the calculation of a cometary orbit is always a sufficiently complex operation, even if it be simply parabolic, and it still takes a skilful computer accustomed to this kind of work, several hours to find approximate values of the different elements. This is not the place for us, of course, to attempt an explanation of the work itself.