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."