Herschel's telescope, forty English feet[18] in length, allowed of the realization of an idea, the advantages of which would not be sufficiently appreciated if I did not here recall to mind some facts.

In any telescope, whether refracting or reflecting, there are two princ.i.p.al parts: the part that forms the aerial 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 gla.s.s, 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-gla.s.s. 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 princ.i.p.al 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 princ.i.p.al 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 princ.i.p.al 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 quant.i.ty 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 circ.u.mference, 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 nebulae 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 ent.i.tled _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, a.s.sistant 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 gla.s.s. 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, a.s.sign to that ill.u.s.trious 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 a.s.sertions 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 ma.s.s, 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 circ.u.mstances 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 pa.s.sed 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 Macon, 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 pa.s.sed 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 circ.u.mstances, 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 pa.s.ses the terminal angles of bodies, the ill.u.s.trious 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) surpa.s.s the convex eye-piece by a great deal, both as regards clearness and definition.

Herschel a.s.signs 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 advertis.e.m.e.nt 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 advertis.e.m.e.nt was formed. The solar rays, after having crossed each other, finding nothing on their route, went on and lost themselves in s.p.a.ce. 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 advertis.e.m.e.nt, 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 quant.i.ty 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 advertis.e.m.e.nt 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 a.s.sure yourself that _e_ Coronae 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_ Lyrae. Look at those stars for a long time, so as to acquire the habit of observing such objects. Then pa.s.s on to _x_ Ursae 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 _e_ Coronae.

Indeed _e_ Coronae 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 ent.i.tled, _On the s.p.a.ce-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 Ca.s.segrain 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 ill.u.s.trious 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 ill.u.s.trious 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 circ.u.mstance. I do not find, indeed, that the almost constant a.s.sociation 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 cla.s.sification 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.