Chapter IV (1)

REVIEW OF THE SCIENTIFIC LABORS OF WILLIAM HERSCHEL.

In this chapter I shall endeavor to give such explanations as will enable the general reader to follow the course of discovery in each branch of astronomy and physics, regularly through the period of HERSCHEL'S life, and up to the state in which he left it.

A more detailed and precise account, which should appeal directly to the professional astronomer, will not be needed, since ARAGO has already fulfilled this want in his "_Analyse de la vie et des travaux de Sir WILLIAM HERSCHEL_," published in 1842. The few misconceptions there contained will be easily corrected by those to whom alone they are of consequence. The latter class of readers may also consult the abstracts of HERSCHEL'S memoirs, which have been given in "_A Subject-index and a Synopsis of the Scientific Writings of Sir WILLIAM HERSCHEL_," prepared by Dr. HASTINGS and myself, and published by the Smithsonian Institution.

An accurate sketch of the state of astronomy in England and on the Continent, in the years 1780-1820, need not be given. It will be enough if we remember that of the chief observatories of Europe, public and private, no one was actively devoted to such labors as were undertaken by HERSCHEL at the very beginning of his career.

His observations on variable stars, indeed, were in the same line as those of PIGOTT; FLAUGERGUES and DARQUIER, in France, had perhaps preceded him in minute scrutiny of the sun's surface, etc.; but, even in that department of observation, he at once put an immense distance between himself and others by the rapid and extraordinary advances in the size and in the excellence of his telescopes. Before his time the principal aids to observation were the Gregorian and Newtonian telescopes of SHORT, and the small achromatics of DOLLOND.[31]

We have seen, in what goes before, how his patient zeal had succeeded in improving upon these. There was no delay, and no rest. Steadily the art of making reflectors was urged forward, until he had finally in his hands the forty-foot telescope.

It must be admitted that this was the limit to which the manufacture of powerful telescopes could be pushed in his generation. The optical and mechanical difficulties which prevented a farther advance required time for their solution; and, indeed, some of these difficulties are scarcely solved at this day. It may fairly be said that no reflector larger than three feet in aperture has yet realized our expectations.

_The Improvement of Telescopes and Optical Apparatus._

It will be of interest to give in this place some connected account of the large forty-foot reflector, of four feet aperture, made by HERSCHEL. Its history extends from 1785 to 1811. Its manufacture was considered by his cotemporaries as his greatest triumph. As a machine, it was extremely ingenious in all its parts, as may be seen from the elaborate description and plates of it published in the _Philosophical Transactions_ for 1795. One of its mirrors certainly had good definition, for, by means of it, the two small satellites of _Saturn_ (_Mimas_ and _Enceladus_) were discovered, and these discoveries alone would make it famous. Perhaps more was expected of it by the public in general than it absolutely performed. Its merits were after a while decried, and HERSCHEL even felt obliged to state why he did not always employ it in his observations. His reasons were perfectly valid, and such as any one may understand. The time required to get so large a machine into working order was a serious tax; it required more assistants than his twenty-foot telescope, and he says, "I have made it a rule never to employ a larger telescope when a smaller will answer the purpose."

It still remains as a remarkable feat of engineering and an example of great optical and mechanical skill. It led the way to the large reflectors of Lord ROSSE, some sixty years later, and several of the forty-foot telescopes of the present day even have done less useful work. Its great feat, however, was to have added two satellites to the solar system. From the published accounts of it the following is taken:

"When I resided at Bath I had long been acquainted with the theory
of optics and mechanics, and wanted only that experience so
necessary in the practical part of these sciences. This I acquired
by degrees at that place, where in my leisure hours, by way of
amusement, I made several two-foot, five-foot, seven-foot, ten-foot,
and twenty-foot Newtonian telescopes, beside others, of the
Gregorian form, of eight, twelve, and eighteen inches, and two,
three, five, and ten feet focal length. In this way I made not less
than two hundred seven-foot, one hundred and fifty ten-foot, and
about eighty twenty-foot mirrors, not to mention the Gregorian
telescopes.[32]

"The number of stands I invented for these telescopes it would not
be easy to assign. . . . In 1781 I began to construct a thirty-foot
aërial reflector, and having made a stand for it, I cast the mirror
thirty-six inches in diameter. This was cracked in cooling. I cast
it a second time, and the furnace I had built in my house broke."

Soon after, the Georgian planet was discovered, and this interrupted the work for a time.

"In the year 1783 I finished a very good twenty-foot reflector with
a large aperture, and mounted it upon the plan of my present
telescope. After two years' observation with it, the great advantage
of such apertures appeared so clearly to me that I recurred to my
former intention of increasing them still further; and being now
sufficiently provided with experience in the work which I wished to
undertake, the President of the Royal Society, who is always ready
to promote useful undertakings, had the goodness to lay my design
before the king. His Majesty was graciously pleased to approve of
it, and with his usual liberality to support it with his royal
bounty.

"In consequence of this arrangement I began to construct the
forty-foot telescope about the latter end of 1785.[33] The woodwork
of the stand and machines for giving the required motions to the
instrument were immediately put in hand. In the whole of the
apparatus none but common workmen were employed, for I made drawings
of every part of it, by which it was easy to execute the work, as I
constantly inspected and directed every person's labor; though
sometimes there were not less than forty different workmen employed
at the same time. While the stand of the telescope was preparing, I
also began the construction of the great mirror, of which I
inspected the casting, grinding, and polishing, and the work was in
this manner carried on with no other interruption than that
occasioned by the removal of all the apparatus and materials from
where I then lived, to my present situation at Slough.

"Here, soon after my arrival, I began to lay the foundation upon
which by degrees the whole structure was raised as it now stands,
and the speculum being highly polished and put into the tube, I had
the first view through it on February 19, 1787. I do not, however,
date the completing of the instrument till much later. For the first
speculum, by a mismanagement of the person who cast it, came out
thinner on the centre of the back than was intended, and on account
of its weakness would not permit a good figure to be given to it.

"A second mirror was cast January 26, 1788, but it cracked in
cooling. February 16 we recast it, and it proved to be of a proper
degree of strength. October 24 it was brought to a pretty good
figure and polish, and I observed the planet _Saturn_ with it. But
not being satisfied, I continued to work upon it till August 27,
1789, when it was tried upon the fixed stars, and I found it to give
a pretty sharp image. Large stars were a little affected with
scattered light, owing to many remaining scratches on the mirror.
August the 28th, 1789, having brought the telescope to the parallel
of _Saturn_, I discovered a _sixth_ satellite of that planet, and
also saw the spots upon _Saturn_ better than I had ever seen them
before, so that I may date the finishing of the forty-foot telescope
from that time."

Another satellite of _Saturn_ was discovered with the forty-foot on the 17th of September (1789). It was used for various observations so late as 1811. On January 19, of that year, HERSCHEL observed the nebula of _Orion_ with it. This was one of his last observations.

The final disposition of the telescope is told in the following extract from a letter of Sir JOHN HERSCHEL'S to Mr. WELD, Secretary of the Royal Society:

"COLLINGWOOD, _March 13, 1847_.

. . . "In reply to your queries, respecting the forty-foot
reflecting telescope constructed by my father, I have to state that
King GEORGE III. munificently defrayed the _entire_ cost of that
instrument (including, of course, all preparatory cost in the nature
of construction of tools, and of the apparatus for casting, grinding,
and figuring the reflectors, of which two were constructed), at a
total cost of £4,000. The woodwork of the telescope being so far
decayed as to be dangerous, in the year 1839 I pulled it down, and
piers were erected on which the tube was placed, _that_ being of
iron and so well preserved, that, although not more than
one-twentieth of an inch thick, when in the horizontal position it
sustained within it all my family, and continues to sustain inclosed
within it, to this day, not only the heavier of the two reflectors,
but also all the more important portions of the machinery. . . .
The mirror and the rest of the polishing apparatus are on the
premises. The iron grinding tools and polishers are placed
underneath the tube, let into the ground, and level with the surface
of the gravelled area in which it stands.". . .

The closing of the tube was done with appropriate ceremony on New-Year's-Day, 1840, when, after a procession through it by the family at Slough, a poem, written by Sir JOHN, was read, the machinery put into its present position, and the tube sealed.

The memoir on the forty-foot telescope shows throughout that HERSCHEL'S prime object was not the making of the telescope itself, but that his mind was constantly directed towards the uses to which it was to be put--towards the questions which he wished it to answer.

Again and again, in his various papers, he returns to the question of the _limit of vision_. As BESSEL has said:

"The naked eye has its limit of vision in the stars of the sixth
magnitude. The light of fainter stars than these does not affect the
retina enough for them to be seen. A very small telescope penetrates
to smaller, and, in general, without doubt, to more distant stars.
A more powerful one penetrates deeper into space, and as its power is
increased, so the boundaries of the visible universe are widened,
and the number of stars increased to millions and millions. Whoever
has followed the history of the series of HERSCHEL'S telescopes will
have observed this. But HERSCHEL was not content with the bare fact,
but strove ever to know _how far_ a telescope of a certain
construction and size could penetrate, compared with the naked and
unassisted eye. These investigations were never for the discovery of
new facts concerning the working of his instruments; it was for the
knowledge of the distribution of the fixed stars in space itself
that he strove. . . . HERSCHEL'S instruments were designed to aid
vision to the last extent. They were only secondarily for the taking
of measures. His efforts were not for a knowledge of the _motions_,
but of the _constitution_ and _construction_ of the heavenly
bodies."

Besides the stands for his telescopes, which were both ingenious and convenient, HERSCHEL devised many forms of apparatus for facilitating the art of observation. His micrometers for measuring position angles, his lamp micrometer, the method of limiting apertures, and the methods he used for viewing the sun may be mentioned among these.

Points in practical astronomy are considered all through the years of observation. A reference to his original papers will show how numerous, how varied, and how valuable these are. I cannot forbear quoting here the account of a precaution observed during his examination of the belts on _Saturn_ (1794).

It is the most striking example of how fully HERSCHEL realized that the eye of the observer is a material part of the optical apparatus of astronomy. Simple as this principle may appear, it was an absolute novelty in his day.

In making these observations, he says:

"I took care to bend my head so as to receive the picture of the
belt in the same direction as I did formerly. This was a precaution
that occurred to me, as there was a possibility that the vertical
diameter of the retina might be more or less sensitive than the
horizontal one."

Astronomers will recognize in this the first suggestion of the processes which have led to important results in the hands of Dr. OTTO STRUVE and others in the comparison of the measures of double stars by different observers, each of whom has a personal habit of observation, which, if not corrected, may affect his results in the way which HERSCHEL was striving to avoid.

_Researches on the Relative Brightness of the
Stars: Variable Stars._

No research of HERSCHEL'S was more laborious than the elaborate classification of the stars according to their comparative brightness, which he executed during the years 1796 to 1799. It was directly in the line of his main work--to find out the construction of the heavens.

His first paper had been upon the variable star _Mira Ceti_. Here was a sun, shining by its native brightness, which waxed and waned like the moon itself. This star is periodic. It is for a long period invisible to the unassisted eye. Then it can just be seen, and increases in brightness for a little over a month, and attains a maximum brilliancy. From this it decreases for nearly three months, and after becoming invisible, remains so for five or six months. Its whole period is about 333 days. Are all other stars constant in brightness? The example of _Mira Ceti_ and of other known variables makes this at least doubtful. But the sun itself may vary for all that we know. It is a simple star like the rest.

This question of variability in general is an important one, then. It can only be tested by making accurate catalogues of the relative brilliance of stars at various times, and by comparing these. No such general catalogue existed before HERSCHEL'S time, and led by the discrepancies in isolated cases, which he found between his own estimates and those of his predecessors, he made from observation a series of four catalogues, in which were set down the order of sequence of the stars of each constellation.

The method adopted by HERSCHEL was perfectly simple in principle, though most laborious in practice. Suppose any number of stars, A, B, C, D, E, . . . etc., near enough to each other to be well compared. The process consists simply in writing down the names of the stars, A, B, C, etc., in the order of their relative brightness. Thus if for a group of eight stars we have found at one epoch A, B, C, D, E, F, G, H, and if at another time the order was A, B, C, D, F, E, G, H, symptoms of variability are pointed out. Repeated observations, where the same star is found in different sequences, will decide the question. Thus, for the stars visible to the naked eye, we know exactly the state of the sky in HERSCHEL'S day, now nearly a century ago. Any material change cannot escape us. These catalogues have been singularly overlooked by the observers of our generation who have followed this branch of observation, and it was not till 1876 that they received proper attention and a suitable reduction (at the hands of Mr. C. S. PIERCE).

We owe to HERSCHEL the first trustworthy account of the stars visible to the naked eye, and since the date of his labors (about 1800) we have similar views published by ARGELANDER (1839), HEIS (1848), ARGELANDER and SCHÖNFELD (1857), GOULD (1860 and 1872), and HOUZEAU (1875). Thus his labors have been well followed up.

In the prosecution of this work HERSCHEL found stars whose light was progressively diminishing, others which regularly increased, one star whose light periodically varies (_[alpha] Herculis_), and at least one star (55 _Herculis_) which has utterly disappeared. On October 10, 1781, and April 11, 1782, he observed this latter star, but in May, 1791, it had totally vanished. There was no trace remaining.

The discovery of the variability of _[alpha] Herculis_ was a more important one than would at first sight appear. Up to that time the only variable stars known were seven in number. Their periods were four hundred and ninety-four, four hundred and four, three hundred and thirty-four, seven, six, five, and three days. These periods seemed to fall into two groups, one of from three hundred to five hundred days, the other comparatively much shorter, of three to seven days. _[alpha] Herculis_ came to occupy the middle place between these groups, its period being about sixty days.

The cause of these strange and regular variations of brightness was supposed by HERSCHEL to be the rotation of the star bodily on an axis, by which revolution different parts of its surface, of different brilliancy, were successively and periodically presented to us. This explanation it might have been difficult to receive, when the periods of the known variables were so markedly various in length. His own discovery came to bridge over the interval, and quite confirmed him in his belief. He returned to the subject of the revolution of stars about their axes again and again, and connected it with the revolution of satellites.

He found that the satellites of _Jupiter_ and one of _Saturn's_ periodically changed in brightness, and by quite simple means showed that their periods of rotation were at least approximately the same as their periods of revolution about their primaries. In this case, as in every other, he considered a discovery in each and every one of its possible bearings. There are no instances where he has singularly overlooked the consequences of his observations.

_Researches on Double Stars._

The double stars were the subject of HERSCHEL'S earliest and of his latest papers. In 1782 he published his "_Catalogue of Double Stars_," and his last published memoir (1822) was on the same subject.

The question of determining the parallax of stars first brought HERSCHEL to the discovery of double stars. If two stars, A and B, appear very close together, and if, in reality, the star B is very many times more distant from the earth than A, although seen along the same line of sight, then the revolution of the earth in its orbit will produce changes in the relative situation of A and B, and, in fact, B will describe a small orbit about A, due to this revolution. This idea had been proposed by GALILEO, and measures on this plan had been made by LONG, with negative results. But HERSCHEL, in reviewing their work, declares that the stars chosen by LONG were not suitable to the purpose. It is necessary, among other things, to the success of this method, that it should be certain that the star B is really very much more distant than the star A. The only general test of the distance of stars is their brilliancy, and HERSCHEL decided to use only stars for this research which had two components very greatly different in brightness. A must be very bright (and presumably near to us), and B must be very close to A, and very faint (and thus, presumably, very distant).

It was in the search for such pairs of stars that the _Catalogue of Double Stars_ (1782) was formed. HERSCHEL'S first idea of a double star made such pairs as he found, to consist of two stars _accidentally_ near to each other. A was near to us, and appeared projected in a certain place on the celestial sphere. B was many times more distant, but, by chance, was seen along the same line, and made with A an _optical_ double. If the two stars were at the same distance from the earth, if they made part of the same physical system, if one revolved around the other, then this method of gaining a knowledge of their distance failed. Even in his first memoir on the subject, a surmise that this latter state might occur in some cases, was expressed by HERSCHEL. The notes on some of the pairs declare that a motion of one of them was suspected. But this motion might be truly orbital--of one star about the other as a centre--or it might simply be that one star was moving by its own _proper_ motion, and leaving the other behind. It was best to wait and see. The first Catalogue of Double Stars contained two hundred and three instances of such associations. These were observed from time to time, and new pairs discovered. The paper of MICHELL, "An Inquiry into the probable Parallax and Magnitude of the Fixed Stars, from the Quantity of Light which they Afford, and the Particular Circumstances of their Situation" (1767), was read and pondered. By 1802 HERSCHEL had become certain that there existed in the heavens real pairs of stars, both at the same distance from the earth, which were physically connected with each other. The arguments of MICHELL have been applied by BESSEL to the case of one of HERSCHEL'S double stars, in much the same order in which the argument ran in HERSCHEL'S own mind, as follows:

The star _Castor_ (_[alpha] Geminorum_) is a double star, where A is of the second, and B of the fourth, magnitude. To the naked eye these two appear as one star. With a telescope this is seen to be two stars, some 5" apart. In the whole sky there are not above fifty such stars as the brighter of the two, and about four hundred of the brilliancy of B. These fifty and four hundred stars are scattered over the vault of heaven, almost at random. No law has yet been traced by which we can say that here or here there shall be a bright star like A, or a fainter one like B. In general the distribution appears to be fortuitous. How then can we account for one of the four hundred stars like B placed so close to one of the fifty like A?

The chances are over four hundred thousand to one that the association in position is not accidental. This argument becomes overwhelming when the same association is found in many other cases. There were two hundred and three doubles in the Catalogue of 1782 alone, and many thousands are now known.

By a process like this, HERSCHEL reached his grand discovery of true binary systems, where one sun revolves about another. For he saw that if the two stars are near together in space, they could not stand still in face of each other, but that they must revolve in true orbits. Here was the discovery which came to take the place of the detection of the parallaxes of the fixed stars.

He had failed in one research, but he was led to grand conclusions. Was the force that these distant pairs of suns obeyed, the force of gravitation? This he could not settle, but his successors have done so. It was not till about 1827 that SAVARY, of the Paris Observatory, showed that one of HERSCHEL'S doubles was subjected to the law of gravitation, and thus extended the power of this law from our system to the universe at large. HERSCHEL himself lived to see some of his double stars perform half a revolution.

Of HERSCHEL'S discoveries, ARAGO thinks this has "le plus d'avenir." It may well be so. The laws which govern our solar system have been extended, through his researches, to regions of unknown distance. The binary stars will afford the largest field for research into the laws which govern them, and together with the clusters and groups, they will give a firm basis by which to study the distribution of stars in general, since here we have the great advantage of knowing, if not the real distance of the two stars from the earth, at least that this distance is alike for both.

_Researches on Planets and Satellites._

After HERSCHEL'S first publication on the mountains of the Moon (1780), our satellite appears to have occupied him but little. The observation of volcanoes (1787) and of a lunar eclipse are his only published ones. The planets _Mercury_, _Venus_, _Mars_, and _Jupiter_, although they were often studied, were not the subjects of his more important memoirs. The planet _Saturn_, on the contrary, seems never to have been lost sight of from the time of his first view of it in 1772.

The field of discovery always appears to be completely occupied until the advent of a great man, who, even by his way of putting old and familiar facts, shows the paths along which discoveries must come, if at all. This faculty comes from profound reflection on the nature of the subject itself, from a sort of transmuting power which changes the words of the books into the things of reality. HERSCHEL'S paper on _Saturn_, in 1790, is an admirable example of this.

HERSCHEL'S observations on _Saturn_ began in 1772. From 1790 to 1808 he published six memoirs on the figure, the ring, and the satellites of this planet. The spheroidal shape of the ball was first discovered by him, and we owe much of our certain knowledge of the constitution of the rings to his work. The sixth and seventh satellites, _Mimas_ and _Enceladus_, were discovered by him in 1789. The periods of rotation of the ball and of the ring were also fixed. In his conclusions as to the real figure of the rings, there is a degree of scientific caution which is truly remarkable, and which to-day seems almost excessive.

In his paper of 1792, HERSCHEL shows that the most distant satellite of _Saturn_--_Japetus_--turns once on its axis in each revolution about its primary, just as our moon does. He says of this:

"I cannot help reflecting with some pleasure on the discovery of an
analogy which shows that a certain uniform plan is carried on among
the secondary planets of our solar system; and we may conjecture
that probably most of the satellites are governed by the same law;
especially if it be founded on such a construction of their figure
as makes them more ponderous towards their primary planets."

I believe the last suggestion to have been the first statement of the possible arrangement of matter in satellites, which was afterwards so forcibly maintained by HANSEN in his theory of the moon. HANSEN'S researches show the consequences of such an arrangement, although they do not prove its existence.

It should be recorded that the explanation which is to-day received of the belts and bands upon _Jupiter_, is, I believe, first found in HERSCHEL'S memoir on _Venus_ (1793). His memoir of 1797, on the changeable brightness of the satellites of _Jupiter_, has already been referred to. The times of the rotation of the satellites on their axes was first determined by HERSCHEL from these observations, which also contain accounts of the curious, and as yet unexplained, phenomena attending their appearances on the disc of the planet.

HERSCHEL discovered in January, 1787, the two brighter satellites of _Uranus_, now called _Oberon_ and _Titania_. They are among the faintest objects in the solar system. A later discussion of all his observations led him to the belief that there were four more, and he gives his observations and computations in full. He says that of the existence of additional satellites he has no doubt. Of these four, three were exterior to the most distant satellite _Oberon_, the other was "interior" to _Titania_.

It was not until 1834 that even _Oberon_ and _Titania_ were again observed (by Sir JOHN HERSCHEL) with a telescope of twenty feet, similar to that which had discovered them, and not until 1847 was the true state of this system known, when Mr. LASSELL discovered _Ariel_ and _Umbriel_, two satellites interior to _Titania_, neither of which was HERSCHEL'S "interior" satellite. In 1848 and later years Mr. LASSELL, by the aid of telescopes constructed by himself, fully settled the fact that only four satellites of this planet existed. In 1874 I examined the observations of HERSCHEL on his supposed "interior" satellite, thinking that it might be possible that among the very few glimpses of it which he recorded, some might have belonged to _Ariel_ and some to _Umbriel_, and that by combining rare and almost accidental observations of two satellites which really existed, he had come to announce the existence of an "interior" satellite which had no existence in fact. Such I believe to be the case. In 1801, April 17, HERSCHEL describes an interior satellite in the position angle 189°, distant 18" from the planet. At that instant _Umbriel_, one of Mr. LASSELL'S satellites, was in the position 191°, and distant 21" from _Uranus_, in the most favorable position for seeing it. The observation of 1794, March 27, _may_ belong to _Ariel_. At the best the investigation is of passing interest only, and has nothing to do with the question of the discovery of the satellites. HERSCHEL discovered the two brighter ones, and it was only sixty years later that they were properly re-observed by Mr. LASSELL, who has the great honor of having added as many more, and who first settled the vexed question of satellites _exterior_ to _Oberon_, and this with a reflecting telescope made by himself, which is unequalled by any other of its dimensions.

_Researches on the Nature of the Sun._

In the introduction to his paper on the _Nature and Construction of the Sun and Fixed Stars_ (1795), HERSCHEL recounts what was known of the nature of the sun at that time. NEWTON had shown that it was the centre of the system; GALILEO and his successors had determined its rotation, the place of its equator, its real diameter, magnitude, density, distance, and the force of gravity on its surface. He says:

"I should not wonder if, considering all this, we were induced to
think that nothing remained to be added; and yet we are still very
ignorant in regard to the internal construction of the sun." "The
spots have been supposed to be solid bodies, the smoke of
volcanoes, the scum floating on an ocean of fluid matter, clouds,
opaque masses, and to be many other things." "The sun itself has
been called a globe of fire, though, perhaps, metaphorically." "It
is time now to profit by the observations we are in possession of.
I have availed myself of the labors of preceding astronomers, but
have been induced thereto by my own actual observation of the solar
phenomena."

HERSCHEL then refers to the theories advanced by his friend, Prof. WILSON, of Glasgow, in 1774. WILSON maintained that the spots were depressions below the sun's atmosphere, vast hollows as it were, at the bases of which the true surface of the sun could be seen.

The essence of his theory was the existence of two different kinds of matter in the sun: one solid and non-luminous--the nucleus--the other gaseous and incandescent--the atmosphere. Vacant places in the atmosphere, however caused, would show the black surface of the solid mass below. These were the spots. No explanation could be given of the _faculæ_, bright streaks, which appear on the sun's surface from time to time; but his theory accounted for the existence of the black _nuclei_ of the spots, and for the existence of the _penumbræ_ about these. The penumbra of a spot was formed by the thinner parts of the atmosphere about the vacancy which surrounded the nucleus.

This theory of WILSON'S was adopted by HERSCHEL as a basis for his own, and he brought numerous observations to confirm it, in the modified shape which he gave to it.

According to HERSCHEL, the sun consisted of three essentially different parts. First, there was a solid nucleus, non-luminous, cool, and even capable of being inhabited. Second, above this was an atmosphere proper; and, lastly, outside of this was a layer in which floated the clouds, or bodies which gave to the solar surface its intense brilliancy:

"According to my theory, a dark spot in the sun is a place in its
atmosphere which happens to be free from luminous decompositions"
above it.

The two atmospheric layers, which will be of varying thickness about a spot, will account for all the shades of darkness seen in the penumbra. Ascending currents from the solar surface will elevate certain regions, and may increase the solar activity near by, and will thus give rise to faculæ, which HERSCHEL shows to be elevated above the general surface. It will not be necessary to give a further account of this theory. The data in the possession of the modern theorist is a thousand-fold that to be derived from HERSCHEL'S observations, and, while the subject of the internal construction of the sun is to-day unsettled, we know that many important, even fundamental, portions of his theory are untenable. A remark of his should be recorded, however, as it has played a great part in such theories:

"That the emission of light must waste the sun, is not a difficulty
that can be opposed to our hypothesis. Many of the operations of
Nature are carried on in her great laboratory which we cannot
comprehend. Perhaps the many telescopic comets may restore to the
sun what is lost by the emission of light."

Arguments in favor of the habitability of both sun and moon are contained in this paper; but they rest more on a metaphysical than a scientific basis, and are to-day justly forgotten.

_Researches on the Motion of the Sun and of
the Solar System in Space._

In 1782 HERSCHEL writes, in regard to some of his discoveries of double stars:

"These may serve another very important end. I will just mention it,
though it is foreign to my present purpose. Several stars of the
first magnitude have been observed or suspected to have a proper
motion; hence we may surmise that our sun, with all its planets and
comets, may also have a motion towards some particular point of the
heavens. . . . If this surmise should have any foundation, it will show
itself in a series of some years in a kind of systematical parallax,
or change, due to the motion of the whole solar system."

In 1783 he published his paper _On the Proper Motion of the Solar System_, which contained the proofs of his surmises of a year before. That certain of the stars had in fact a _proper_ motion had been well established by the astronomers of the eighteenth century. After all allowances had been made for the effects of precession and other displacements of a star's position which were produced by motions of the earth, it was found that there were still small outstanding differences which must be due to the motion of the star itself--its proper motion. The quantity of this motion was not well known for any star when HERSCHEL'S researches began. Before they were concluded, however, MASKELYNE had deduced the proper motions of thirty-six stars--the fundamental stars, so called--which included in their number _Sirius_, _Procyon_, _Arcturus_, and generally the brightest stars.

It is _à priori_ evident that stars, in general, must have proper motions, when once we admit the universality of gravitation. That any fixed star should be entirely at rest would require that the attractions on all sides of it should be exactly balanced. Any change in the position of this star would break up this balance, and thus, in general, it follows that stars must be in motion, since all of them cannot occupy such a critical position as has to be assumed. If but one fixed star is in motion, this affects all the rest, and we cannot doubt but that every star, our sun included, is in motion by an amount which varies from small to great. If the sun alone had a motion, and the other stars were at rest, the consequence of this would be that all the fixed stars would appear to be retreating _en masse_ from that point in the sky towards which we were moving. Those nearest us would move more rapidly, those more distant less so. And in the same way, the stars from which the solar system was receding would seem to be approaching each other. If the stars, instead of being quite at rest, as just supposed, had motions proper to themselves, then we should have a double complexity. They would still appear to an observer in the solar system to have motions, and part of these motions would be truly proper to the stars, and part would be due to the advance of the sun itself in space.

Observations can show us only the _resultant_ of these two motions. It is for reasoning to separate this resultant into its two components. At first the question is to determine whether the results of observation indicate any solar motion at all. If there is none, the proper motions of stars will be directed along all possible lines. If the sun does truly move, then there will be a general agreement in the resultant motions of the stars near the ends of the line along which it moves, while those at the sides, so to speak, will show comparatively less systematic effect. It is as if one were riding in the rear of a railway train and watching the rails over which it has just passed. As we recede from any point, the rails at that point seem to come nearer and nearer together.

If we were passing through a forest, we should see the trunks of the trees from which we were going apparently come nearer and nearer together, while those on the sides of us would remain at their constant distance, and those in front would grow further and further apart.

These phenomena, which occur in a case where we are sensible of our own motion, serve to show how we may deduce a motion, otherwise unknown, from the appearances which are presented by the stars in space.

In this way, acting upon suggestions which had been thrown out previously to his own time by LAMBERT, MAYER, and BRADLEY, HERSCHEL demonstrated that the sun, together with all its system, was moving through space in an unknown and majestic orbit of its own. The centre round which this motion is directed cannot yet be assigned. We can only know the point in the heavens towards which our course is directed--"the apex of solar motion."

By a study of the proper motions assigned by MASKELYNE to the brighter stars, HERSCHEL was able to define the position of the solar apex with an astonishing degree of accuracy. His calculations have been several times repeated with the advantage of modern analytical methods, and of the hundred-fold material now at our disposition, but nothing essential has been added to his results of 1805, which were based upon such scanty data; and his paper of 1782 contains the announcement of the discovery itself.

His second paper on the _Direction_ and _Velocity_ of the solar system (1805) is the best example that can possibly be given of his marvellous skill in reaching the heart of a matter, and it may be the one in which his philosophical powers appear in their highest exercise. For sustained reflection and high philosophic thought it is to be ranked with the researches of NEWTON in the _Principia_.

_Researches on the Construction of the Heavens._

HERSCHEL'S papers on the Construction of the Heavens, as he named it, extended over his whole scientific life. By this he specially means the method according to which the stars, the clusters, the nebulæ, are spread through the regions of space, the causes that have led to this distribution, and the laws to which it is subjected.

No single astronomical fact is unimportant in the light which it may throw on the scheme of the whole, and each fact is to be considered in this light. As an instance: his discovery of the variable star _[alpha] Herculis_, which has a period of sixty days, was valuable in itself as adding one more to the number of those strange suns whose light is now brighter, now fainter, in a regular and periodic order. But the chief value of the discovery was that now we had an instance of a periodic star which went through all its phases in sixty days, and connected, as it were, the stars of short periods (three to seven days) with those of very long ones (three hundred to five hundred days), which two groups had, until then, been the only ones known. In the same way all his researches on the parallaxes of stars were not alone for the discovery of the distance of any one or two single stars, but to gain a unit of celestial measure, by means of which the depths of space might be sounded.

Astronomy in HERSCHEL'S day considered the bodies of the solar system as separated from each other by distances, and as filling a cubical space. The ideas of near and far, of up and down, were preserved, in regard to them, by common astronomical terms. But the vast number of stars seemed to be thought of, as they appear in fact to exist, lying on the surface of a hollow sphere. The immediate followers of BRADLEY used these fixed stars as points of reference by which the motions within the solar system could be determined, or, like LACAILLE and LALANDE, gathered those immense catalogues of their positions which are so indispensable to the science. MICHELL and HERSCHEL alone, in England, occupied their thoughts with the nature and construction of the heavens--the one in his study, the other through observation.[34] They were concerned with all three of the dimensions of space.

In his memoir of 1784, HERSCHEL says:

"Hitherto the sidereal heavens have, not inadequately for the
purpose designed, been represented by the concave surface of a
sphere, in the centre of which the eye of an observer might be
supposed to be placed.

"It is true the various magnitudes of the fixed stars even then
plainly suggested to us, and would have better suited, the idea of
an expanded firmament of three dimensions; but the observations upon
which I am now going to enter still farther illustrate and enforce
the necessity of considering the heavens in this point of view. In
future, therefore, we shall look upon those regions into which we
may now penetrate by means of such large telescopes, as a naturalist
regards a rich extent of ground or chain of mountains containing
strata variously inclined and directed, as well as consisting of
very different materials. The surface of a globe or map, therefore,
will but ill delineate the interior parts of the heavens."

HERSCHEL'S method of study was founded on a mode of observation which he called _star-gauging_. It consisted in pointing a powerful telescope toward various parts of the heavens, and ascertaining by actual count how thick the stars were in each region. His twenty-foot reflector was provided with such an eye-piece that, in looking into it, he saw a portion of the heavens about 15' in diameter. A circle of this size on the celestial sphere has about one quarter the apparent surface of the sun, or of the full moon. On pointing the telescope in any direction, a greater or less number of stars were visible. These were counted, and the direction in which the telescope pointed was noted. Gauges of this kind were made in all parts of the sky, and the results were tabulated in the order of right ascension.

The following is an extract from the gauges, and gives the average number of stars in each field at the points noted in right ascension and north polar distance:

----------------------------------------------------------
| N. P. D. || | N. P. D.
R. A. | 78° to 80°. || R. A. | 92° to 94°.
| No. of Stars. || | No. of Stars.
------------|-----------------||-----------|--------------
H. M. | || H. M. |
11 6 | 3.1 || 15 10 | 9.4
12 31 | 3.4 || 15 22 | 10.6
12 44 | 4.6 || 15 47 | 10.6
12 49 | 3.9 || 16 8 | 12.1
13 5 | 3.8 || 16 25 | 13.6
14 30 | 3.6 || 16 37 | 18.6
----------------------------------------------------------

In this small table, it is plain that a different law of clustering or of distribution obtains in the two regions. Such differences are still more marked, if we compare the extreme cases found by HERSCHEL, as R. A. = 19h 41m, N. P. D. = 74° 33', number of stars per field = 588; and R. A. = 16h 10m, N. P. D. = 113° 4', number of stars = 1.1.

The number of stars in certain portions is very great. For example, in the Milky Way, near _Orion_, six fields of view promiscuously taken gave 110, 60, 70, 90, 70, and 74 stars each, or a mean of 79 stars per field. The most vacant space in this neighborhood gave 60 stars. So that as HERSCHEL'S sweeps were two degrees wide in declination, in one hour (15°) there would pass through the field of his telescope 40,000 or more stars. In some of the sweeps this number was as great as 116,000 stars in a quarter of an hour.

When HERSCHEL first applied his telescope to the Milky Way, he believed that it completely resolved the whole whitish appearance into small stars. This conclusion he subsequently modified. He says:

"It is very probable that the great stratum called the Milky Way is
that in which the sun is placed, though perhaps not in the very
centre of its thickness.

"We gather this from the appearance of the Galaxy, which seems to
encompass the whole heavens, as it certainly must do if the sun is
within it. For, suppose a number of stars arranged between two
parallel planes, indefinitely extended every way, but at a given
considerable distance from each other; and calling this a sidereal
stratum, an eye placed somewhere within it will see all the stars in
the direction of the planes of the stratum projected into a great
circle, which will appear lucid on account of the accumulation of
the stars, while the rest of the heavens, at the sides, will only
seem to be scattered over with constellations, more or less crowded
according to the distance of the planes, or number of stars
contained in the thickness or sides of the stratum.

"If the eye were placed somewhere without the stratum, at no very
great distance, the appearance of the stars within it would assume
the form of one of the smaller circles of the sphere, which would be
more or less contracted according to the distance of the eye; and,
if this distance were exceedingly increased, the whole stratum might
at last be drawn together into a lucid spot of any shape, according
to the length, breadth, and height of the stratum.

"Suppose that a smaller stratum should branch out from the former in
a certain direction, and that it also is contained between two
parallel planes, so that the eye is contained within the great
stratum somewhere before the separation, and not far from the place
where the strata are still united. Then this second stratum will not
be projected into a bright circle like the former, but it will be
seen as a lucid branch proceeding from the first, and returning
into it again at a distance less than a semicircle. If the bounding
surfaces are not parallel planes, but irregularly curved surfaces,
analogous appearances must result."

The Milky Way, as we see it, presents the aspect which has been just accounted for, in its general appearance of a girdle around the heavens and in its bifurcation at a certain point, and HERSCHEL'S explanation of this appearance, as just given, has never been seriously questioned. One doubtful point remains: are the stars scattered all through space? or are they near its bounding planes, or clustered in any way within this space so as to produce the same result to the eye as if uniformly distributed?

HERSCHEL assumed that they were nearly equably arranged all through the space in question. He only examined one other arrangement, _viz._, that of a ring of stars surrounding the sun, and he pronounced against such an arrangement, for the reason that there is absolutely nothing in the size or brilliancy of the sun to cause us to suppose it to be the centre of such a gigantic system. No reason, except its importance to us personally, can be alleged for such a supposition. Every star will have its own appearance of a Galaxy or Milky Way, which will vary according to the situation of the star.

Such an explanation will account for the general appearances of the Milky Way and of the rest of the sky, supposing the stars equally or nearly equally distributed in space. On this supposition, the system must be deeper where the stars appear most numerous.

HERSCHEL endeavored, in his early memoirs, to explain this inequality of distribution on the fundamental assumption that the stars were nearly equably distributed in space. If they were so distributed, then the number of stars visible in any gauge would show the thickness of the stellar system in the direction in which the telescope was pointed. At each pointing, the field of view of the instrument includes all the visible stars situated within a cone, having its vortex at the observer's eye, and its base at the very limits of the system, the angle of the cone (at the eye) being 15'. Then the cubes of the perpendiculars let fall from the eye, on the plane of the bases of the various visual cones, are proportional to the solid contents of the cones themselves, or, as the stars are supposed equally scattered within all the cones, the cube roots of the numbers of stars in each of the fields express the relative lengths of the perpendiculars. A _section_ of the sidereal system along any great circle can be constructed from the data furnished by the gauges in the following way:

The solar system is within the mass of stars. From this point lines are drawn along the different directions in which the gauging telescope was pointed. On these lines are laid off lengths proportional to the cube roots of the number of stars in each gauge. The irregular line joining the terminal points will be approximately the bounding curve of the stellar system in the great circle chosen. Within this line the space is nearly uniformly filled with stars. Without it is empty space. A similar section can be constructed in any other great circle, and a combination of all such would give a representation of the shape of our stellar system. The more numerous and careful the observations, the more elaborate the representation, and the 863 gauges of HERSCHEL are sufficient to mark out with great precision the main features of the Milky Way, and even to indicate some of its chief irregularities.

On the fundamental assumption of HERSCHEL (equable distribution), no other conclusion can be drawn from his statistics but the one laid down by him.

This assumption he subsequently modified in some degree, and was led to regard his gauges as indicating not so much the _depth of the system_ in any direction, as the _clustering power or tendency_ of the stars in those special regions. It is clear that if in any given part of the sky, where, on the average, there are ten stars (say) to a field, we should find a certain small portion having 100 or more to a field, then, on HERSCHEL'S first hypothesis, rigorously interpreted, it would be necessary to suppose a spike-shaped protuberance directed from the earth, in order to explain the increased number of stars. If many such places could be found, then the probability is great that this explanation is wrong. We should more rationally suppose some real inequality of star distribution here. It is, in fact, in just such details that the method of HERSCHEL breaks down, and a careful examination of his system leads to the belief that it must be greatly modified to cover all the known facts, while it undoubtedly has, in the main, a strong basis.

The stars are certainly not uniformly distributed, and any general theory of the sidereal system must take into account the varied tendency to aggregation in various parts of the sky.

In 1817, HERSCHEL published an important memoir on the same subject, in which his first method was largely modified, though not abandoned. Its fundamental principle was stated by him as follows: