Chapter X: Part 10

In any telescope, whether refracting or reflecting, there are two principal parts: the part that forms the aërial images of the distant objects, and the small lens by the aid of which these images are enlarged just as if they consisted of radiating matter. When the image is produced by means of a lenticular glass, the place it occupies will be found in the prolongation of the line that extends from the object to the centre of the lens. The astronomer, furnished with an eye-piece, and wishing to examine that image, must necessarily place himself _beyond_ the point where the rays that form it have crossed each other; _beyond_, let us carefully remark, means _farther off_ from the object-glass. The observer's head, his body, cannot then injure the formation or the brightness of the image, however small may be the distance from which we have to study it. But it is no longer thus with the image formed by means of reflection. For the image is now placed between the object and the reflecting mirror; and when the astronomer approaches in order to examine it, he inevitably intercepts, if not the totality, at least a very considerable portion of the luminous rays, which would otherwise have contributed to give it great splendour. It will now be understood, why in optical instruments where the images of distant objects are formed by the reflection of light, it has been necessary to carry the images, by the aid of a second reflection, out of the tube that contains and sustains the principal mirror. When the small mirror, on the surface of which the second reflection is effected, is plane, and inclined at an angle of 45° to the axis of the telescope; when the image is reflected laterally, through an opening made near the edge of the tube and furnished with an eye-piece; when, in a word, the astronomer looks definitively in a direction perpendicular to the line described by the luminous rays coming from the object and falling on the centre of the great mirror, then the telescope is called _Newtonian_. But in the _Gregorian_ telescope, the image formed by the principal mirror falls on a second mirror, which is very small, slightly curved, and parallel to the first. The small mirror reflects the first image and throws it beyond the large mirror, through an opening made in the middle of that principal mirror.

Both in the one and in the other of these two telescopes, the small mirror interposed between the object and the great mirror forms relative to the latter a sort of screen which prevents its entire surface from contributing towards forming the image. The small mirror, also, in regard to intensity, gives some trouble.

Let us suppose, in order to clear up our ideas, that the material of which the two mirrors are made, reflects only half of the incident light. In the course of the first reflection, the immense quantity of rays that the aperture of the telescope had received, may be considered as reduced to half. Nor is the diminution less on the small mirror. Now, half of half is a quarter. Therefore the instrument will send to the eye of the observer only a quarter of the incident light that its aperture had received. These two causes of diminished light not existing in a refracting telescope, it would give, under parity of dimensions, four times more[19] light than a Newtonian or Gregorian telescope gives.

Herschel did away with the small mirror in his large telescope. The large mirror is not mathematically centred in the large tube that contains it, but is placed rather obliquely in it. This slight obliquity causes the images to be formed not in the axis of the tube, but very near its circumference, or outer mouth, we may call it. The observer may therefore look at them there direct, merely by means of an eye-piece. A small portion of the astronomer's head, it is true, then encroaches on the tube; it forms a screen, and interrupts some incident rays. Still, in a large telescope, the loss does not amount to half by a great deal; which it would inevitably do if the small mirror were there.

Those telescopes, in which the observer, placed at the anterior extremity of the tube, looks direct into the tube and turns his back to the objects, were called by Herschel _front view telescopes_. In vol. lxxvi. of the _Philosophical Transactions_ he says, that the idea of this construction occurred to him in 1776, and that he then applied it unsuccessfully to a ten-foot telescope; that during the year 1784, he again made a fruitless trial of it in a twenty-foot telescope. Yet I find that on the 7th of September 1784, he recurred to a _front view_ in observing some nebulæ and groups of stars. However discordant these dates may be, we cannot without injustice neglect to remark, that a front view telescope was already described in 1732, in volume vi. of the collection entitled _Machines and Inventions approved by the Academy of Sciences_. The author of this innovation is Jaques Lemaire, who has been unduly confounded with the English Jesuit, Christopher Maire, assistant to Boscovitch, in measuring the meridian comprised between Rome and Rimini. Jaques Lemaire having only telescopes of moderate dimensions in view, was obliged, in order not to sacrifice any of the light, to place the great mirror so obliquely, that the image formed by its surface should fall entirely outside the tube of the instrument. So great a degree of inclination would certainly deform the objects. The _front view_ construction is admissible only in very large telescopes.

I find in the _Transactions_ for 1803, that in solar observations, Herschel sometimes employed telescopes, the great mirror of which was made of glass. It was a telescope of this sort that he used for observing the transit of Mercury on the 9th of November, 1802. It was seven English feet long, and six inches and three tenths in diameter.

Practical astronomers know how much the mounting of a telescope contributes to produce correct observations. The difficulty of a solid yet very movable mounting, increases rapidly with the dimensions and weight of an instrument. We may then conceive that Herschel had to surmount many obstacles, to mount a telescope suitably, of which the mirror alone weighed upwards of 1000 kilogrammes (_a ton_). But he solved this problem to his entire satisfaction by the aid of a combination of spars, of pulleys, and of ropes, of all which a correct idea may be formed by referring to the woodcut we have given in our _Treatise on Popular Astronomy_ (vol. i.). This great apparatus, and the entirely different stands that Herschel imagined for telescopes of smaller dimensions, assign to that illustrious observer a distinguished place amongst the most ingenious mechanics of our age.

Persons in general, I may even say the greater part of astronomers, know not what was the effect that the great forty-foot telescope had in the labours and discoveries of Herschel. Still, we are not less mistaken when we fancy that the observer of Slough always used this telescope, than in maintaining with Baron von Zach (see _Monatliche Correspondenz_, January, 1802), that the colossal instrument was of no use at all, that it did not contribute to any one discovery, that it must be considered as a mere object of curiosity. These assertions are distinctly contradicted by Herschel's own words. In the volume of _Philosophical Transactions_ for the year 1795 (p. 350), I read for example: "On the 28th of August 1789, having directed my telescope (of forty feet) to the heavens, I discovered the sixth satellite of Saturn, and I perceived the spots on that planet, better than I had been able to do before." (See also, relative to this sixth satellite, the _Philosophical Transactions_ for 1790, p. 10.) In that same volume of 1790, p. 11, I find: "The great light of my forty-foot telescope was then so useful, that on the 17th of September 1789, I remarked the seventh satellite, then situated at its greatest western elongation."

The 10th of October, 1791, Herschel saw the ring of Saturn and the fourth satellite, looking in at the mirror of his forty-foot telescope, with his naked eye, without any sort of eye-piece.

Let us acknowledge the true motives that prevented Herschel from oftener using his telescope of forty feet. Notwithstanding the excellence of the mechanism, the manoeuvring of that instrument required the constant aid of two labourers, and that of another person charged with noting the time at the clock. During some nights when the variation of temperature was considerable, this telescope, on account of its great mass, was always behindhand with the atmosphere in thermometric changes, which was very injurious to the distinctness of the images.

Herschel found that in England, there are not above a hundred hours in a year during which the heavens can be advantageously observed with a telescope of forty feet, furnished with a magnifying power of a thousand. This remark led the celebrated astronomer to the conclusion, that, to take a complete survey of the heavens with his large instrument, though each successive field should remain only for an instant under inspection, would not require less than eight hundred years.

Herschel explains in a very natural way the rare occurrence of the circumstances in which it is possible to make good use of a telescope of forty feet, and of very large aperture.

A telescope does not magnify real objects only, but magnifies also the apparent irregularities arising from atmospheric refractions; now, all other things being equal, these irregularities of refraction must be so much the stronger, so much the more frequent, as the stratum of air is thicker through which the rays have passed to go and form the image.

Astronomers experienced extreme surprise, when in 1782, they learned that Herschel had applied linear magnifying powers of a thousand, of twelve hundred, of two thousand two hundred, of two thousand six hundred, and even of six thousand times, to a reflecting telescope of seven feet in length. The Royal Society of London experienced this surprise, and officially requested Herschel to give publicity to the means he had adopted for ascertaining such amounts of magnifying power in his telescopes. Such was the object of a memoir that he inserted in vol. lxxii. of the _Philosophical Transactions_; and it dissipated all doubts. No one will be surprised that magnifying powers, which it would seem ought to have shown the Lunar mountains, as the chain of Mont Blanc is seen from Maçon, from Lyons, and even from Geneva, were not easily believed in. They did not know that Herschel had never used magnifying powers of three thousand, and six thousand times, except in observing brilliant stars; they had not remembered that light reflected by planetary bodies, is too feeble to continue distinct under the same degree of magnifying power as the actual light of the fixed stars does.

Opticians had given up, more from theory than from careful experiments, attempting high magnifying powers, even for reflecting telescopes. They thought that the image of a small circle cannot be distinct, cannot be sharp at the edges, unless the pencil of rays coming from the object in nearly parallel lines, and which enters the eye after having passed through the eye-piece, be sufficiently broad. This being once granted, the inference followed, that an image ceases to be well defined, when it does not strike at least two of the nervous filaments of the retina with which that organ is supposed to be overspread. These gratuitous circumstances, grafted on each other, vanished in presence of Herschel's observations. After having put himself on his guard against the effects of diffraction, that is to say, against the scattering that light undergoes when it passes the terminal angles of bodies, the illustrious astronomer proved, in 1786, that objects can be seen well defined by means of pencils of light whose diameter does not equal five tenths of a millimetre.

Herschel looked on the almost unanimous opinion of the double lens eye-piece being preferable to the single lens eye-piece, as a very injurious prejudice in science. For experience proved to him, notwithstanding all theoretic deductions, that with equal magnifying powers, in reflecting telescopes at least (and this restriction is of some consequence), the images were brighter and better defined with single than with double eye-pieces. On one occasion, this latter eye-piece would not show him the bands of Saturn, whilst by the aid of a single lens they were perfectly visible. Herschel said: "The double eye-piece must be left to amateurs and to those who, for some particular object, require a large field of vision." (_Philosophical Transactions, 1782, pages 94 and 95._)

It is not only relative to the comparative merit of single or double eye-pieces that Herschel differs from the general opinions of opticians; he thinks, moreover, that he has proved by decisive experiments, that concave eye-pieces (like that used by Galileo) surpass the convex eye-piece by a great deal, both as regards clearness and definition.

Herschel assigns the date of 1776 to the experiments which he made to decide this question. (_Philosophical Transactions_, year 1815, p. 297.) Plano-concave and double concave lenses produced similar effects. In what did these lenses differ from the double convex lenses? In one particular only: the latter received the rays reflected by the large mirror of the telescope, after their union at the focus, whereas the concave lenses received the same rays before that union. When the observer made use of a convex lens, the rays that went to the back of the eye to form an image on the retina, had crossed each other before in the air; but no crossing of this kind took place when the observer used a concave lens. Holding the double advantage of this latter sort of lens over the other, as quite proved, one would be inclined, like Herschel, to admit, "that a certain mechanical effect, injurious to clearness and definition, would accompany the focal crossing of the rays of light."[20]

This idea of the crossing of the rays suggested an experiment to the ingenious astronomer, the result of which deserves to be recorded.

A telescope of ten English feet was directed towards an advertisement covered with very small printing, and placed at a sufficient distance. The convex lens of the eye-piece was carried not by a tube properly so called, but by four rigid fine wires placed at right angles. This arrangement left the focus open in almost every direction. A concave mirror was then placed so that it threw a very condensed image of the sun laterally on the very spot where the image of the advertisement was formed. The solar rays, after having crossed each other, finding nothing on their route, went on and lost themselves in space. A screen, however, allowed the rays to be intercepted at will before they united.

This done, having applied the eye to the eye-piece and directed all his attention to the telescopic image of the advertisement, Herschel did not perceive that the taking away and then replacing the screen made the least change in the brightness or definition of the letters. It was therefore of no consequence, in the one instance as well as in the other, whether the immense quantity of solar rays crossed each other at the very place where, _in another direction_, the rays united that formed the image of the letters. I have marked in Italics the words that especially show in what this curious experiment differs from the previous experiments, and yet does not entirely contradict them. In this instance the rays of various origin, those coming from the advertisement and from the sun, crossed each other respectively in almost rectangular directions; during the comparative examination of the stars with convex and with concave eye-pieces, the rays that seemed to have a mutual influence, had a common origin and crossed each other at very acute angles. There seems to be nothing, then, in the difference of the results at which we need to be much surprised.

Herschel increased the catalogue, already so extensive, of the mysteries of vision, when he explained in what manner we must endeavour to distinguish separately the two members of certain double stars very close to each other. He said if you wish to assure yourself that _ê_ Coronæ is a double star, first direct your telescope to _a_ Geminorum, to _z_ Aquarii, to _m_ Draconis, to _r_ Herculis, to _a_ Piscium, to _e_ Lyræ. Look at those stars for a long time, so as to acquire the habit of observing such objects. Then pass on to _x_ Ursæ majoris, where the closeness of the two members is still greater. In a third essay select _i_ Bootis (marked 44 by Flamsteed and _i_ in Harris's maps)[21], the star that precedes _a_ Orionis, _n_ of the same constellation, and you will then be prepared for the more difficult observation of _ê_ Coronæ. Indeed _ê_ Coronæ is a sort of miniature of _i_ Bootis, which may itself be considered as a miniature of _a_ Gem. (_Philosophical Transactions_, 1782, p. 100.)

As soon as Piazzi, Olbers, and Harding had discovered three of the numerous telescopic planets now known, Herschel proposed to himself to determine their real magnitudes; but telescopes not having then been applied to the measurement of excessively small angles, it became requisite, in order to avoid any illusion, to try some experiments adapted to giving a scale of the powers of those instruments. Such was the labour of that indefatigable astronomer, of which I am going to give a compressed abridgment.

The author relates first, that in 1774, he endeavoured to ascertain experimentally, with the naked eye and at the distance of distinct vision, what angle a circle must subtend to be distinguished by its form from a square of similar dimensions. The angle was never smaller than 2' 17"; therefore at its maximum it was about one fourteenth of the angle subtended by the diameter of the moon.

Herschel did not say, either of what nature the circles and squares of paper were that he used, nor on what background they were projected. It is a lacuna to be regretted, for in those phenomena the intensity of light must be an important feature. However it may have been, the scrupulous observer not daring to extend to telescopic vision what he had discovered relative to vision with the naked eye, he undertook to do away with all doubt, by direct observations.

On examining some pins' heads placed at a distance in the open air, with a three-foot telescope, Herschel could easily discern that those bodies were round, when the subtended angles became, after their enlargement, 2' 19". This is almost exactly the result obtained with the naked eye.

When the globules were darker; when, instead of pins' heads, small globules of sealing-wax were used, their spherical form did not begin to be distinctly visible till the moment when the subtended magnified angles, that is, the moment when the natural angle multiplied by the magnifying power, amounted to five minutes.

In a subsequent series of experiments, some globules of silver placed very far from the observer, allowed their globular form to be perceived, even when the magnified angle remained below two minutes.

Under equality of subtended angle, then, the telescopic vision with strong magnifying powers showed itself superior to the naked eye vision. This result is not unimportant.

If we take notice of the magnifying powers used by Herschel in these laborious researches, powers that often exceeded five hundred times, it will appear to be established that the telescopes possessed by modern astronomers, may serve to verify the round form of distant objects, the form of celestial bodies even when the diameters of those bodies do not subtend naturally (to the naked eye), angles of above three tenths of a second: and 500, multiplied by three tenths of a second, give 2' 30".

Refracting telescopes were still ill understood instruments, the result of chance, devoid of certain theory, when they already served to reveal brilliant astronomical phenomena. Their theory, in as far as it depended on geometry and optics, made rapid progress. These two early phases of the problem leave but little more to be wished for; it is not so with a third phase, hitherto a good deal neglected, connected with physiology, and with the action of light on the nervous system. Therefore, we should search in vain in old treatises on optics and on astronomy, for a strict and complete discussion on the comparative effect that the size and intensity of the images, that the magnifying power and the aperture of a telescope may have, by night and by day, on the visibility of the faintest stars. This lacuna Herschel tried to fill up in 1799; such was the aim of the memoir entitled, _On the space-penetrating Power of Telescopes_.

This memoir contains excellent things; still, it is far from exhausting the subject. The author, for instance, entirely overlooks the observations made by day. I also find, that the hypothetical part of the discussion is not perhaps so distinctly separated from the rigorous part as it might be; that disputable numbers, though given with a degree of precision down to the smallest decimals, do not look well as terms of comparison with some results which; on the contrary, rest on observations bearing mathematical evidence.

Whatever may be thought of these remarks, the astronomer or the physicist who would like again to undertake the question of visibility with telescopes, will find some important facts in Herschel's memoir, and some ingenious observations, well adapted to serve them as guides.

FOOTNOTES:

[18] Conforming to general usage, and to Sir W. Herschel himself, we shall allude to this instrument as the _forty-foot_ telescope, though M. Arago adheres to thirty-nine feet and drops the inches, probably because the Parisian foot is rather longer than the English.--_Translator's Note_.

[19] It would be more correct to say four times _as much_ light.--_Translator_.

[20] On comparing the Cassegrain telescopes with a small convex mirror, to the Gregorian telescopes with a small concave mirror, Captain Kater found that the former, in which the luminous rays do not cross each other before falling on the small mirror, possess, as to intensity, a marked advantage over the latter, in which this crossing takes place.

[21] In the selection of _i_ Bootis as a test, Arago has taken the precaution of giving its corresponding denomination in other catalogues, and Bailey appends the following note, No. 2062, to 44 Bootis. "In the British Catalogue this star is not denoted by any letter: but Bayer calls it _i_, and on referring to the earliest MS. Catalogue in MSS. vol. xxv., I find it is there so designated; I have therefore restored the letter." (See Bailey's Edition of Flamsteed's British Catalogue of Stars, 1835.) The distance between the two members of this double star is 3".7 and position 23°.5. See "Bedford Cycle."--_Translator_.

LABOURS IN SIDEREAL ASTRONOMY.

The curious phenomenon of a periodical change of intensity in certain stars, very early excited a keen attention in Herschel. The first memoir by that illustrious observer presented to the Royal Society of London and inserted in the _Philosophical Transactions_ treats precisely of the changes of intensity of the star _o_ in the neck of the Whale.

This memoir was still dated from Bath, May, 1780. Eleven years after, in the month of December, 1791, Herschel communicated a second time to that celebrated English Society the remarks that he had made by sometimes directing his telescopes to the mysterious star. At both those epochs the observer's attention was chiefly applied to the absolute values of the _maxima_ and _minima_ of intensity.

The changeable star in the Whale was not the only periodical star with which Herschel occupied himself. His observations of 1795 and of 1796 proved that _a_ Herculis also belongs to the category of variable stars, and that the time requisite for the accomplishment of all the changes of intensity, and for the star's return to any given state, was sixty days and a quarter. When Herschel obtained this result, about ten changeable stars were already known; but they were all either of very long or very short periods. The illustrious astronomer considered that, by introducing between two groups that exhibited very short and very long periods, a star of somewhat intermediate conditions,--for instance, one requiring sixty days to accomplish all its variations of intensity,--he had advanced the theory of these phenomena by an essential step; the theory at least that attributes every thing to a movement of rotation round their centres which the stars may undergo.

Sir William Herschel's catalogues of double stars offer a considerable number to which he ascribes a decided green or blue tint. In binary combinations, when the small star appears very blue or very green, the large one is usually yellow or red. It does not appear that the great astronomer took sufficient interest in this circumstance. I do not find, indeed, that the almost constant association of two complementary colours (of yellow and blue, or of red and green), ever led him to suspect that one of those colours might not have any thing real in it, that it often might be a mere illusion, a mere result of contrast. It was only in 1825, that I showed that there are stars whose contrast really explains their apparent colour; but I have proved besides, that blue is incontestably the colour of certain insulated stars, or stars that have only white ones, or other blue ones in their vicinity. Red is the only colour that the ancients ever distinguished from white in their catalogues.

Herschel also endeavoured to introduce numbers in the classification of stars as to magnitude; he has endeavoured, by means of numbers, to show the comparative intensity of a star of first magnitude, with one of second, or one of third magnitude, &c.

In one of the earliest of Herschel's memoirs, we find, that the apparent sidereal diameters are proved to be for the greater part factitious, even when the best made telescopes are used. Diameters estimated by seconds, that is to say, reduced according to the magnifying power, diminish as the magnifying power is increased. These results are of the greatest importance.

In the course of his investigation of sidereal parallax, though without finding it, Herschel made an important discovery; that of the proper motion of our system. To show distinctly the direction of the motion of the solar system, not only was a displacement of the sidereal perspective required, but profound mathematical knowledge, and a peculiar tact. This peculiar tact Herschel possessed in an eminent degree. Moreover, the result deduced from the very small number of proper motions known at the beginning of 1783, has been found almost to agree with that found recently by clever astronomers, by the application of subtile analytical formulæ, to a considerable number of exact observations.

The proper motions of the stars have been known and proved for more than a century, and already Fontenelle used to say in 1738, that the sun probably also moved in a similar way. The idea of partly attributing the displacement of the stars to a motion of the sun, had suggested itself to Bradley and to Mayer. And Lambert especially had been very explicit on the subject. Until then, however, there were only conjectures and mere probabilities. Herschel passed those limits. He himself proved that the sun positively moves; and that, in this respect also, that immense and dazzling body must be ranged among the stars; that the apparently inextricable irregularities of numerous sidereal proper motions arise in great measure from the displacement of the solar system; that, in short, the point of space towards which we are annually advancing, is situated in the constellation of Hercules.

These are magnificent results. The discovery of the proper motion of our system will always be accounted among Herschel's highest claims to glory, even after the mention that my duty as historian has obliged me to make of the anterior conjectures by Fontenelle, by Bradley, by Mayer, and by Lambert.

By the side of this great discovery we should place another, that seems likely to expand in future. The results which it allows us to hope for will be of extreme importance. The discovery here alluded to was announced to the learned world in 1803; it is that of the reciprocal dependence of several stars, connected the one with the other, as the several planets and their satellites of our system are with the sun.

Let us to these immortal labours add the ingenious ideas that we owe to Herschel on the nebulæ, on the constitution of the Milky-way, on the universe as a whole; ideas which almost by themselves constitute the actual history of the formation of the worlds, and we cannot but have a deep reverence for that powerful genius that has scarcely ever erred, notwithstanding an ardent imagination.

LABOURS RELATIVE TO THE SOLAR SYSTEM.

Herschel occupied himself very much with the sun, but only relative to its physical constitution. The observations that the illustrious astronomer made on this subject, the consequences that he deduced from them, equal the most ingenious discoveries for which the sciences are indebted to him.

In his important memoir in 1795, the great astronomer declares himself convinced that the substance by the intermediation of which the sun shines, cannot be either a liquid, or an elastic fluid. It must be analogous to our clouds, and float in the transparent atmosphere of that body. The sun has, according to him, two atmospheres, endowed with motions quite independent of each other. An elastic fluid of an unknown nature is being constantly formed on the dark surface of the sun, and rising up on account of its specific lightness, it forms the _pores_ in the stratum of reflecting clouds; then, combining with other gases, it produces the wrinkles in the region of luminous clouds. When the ascending currents are powerful, they give rise to the _nuclei_, to the _penumbræ_, to the _faculæ_. If this explanation of the formation of solar spots is well founded, we must expect to find that the sun does not constantly emit similar quantities of light and heat. Recent observations have verified this conclusion. But large nuclei, large penumbræ, wrinkles, faculæ, do they indicate an abundant luminous and calorific emission, as Herschel thought; that would be the result of his hypothesis on the existence of very active ascending currents, but direct experience seems to contradict it.

The following is the way in which a learned man, Sir David Brewster, appreciates this view of Herschel's: "It is not conceivable that luminous clouds, ceding to the lightest impulses and in a state of constant change, can be the source of the sun's devouring flame and of the dazzling light which it emits; nor can we admit besides, that the feeble barrier formed by planetary clouds would shelter the objects that it might cover, from the destructive effects of the superior elements."

Sir D. Brewster imagines that the non-luminous rays of caloric, which form a constituent part of the solar light, are emitted by the dark nucleus of the sun; whilst the visible coloured rays proceed from the luminous matter by which the nucleus is surrounded. "From thence," he says, "proceeds the reason of light and heat always appearing in a state of combination: the one emanation cannot be obtained without the other. With this hypothesis we should explain naturally why it is hottest when there are most spots, because the heat of the nucleus would then reach us without having been weakened by the atmosphere that it usually has to traverse." But it is far from being an ascertained fact, that we experience increased heat during the apparition of solar spots; the inverse phenomenon is more probably true.

Herschel occupied himself also with the physical constitution of the moon. In 1780, he sought to measure the height of our satellite's mountains. The conclusion that he drew from his observations was, that few of the lunar mountains exceed 800 metres (or 2600 feet). More recent selenographic studies differ from this conclusion. There is reason to observe on this occasion how much the result surmised by Herschel differs from any tendency to the extraordinary or the gigantic, that has been so unjustly assigned as the characteristic of the illustrious astronomer.

At the close of 1787, Herschel presented a memoir to the Royal Society, the title of which must have made a strong impression on people's imaginations. The author therein relates that on the 19th of April, 1787, he had observed in the non-illuminated part of the moon, that is, in the then dark portion, three volcanoes in a state of ignition. Two of these volcanoes appeared to be on the decline, the other appeared to be active. Such was then Herschel's conviction of the reality of the phenomenon, that the next morning he wrote thus of his first observation: "The volcano burns with more violence than last night." The real diameter of the volcanic light was 5000 metres (16,400 English feet). Its intensity appeared very superior to that of the nucleus of a comet then in apparition. The observer added: "The objects situated near the crater are feebly illuminated by the light that emanates from it." Herschel concludes thus: "In short, this eruption very much resembles the one I witnessed on the 4th of May, 1783."

How happens it, after such exact observations, that few astronomers now admit the existence of active volcanoes in the moon? I will explain this singularity in a few words.

The various parts of our satellite are not all equally reflecting. Here, it may depend on the form, elsewhere, on the nature of the materials. Those persons who have examined the moon with telescopes, know how very considerable the difference arising from these two causes may be, how much brighter one point of the moon sometimes is than those around it. Now, it is quite evident that the relations of intensity between the faint parts and the brilliant parts must continue to exist, whatever be the origin of the illuminating light. In the portion of the lunar globe that is illuminated by the sun, there are, everybody knows, some points, the brightness of which is extraordinary compared to those around them; those same points, when they are seen in that portion of the moon that is only lighted by the earth, or in the ash-coloured part, will still predominate over the neighbouring regions by their comparative intensity. Thus we may explain the observations of the Slough astronomer, without recurring to volcanoes. Whilst the great observer was studying in the non-illuminated portion of the moon, the supposed volcano of the 20th of April, 1787, his nine-foot telescope showed him in truth, by the aid of the secondary rays proceeding from the earth, even the darkest spots.

Herschel did not recur to the discussion of the supposed actually burning lunar volcanoes, until 1791. In the volume of the _Philosophical Transactions_ for 1792, he relates that, in directing a twenty-foot telescope, magnifying 360 times, to the entirely eclipsed moon on the 22d of October, 1790, there were visible, over the whole face of the satellite, about a hundred and fifty very luminous red points. The author declares that he will observe the greatest reserve relative to the similarity of all these points, their great brightness, and their remarkable colour.

Yet is not red the usual colour of the moon when eclipsed, and when it has not entirely disappeared? Could the solar rays reaching our satellite by the effect of refraction, and after an absorption experienced in the lowest strata of the terrestrial atmosphere, receive another tint? Are there not in the moon, when freely illuminated, and opposite to the sun, from one to two hundred little points, remarkable by the brightness of their light? Would it be possible for those little points not to be also distinguishable in the moon, when it receives only the portion of solar light which is refracted and coloured by our atmosphere?

Herschel was more successful in his remarks on the absence of a lunar atmosphere. During the solar eclipse of the 5th September, 1793, the illustrious astronomer particularly directed his attention to the shape of the acute horn resulting from the intersection of the limbs of the moon and of the sun. He deduced from his observation that if towards the point of the horn there had been a deviation of only one second, occasioned by the refraction of the solar light in the lunar atmosphere, it would not have escaped him.

Herschel made the planets the object of numerous researches. Mercury was the one with which he least occupied himself; he found its disk perfectly round on observing it during its projection, that is to say, in astronomical language, during its transit over the sun on the 9th of November, 1802. He sought to determine the time of the rotation of Venus since the year 1777. He published two memoirs relative to Mars, the one in 1781, the other in 1784, and the discovery of its being flattened at the poles we owe to him. After the discovery of the small planets, Ceres, Pallas, Juno, and Vesta, by Piazzi, Olbers, and Harding, Herschel applied himself to measuring their angular diameter. He concluded from his researches that those four new bodies did not deserve the name of planets, and he proposed to call them asteroïds. This epithet was subsequently adopted; though bitterly criticized by a historian of the Royal Society of London, Dr. Thomson, who went so far as to suppose that the learned astronomer "had wished to deprive the first observers of those bodies, of all idea of rating themselves as high as him (Herschel) in the scale of astronomical discoverers." I should require nothing farther to annihilate such an imputation, than to put it by the side of the following passage, extracted from a memoir by this celebrated astronomer, published in the _Philosophical Transactions_, for the year 1805: "The specific difference existing between planets and asteroïds appears now, by the addition of a third individual of the latter species, to be more completely established, and that circumstance, in my opinion, has added more to the _ornament_ of our system than the discovery of a new planet could have done."

Although much has not resulted from Herschel's having occupied himself with the physical constitution of Jupiter, astronomy is indebted to him for several important results relative to the duration of that planet's rotation. He also made numerous observations on the intensities and comparative magnitudes of its satellites.

The compression of Saturn, the duration of its rotation, the physical constitution of this planet and that of its ring, were, on the part of Herschel, the object of numerous researches which have much contributed to the progress of planetary astronomy. But on this subject two important discoveries especially added new glory to the great astronomer.

Of the five known satellites of Saturn at the close of the 17th century, Huygens had discovered the fourth; Cassini the others.

The subject seemed to be exhausted, when news from Slough showed what a mistake this was.

On the 28th of August, 1789, the great forty-foot telescope revealed to Herschel a satellite still nearer to the ring than the other five already observed. According to the principles of the nomenclature previously adopted, the small body of the 28th August ought to have been called the first satellite of Saturn, the numbers indicating the places of the other five would then have been each increased by a unity. But the fear of introducing confusion into science by these continual changes of denomination, induced a preference for calling the new satellite the sixth.

Thanks to the prodigious powers of the forty-foot telescope, a last satellite, the seventh, showed itself on the 17th of September, 1789, between the sixth and the ring.

This seventh satellite is extremely faint. Herschel, however, succeeding in seeing it whenever circumstances were very favourable, even by the aid of the twenty-foot telescope.

The discovery of the planet Uranus, the detection of its satellites, will always occupy one of the highest places among those by which modern astronomy is honoured.

On the 13th of March, 1781, between ten and eleven o'clock at night, Herschel was examining the small stars near H Geminorum with a seven-foot telescope, bearing a magnifying power of 227 times. One of these stars seemed to him to have an unusual diameter. The celebrated astronomer, therefore, thought it was a comet. It was under this denomination that it was then discussed at the Royal Society of London. But the researches of Herschel and of Laplace showed later that the orbit of the new body was nearly circular, and Uranus was elevated to the rank of a planet.

The immense distance of Uranus, its small angular diameter, the feebleness of its light, did not allow the hope, that if that body had satellites, the magnitudes of which were, relatively to its own size, what the satellites of Jupiter, of Saturn are, compared to those two large planets, any observer could perceive them, from the earth. Herschel was not a man to be deterred by such discouraging conjectures. Therefore, since powerful telescopes of the ordinary construction, that is to say, with two mirrors conjugated, had not enabled him to discover any thing, he substituted, in the beginning of January, 1787, _front view_ telescopes, that is, telescopes throwing much more light on the objects, the small mirror being then suppressed, and with it one of the causes of loss of light is got rid of.

By patient labour, by observations requiring a rare perseverance, Herschel attained (from the 11th of January, 1787, to the 28th of February, 1794,) to the discovery of the six satellites of his planet, and thus to complete the _world_ of a system that belongs entirely to himself.

There are several of Herschel's memoirs on comets. In analyzing them, we shall see that this great observer could not touch any thing without making further discoveries in the subject.

Herschel applied some of his fine instruments to the study of the physical constitution of a comet discovered by Mr. Pigott, on the 28th September, 1807.

The nucleus was round and well determined. Some measures taken on the day when the nucleus subtended only an angle of a single second, gave as its real angle 6/100 of the diameter of the earth.

Herschel saw no phase at an epoch when only 7/10 of the nucleus could be illuminated by the sun. The nucleus then must shine by its own light.

This is a legitimate inference in the opinion of every one who will allow, on one hand, that the nucleus is a solid body, and on the other, that it would have been possible to observe a phase of 8/10 on a disk whose apparent total diameter did not exceed one or two seconds of a degree.

Very small stars seemed to grow much paler when they were seen through the coma or through the tail of the comet.

This faintness may have only been apparent, and might arise from the circumstance of the stars being then projected on a luminous background. Such is, indeed, the explanation adopted by Herschel. A gaseous medium, capable of reflecting sufficient solar light to efface that of some stars, would appear to him to possess in each stratum a sensible quantity of matter, and to be, for that reason, a cause of real diminution of the light transmitted, though nothing reveals the existence of such a cause.

This argument, offered by Herschel in favour of the system which transforms comets into self-luminous bodies, has not, as we may perceive, much force. I might venture to say as much of many other remarks by this great observer. He tells us that the comet was very visible in the telescope on the 21st of February, 1808; now, on that day, its distance from the sun amounted to 2.7 times the mean radius of the terrestrial orbit; its distance from the observer was 2.9: "What probability would there be that rays going to such distances, from the sun to the comet, could, after their reflection, be seen by an eye nearly three times more distant from the comet than from the sun?"

It is only numerical determinations that could give value to such an argument. By satisfying himself with vague reasoning, Herschel did not even perceive that he was committing a great mistake by making the comet's distance from the observer appear to be an element of visibility. If the comet be self-luminous, its intrinsic splendour (its brightness for unity of surface) will remain constant at any distance, as long as the subtended angle remains sensible. If the body shines by borrowed light, its brightness will vary only according to its change of distance from the sun; nor will the distance of the observer occasion any change in the visibility; always, let it be understood, with the restriction that the apparent diameter shall not be diminished below certain limits.

Herschel finished his observations of a comet that was visible in January, 1807, with the following remark:--

"Of the sixteen telescopic comets that I have examined, fourteen had no solid body visible at their centre; the other two exhibited a central light, very ill defined, that might be termed a nucleus, but a light that certainly could not deserve the name of a disk."

The beautiful comet of 1811 became the object of that celebrated astronomer's conscientious labour. Large telescopes showed him, in the midst of the gazeous head, a rather reddish body of planetary appearance, which bore strong magnifying powers, and showed no sign of phase. Hence Herschel concluded that it was self-luminous. Yet if we reflect that the planetary body under consideration was not a second in diameter, the absence of a phase does not appear a demonstrative argument.

The light of the head had a blueish-green tint. Was this a real tint, or did the central reddish body, only through contrast, make the surrounding vapour appear to be coloured? Herschel did not examine the question in this point of view.

The head of the comet appeared to be enveloped at a certain distance, on the side towards the sun, by a brilliant narrow zone, embracing about a semicircle, and of a yellowish colour. From the two extremities of the semicircle there arose, towards the region away from the sun, two long luminous streaks which limited the tail. Between the brilliant circular semi-ring and the head, the cometary substance seemed dark, very rare, and very diaphanous.

The luminous semi-ring always presented similar appearances in all the positions of the comet; it was not then possible to attribute to it really the annular form, the shape of Saturn's ring, for example. Herschel sought whether a spherical demi-envelop of luminous matter, and yet diaphanous, would not lead to a natural explanation of the phenomenon. In this hypothesis, the visual rays, which on the 6th of October, 1811, made a section of the envelop, or bore almost tangentially, traversed a thickness of matter of about 399,000 kilometres, (248,000 English miles,) whilst the visual rays near the head of the comet did not meet above 80,000 kilometres (50,000 miles) of it. As the brightness must be proportional to the quantity of matter traversed, there could not fail to be an appearance around the comet, of a semi-ring five times more luminous than the central regions. This semi-ring, then, was an effect of projection, and it has revealed a circumstance to us truly remarkable in the physical constitution of comets.

The two luminous streaks that outlined the tail at its two limits, may be explained in a similar manner; the tail was not flat as it appeared to be; it had the form of a conoid, with its sides of a certain thickness. The visual lines which traversed those sides almost tangentially, evidently met much more matter than the visual lines passing across. This maximum of matter could not fail of being represented by a maximum of light.

The luminous semi-ring floated; it appeared one day to be suspended in the diaphanous atmosphere by which the head of the comet was surrounded, at a distance of 518,000 kilometres (322,000 English miles) from the nucleus.

This distance was not constant. The matter of the semi-annular envelop seemed even to be precipitated by slow degrees through the diaphanous atmosphere; finally it reached the nucleus; the earlier appearances vanished; the comet was reduced to a globular nebula.

During its period of dissolution, the ring appeared sometimes to have several branches.

The luminous shreds of the tail seemed to undergo rapid, frequent, and considerable variations of length. Herschel discerned symptoms of a movement of rotation both in the comet and in its tail. This rotatory motion carried unequal shreds from the centre towards the border, and reciprocally. On looking from time to time at the same region of the tail, at the border, for example, sensible changes of length must have been perceptible, which however had no reality in them. Herschel thought, as I have already said, that the beautiful comet of 1811, and that of 1807, were self-luminous. The second comet of 1811 appeared to him to shine only by borrowed light. It must be acknowledged that these conjectures did not rest on any thing demonstrative.

In attentively comparing the comet of 1807 with the beautiful comet of 1811, relative to the changes of distance from the sun, and the modifications resulting thence, Herschel put it beyond doubt that these modifications have something individual in them, something relative to a special state of the nebulous matter. On one celestial body the changes of distance produce an enormous effect, on another the modifications are insignificant.

OPTICAL LABOURS.

I shall say very little on the discoveries that Herschel made in physics. In short, everybody knows them. They have been inserted into special treatises, into elementary works, into verbal instruction; they must be considered as the starting-point of a multitude of important labours with which the sciences have been enriched during several years.

The chief of these is that of the dark radiating heat which is found mixed with light.

In studying the phenomena, no longer with the eye, like Newton, but with a thermometer, Herschel discovered that the solar spectrum is prolonged on the red side far beyond the visible limits. The thermometer sometimes rose higher in that dark region, than in the midst of brilliant zones. The light of the sun then, contains, besides the coloured rays so well characterized by Newton, some invisible rays, still less refrangible than the red, and whose warming power is very considerable. A world of discoveries has arisen from this fundamental fact.

The dark heat emanating from terrestrial objects more or less heated, became also subjects of Herschel's investigations. His work contained the germs of a good number of beautiful experiments since erected upon it in our own day.

By successively placing the same objects in all parts of the solar spectrum Herschel determined the illuminating powers of the various prismatic rays. The general result of these experiments may be thus enunciated:

The illuminating power of the red rays is not very great; that of the orange rays surpasses it, and is in its turn surpassed by the power of the yellow rays. The maximum power of illumination is found between the brightest yellow and the palest green. The yellow and the green possess this power equally. A like assimilation may be laid down between the blue and the red. Finally, the power of illumination in the indigo rays, and above all in the violet, is very weak.

Yet the memoirs of Herschel on Newton's coloured rings, though containing a multitude of exact experiments, have not much contributed to advance the theory of those curious phenomena. I have learnt from good authority, that the great astronomer held the same opinion on this topic. He said that it was the only occasion on which he had reason to regret having, according to his constant method, published his labours immediately, as fast as they were performed.

LAPLACE.

Having been appointed to draw up the report of a committee of the Chamber of Deputies which was nominated in 1842, for the purpose of taking into consideration the expediency of a proposal submitted to the Chamber by the Minister of Public Instruction, relative to the publication of a new edition of the works of Laplace at the public expense, I deemed it to be my duty to embody in the report a concise analysis of the works of our illustrious countryman. Several persons, influenced, perhaps, by too indulgent a feeling towards me, having expressed a wish that this analysis should not remain buried amid a heap of legislative documents, but that it should be published in the _Annuaire du Bureau des Longitudes_, I took advantage of this circumstance to develop it more fully so as to render it less unworthy of public attention. The scientific part of the report presented to the Chamber of Deputies will be found here entire. It has been considered desirable to suppress the remainder. I shall merely retain a few sentences containing an explanation of the object of the proposed law, and an announcement of the resolutions which were adopted by the three powers of the State.