CHAPTER IV.

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

aerial 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 L4,000. 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 SCHOeNFELD (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 deg., distant 18" from

the planet. At that instant _Umbriel_, one of Mr. LASSELL'S satellites,

was in the position 191 deg., 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

_faculae_, 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 _penumbrae_ 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

faculae, 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 _a 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 nebulae, 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 deg. to 80 deg. || R. A. |92 deg. to 94 deg.

| 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 deg. 33', number of stars per field = 588;

and R. A. = 16h 10m, N. P. D. = 113 deg. 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 deg.) 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:

"It is evident that we cannot mean to affirm that the stars of the

fifth, sixth, and seventh magnitudes are really smaller than those

of the first, second, or third, and that we must ascribe the cause

of the difference in the apparent magnitudes of the stars to a

difference in their relative distances from us. On account of the

great number of stars in each class, we must also allow that the

stars of each succeeding magnitude, beginning with the first, are,

one with another, further from us than those of the magnitude

immediately preceding. The relative magnitudes give only relative

distances, and can afford no information as to the real distances at

which the stars are placed.

"A standard of reference for the arrangement of the stars may be had

by comparing their distribution to a certain properly modified

equality of scattering. The equality which I propose does not

require that the stars should be at equal distances from each other,

nor is it necessary that all those of the same nominal magnitude

should be equally distant from us."

It consisted in allotting a certain equal portion of space to every

star, so that, on the whole, each equal portion of space within the

stellar system contains an equal number of stars. The space about each

star can be considered spherical. Suppose such a sphere to surround our

own sun. Its radius will not differ greatly from the distance of the

nearest fixed star, and this is taken as the unit of distance.

Suppose a series of larger spheres, all drawn around our sun as a

centre, and having the radii 3, 5, 7, 9, etc. The contents of the

spheres being as the cubes of their diameters, the first sphere will

have 3 x 3 x 3 = 27 times the volume of the unit sphere, and will

therefore be large enough to contain 27 stars; the second will have 125

times the volume, and will therefore contain 125 stars, and so on with

the successive spheres. For instance, the sphere of radius 7 has room

for 343 stars, but of this space 125 parts belong to the spheres inside

of it; there is, therefore, room for 218 stars between the spheres of

radii 5 and 7.

HERSCHEL designates the several distances of these layers of stars as

orders; the stars between spheres 1 and 3 are of the first order of

distance, those between 3 and 5 of the second order, and so on.

Comparing the room for stars between the several spheres with the number

of stars of the several magnitudes which actually exists in the sky, he

found the result to be as follows:

--------------------------------------------------------

Order of | Number of | | Number of

Distance. | Stars there | Magnitude. | Stars of that

| is Room for. | | Magnitude.

--------------------------------------------------------

1........ | 26 | 1 | 17

2........ | 98 | 2 | 57

3........ | 218 | 3 | 206

4........ | 386 | 4 | 454

5........ | 602 | 5 | 1,161

6........ | 866 | 6 | 6,103

7........ | 1,178 | 7 | 6,146

8........ | 1,538 | |

---------------------------------------------------------

The result of this comparison is, that if the order of magnitudes could

indicate the distance of the stars, it would denote at first a gradual

and afterward a very abrupt condensation of them, at and beyond the

region of the sixth-magnitude stars.

If we assume the brightness of any star to be inversely proportional to

the square of its distance, it leads to a scale of distance different

from that adopted by HERSCHEL, so that a sixth-magnitude star on the

common scale would be about of the eighth order of distance according to

this scheme--that is, we must remove a star of the first magnitude to

eight times its actual distance to make it shine like a star of the

sixth magnitude.

On the scheme here laid down, HERSCHEL subsequently assigned the _order_

of distance of various objects, mostly star-clusters, and his estimates

of these distances are still quoted. They rest on the fundamental

hypothesis which has been explained, and the error in the assumption of

equal intrinsic brilliancy for all stars affects these estimates. It is

perhaps probable that the hypothesis of equal brilliancy for all stars

is still more erroneous than the hypothesis of equal distribution, and

it may well be that there is a very large range indeed in the actual

dimensions and in the intrinsic brilliancy of stars at the same order of

distance from us, so that the tenth-magnitude stars, for example, may be

scattered throughout the spheres which HERSCHEL would assign to the

seventh, eighth, ninth, tenth, eleventh, twelfth, and thirteenth

magnitudes. However this may be, the fact remains that it is from

HERSCHEL'S groundwork that future investigators must build. He found the

whole subject in utter confusion. By his observations, data for the

solution of some of the most general questions were accumulated, and in

his memoirs, which STRUVE well calls "immortal," he brought the

scattered facts into order and gave the first bold outlines of a

reasonable theory. He is the founder of a new branch of astronomy.

_Researches for a Scale of Celestial Measures.

Distances of the Stars._

If the stars are _supposed_ all of the same absolute brightness, their

brightness to the eye will depend only upon their distance from us. If

we call the brightness of one of the fixed stars at the distance of

_Sirius_, which may be used as the unity of distance, 1, then if it is

moved to the distance 2, its apparent brightness will be one-fourth; if

to the distance 3, one-ninth; if to the distance 4, one-sixteenth, and

so on, the apparent brightness diminishing as the square of the distance

increases. The distance may be taken as an order of magnitude. Stars at

the _distances_ two, three, four, etc., HERSCHEL called of the second,

third, and fourth magnitudes.

By a series of experiments, the details of which cannot be given here,

HERSCHEL determined the space-penetrating power of each of his

telescopes. The twenty-foot would penetrate into space seventy-five

times farther than the naked eye; the twenty-five foot, ninety-six

times; and the forty-foot, one hundred and ninety-two times. If the

seventh-magnitude stars are those just visible to the naked eye, and if

we still suppose all stars to be of equal intrinsic brightness, such

seventh-magnitude stars would remain visible in the forty-foot, even if

removed to 1,344 times the distance of _Sirius_ (1,344 = 7 x 192).

If, further, we suppose that the visibility of a star is strictly

proportional to the total intensity of the light from it which strikes

the eye, then a condensed cluster of 25,000 stars of the 1,344th

magnitude could still be seen in the forty-foot at a distance where each

star would have become 25,000 times fainter, that is, at about 158 times

the distance of _Sirius_ (158 x 158 = 24,964). The light from the

nearest star requires some three years to reach the earth. From a star

1,344 times farther it would require about 4,000 years, and for such a

cluster as we have imagined no less than 600,000 years are needed. That

is, the light by which we see such a group has not just now left it.

On the contrary, it has been travelling through space for centuries and

centuries since it first darted forth. It is the ancient history of such

groups that we are studying now, and it was thus that HERSCHEL declared

that telescopes penetrated into time as well as into space.

Other more exact researches on the relative light of stars were made by

HERSCHEL. These were only one more attempt to obtain a scale of

celestial distances, according to which some notion of the limits and of

the interior dimensions of the universe could be gained. Two telescopes,

_exactly equal_ in every respect, were chosen and placed side by side.

Pairs of stars which were _exactly equal_, were selected by means of

them. By diminishing the aperture of one telescope directed to a bright

star, and keeping the other telescope unchanged and directed to a

fainter star, the two stars could be equalized in light, and, from the

relative size of the apertures, the relative light of this pair of stars

could be accurately computed, and so on for other pairs. This was the

first use of the method of _limiting apertures_. His general results

were that the stars of the first magnitude would still remain visible to

the naked eye, even if they were at a distance from us _twelve_ times

their actual distance.

This method received a still further development at his hands. He did

not leave it until he had gained all the information it was capable of

giving. He prepared a set of telescopes collecting 4, 9, 16, etc.

(2 x 2, 3 x 3, 4 x 4, etc.), times as much light as the naked eye.

These were to extend the determinations of distance to the telescopic

stars. For example, a certain portion of the heavens which he examined

contained no star visible to the naked eye, but many telescopic stars.

We cannot say that no one of these is as bright in itself as some of our

first-magnitude stars. The smallest telescope of the set showed a large

number of stars; these must, then, be _twice_ as far from us, on the

average, as the stars just visible to the naked eye. But first-magnitude

stars, like _Sirius_, _Procyon_, _Arcturus_, etc., become just visible

to the eye if removed to twelve times their present distance. Hence the

stars seen in this first telescope of the set were between twelve and

twenty-four times as far from us as _Arcturus_, for example.

"At least," as HERSCHEL says, "we are certain that if stars of the size

and lustre of _Sirius_, _Arcturus_, etc., were removed into the

profundity of space I have mentioned, they would then appear like the

stars which I saw." With the next telescope, which collected nine times

more light than the eye, and brought into view objects three times more

distant, other and new stars appeared, which were then (3 x 12)

thirty-six times farther from us than _Arcturus_. In the same way, the

seven-foot reflector showed stars 204 times, the ten-foot 344 times,

the twenty-foot 900 times farther from us than the average

first-magnitude star. As the light from such a star requires three years

to reach us, the light from the faintest stars seen by the twenty-foot

would require 2,700 years (3 x 900).

But HERSCHEL was now (1817) convinced that the twenty-foot telescope

could not penetrate to the boundaries of the Milky Way; the faintest

stars of the Galaxy must then be farther from us even than nine hundred

times the distance of _Arcturus_, and their light must be at least 3,000

years old when it reaches us.

There is no escaping a certain part of the consequences established by

HERSCHEL. It is indeed true that unless a particular star is of the same

intrinsic brightness as our largest stars, this reasoning does not apply

to it; in just so far as the average star is less bright than the

average brightness of our largest stars, will the numbers which HERSCHEL

obtained be diminished. But for every star of which his hypothesis is

true, we may assert that his conclusions are true, and no one can deny,

with any show of reason, that, on the whole, his suppositions must be

valid. On the whole, the stars which we call faint are farther from us

than the brighter ones; and, on the whole, the brilliancy of our

brightest and nearest stars is not very far from the brilliancy of the

average star in space. We cannot yet define the word _very_ by a

numerical ratio.

The _method_ struck out by HERSCHEL was correct; it is for his

successors to look for the special cases and limitations, to answer the

question, At a certain distance from us, what are the variations which

actually take place in the brilliancy and the sizes of stars? The answer

to this question is to be found in the study of the clusters of regular

forms, where we _know_ the stars to be all at the same distance from us.

_Researches on Light and Heat, Etc._

Frequently in the course of his astronomical work, HERSCHEL found

himself confronted by questions of physics which could not be

immediately answered in the state of the science at that time. In his

efforts to find a method for determining the dimensions of the stellar

universe, he was finally led, as has been shown, to regard the

brightness of a star as, in general, the best attainable measure of its

distance from us. His work, however, was done with telescopes of various

dimensions and powers, and it was therefore necessary to find some law

for comparing the different results among themselves as well as with

those given by observations with an unassisted eye. This necessity

prompted an investigation, published in 1800, in which, after drawing

the distinction between absolute and intrinsic brightness, HERSCHEL gave

an expression for the _space-penetrating power_ of a telescope. The

reasoning at the base of this conception was as follows.

The ratio of the light entering the eye when directed toward a star, to

the whole light given out by the star, would be as the area of the pupil

of the eye to the area of the whole sphere having the star as a centre

and our distance from the star as a radius. If the eye is assisted by a

telescope, the ratio is quite different. In that case the ratio of the

light which enters the eye to the whole light, would be as the area of

the mirror or object-glass to the area of the whole sphere having the

star as a centre and its distance as a radius. Thus the light received

by the _eye_ in the two cases would be as the area of the pupil is to

the area of the object-glass. For instance, if the pupil has a diameter

of two-fifths of an inch, and the mirror a diameter of four inches, then

a hundred times as much light would enter the eye when assisted by the

telescope as when unarmed, since the _area_ of the pupil is

one-hundredth the _area_ of the objective.

If a particular star is just visible to the naked eye, it will be quite

bright if viewed with this special telescope, which makes it one hundred

times more brilliant in appearance. If we could move the star bodily

away from us to a distance ten times its present distance, we could thus

reduce its brightness, as seen with the telescope, to what it was at

first, as seen with the eye alone, _i. e._, to bare visibility. Moving

the star to ten times its present distance would increase the surface of

the sphere which it illuminates a hundred-fold. We cannot move any

special star, but we can examine stars of all brightnesses, and thus

(presumably) of all distances.

HERSCHEL'S argument was, then, as follows: Since with such a telescope

one can see a star ten times as far off as is possible to the naked eye,

this telescope has the power of penetrating into space ten times farther

than the eye alone. But this number ten, also, expresses the ratio of

the diameter of the objective to that of the pupil of the eye,

consequently the general law is that the _space-penetrating power_ of a

telescope is found by dividing the diameter of the mirror in inches by

two-fifths. The diameter of the pupil of the eye (two-fifths of an inch)

HERSCHEL determined by many measures.

This simple ratio would only hold good, however, provided no more light

were lost by the repeated reflections and refractions in the telescope

than in the eye. That light must be so lost was evident, but no data

existed for determining the loss. HERSCHEL was thus led to a long series

of photometric experiments on the reflecting powers of the metals used

in his mirrors, and on the amount of light transmitted by lenses.

Applying the corrections thus deduced experimentally, he found that the

space-penetrating power of his twenty-foot telescope, with which he made

his star-gauges, was sixty-one times that of the unassisted eye, while

the space-penetrating power of his great forty-foot telescope was one

hundred and ninety-two times that of the eye. In support of his

important conclusions HERSCHEL had an almost unlimited amount of

experimental data in the records of his observations, of which he made

effective use.

By far the most important of HERSCHEL'S work in the domain of pure

physics was published in the same year (1800), and related to radiant

heat. The investigation of the space-penetrating powers of telescopes

was undertaken for the sole purpose of aiding him in measuring the

dimensions of the stellar universe, and there was no temptation for him

to pursue it beyond the limits of its immediate usefulness. But here,

though the first hint leading to remarkable discoveries was a direct

consequence of his astronomical work, the novelty and interest of the

phenomena observed induced him to follow the investigation very far

beyond the mere solution of the practical question in which it

originated.

Having tried many varieties of shade-glasses between the eye-piece of

his telescope and the eye, in order to reduce the inordinate degree of

heat and light transmitted by the instrument when directed towards the

sun, he observed that certain combinations of colored glasses permitted

very little light to pass, but transmitted so much heat that they could

not be used; while, on the other hand, different combinations and

differently colored glasses would stop nearly all the heat, but allow an

inconveniently great amount of light to pass. At the same time he

noticed, in the various experiments, that the images of the sun were of

different colors. This suggested the question as to whether there was

not a different heating power proper to each color of the spectrum. On

comparing the readings of sensitive thermometers exposed in different

portions of an intense solar spectrum, he found that, beginning with the

violet end, he came to the maximum of light long before that of heat,

which lay at the other extremity, that is, near the red. By several

experiments it appeared that the maximum of illumination, _i. e._, the

yellow, had little more than half the heat of the full red rays; and

from other experiments he concluded that even the full red fell short of

the maximum of heat, which, perhaps, lay even a little beyond the limits

of the visible spectrum.

"In this case," he says, "radiant heat will at least partly, if not

chiefly, consist, if I may be permitted the expression, of invisible

light; that is to say, of rays coming from the sun, that have such a

momentum[35] as to be unfit for vision. And admitting, as is highly

probable, that the organs of sight are only adapted to receive

impressions from particles of a certain momentum, it explains why

the maximum of illumination should be in the middle of the

refrangible rays; as those which have greater or less momenta are

likely to become equally unfit for the impression of sight."

In his second paper on this subject, published in the same year,

HERSCHEL describes the experiments which led to the conclusion given

above. This paper contains a remarkably interesting passage which

admirably illustrates HERSCHEL'S philosophic method.

"To conclude, if we call light, those rays which illuminate objects,

and radiant heat, those which heat bodies, it may be inquired

whether light be essentially different from radiant heat? In answer

to which I would suggest that we are not allowed, by the rules of

philosophizing, to admit two different causes to explain certain

effects, if they may be accounted for by one. . . . If this be a true

account of the solar heat, for the support of which I appeal to my

experiments, it remains only for us to admit that such of the rays

of the sun as have the refrangibility of those which are contained

in the prismatic spectrum, by the construction of the organs of

sight, are admitted under the appearance of light and colors, and

that the rest, being stopped in the coats and humors of the eye, act

on them, as they are known to do on all the other parts of our body,

by occasioning a sensation of heat."

We now know that the reasoning and conclusion here given are entirely

correct, but they have for their basis only a philosophical conception,

and not a series of experiments designed especially to test their

correctness. Such an experimental test of this important question was

the motive for a third and last paper in this department of physics.

This paper was published in volume ninety of the _Philosophical

Transactions_, and gave the results of two hundred and nineteen

quantitative experiments.

Here we are at a loss to know which to admire most--the marvellous skill

evinced in acquiring such accurate data with such inadequate means, and

in varying and testing such a number of questions as were suggested in

the course of the investigation--or the intellectual power shown in

marshalling and reducing to a system such intricate and apparently

self-contradictory phenomena. It is true that this discussion led him to

a different conclusion from that announced in the previous paper, and,

consequently, to a false conclusion; but almost the only escape from his

course of reasoning lay in a principle which belongs to a later period

of intellectual development than that of HERSCHEL'S own time.

HERSCHEL made a careful determination of the quantitative distribution

of light and of heat in the prismatic spectrum, and discovered the

surprising fact that not only where the light was at a maximum the heat

was very inconsiderable, but that where there was a maximum exhibition

of heat, there was not a trace of light.

"This consideration," he writes, "must alter the form of our

proposed inquiry; for the question being thus at least partly

decided, since it is ascertained that we have rays of heat which

give no light, it can only become a subject of inquiry whether some

of these heat-making rays may not have a power of rendering objects

visible, superadded to their now already established power of

heating bodies. This being the case, it is evident that the _onus

probandi_ ought to lie with those who are willing to establish such

an hypothesis, for it does not appear that Nature is in the habit of

using one and the same mechanism with any two of our senses. Witness

the vibration of air that makes sound, the effluvia that occasion

smells, the particles that produce taste, the resistance or

repulsive powers that affect the touch--all these are evidently

suited to their respective organs of sense."

It is difficult to see how the fallacy of this argument could have been

detected by any one not familiar with the fundamental physiological law

that the nature of a sensation is in no wise determined by the character

of the agent producing it, but only by the character of the nerves acted

upon; but, as already intimated, this law belongs to a later epoch than

the one we are considering. HERSCHEL thus finally concluded that light

and radiant heat were of essentially different natures, and upon this

supposition he explained all of the phenomena which his numerous

experiments had shown him. So complete and satisfactory did this work

appear to the scientific world, that for a long time the question was

looked upon as closed, and not until thirty-five years later was there

any dissent. Then the Italian physicist, MELLONI, with instrumental

means a thousand times more delicate than that of HERSCHEL, and with a

far larger store of cognate phenomena, collected during the generation

which had elapsed, to serve as a guide, discovered the true law. This,

as we have seen, was at first adopted by HERSCHEL on philosophical

grounds, and then rejected, since he did not at that time possess the

key which alone could have enabled him to properly interpret his

experiments.

It is well to summarize the capital discoveries in this field made by

HERSCHEL, more particularly because his claims as a discoverer seem to

have been strangely overlooked by historians of the development of

physical science. He, before any other investigator, showed that radiant

heat is refracted according to the laws governing the refraction of

light by transparent media; that a portion of the radiation from the sun

is incapable of exciting the sensation of vision, and that this portion

is the less refrangible; that the different colors of the spectrum

possess very unequal heating powers, which are not proportional to their

luminosity; that substances differ very greatly in their power of

transmitting radiant heat, and that this power does not depend solely

upon their color; and that the property of diffusing heat is possessed

to a varying degree by different bodies, independently of their color.

Nor should we neglect to emphasize, in this connection, the importance

of his measurements of the intensity of the heat and light in the

different portions of the solar spectrum. It is the more necessary to

state HERSCHEL'S claims clearly, as his work has been neglected by those

who should first have done him justice. In his "History of Physics,"

POGGENDORFF has no reference to HERSCHEL. In the collected works of

VERDET, long bibliographical notes are appended to each chapter, with

the intention of exhibiting the progress and order of discovery. But all

of HERSCHEL'S work is overlooked, or indexed under the name of his son.

One little reference in the text alone shows that his very name was not

unknown. Even in the great work of HELMHOLTZ on physiological optics,

HERSCHEL'S labors are not taken account of.

It is easy to account for this seemingly strange neglect. HERSCHEL is

known to this generation only as an astronomer. A study of his memoirs

will show that his physical work alone should give him a very high rank

indeed, and I trust that the brief summaries, which alone can be given

here, will have made this plain.

* * * * *

We may conclude from the time expended, the elaborate nature of the

experiments involved, and the character of the papers devoted to their

consideration, that the portion of HERSCHEL'S researches in physics

which interested him to the greatest degree, was the investigation of

the optical phenomena known as NEWTON'S rings. In 1792 he obtained the

two object-glasses of HUYGHENS, which were in the possession of the

Royal Society, for the purpose of repeating NEWTON'S experiments, and in

1810 he read the last of his three papers on the subject.

Sir ISAAC NEWTON had given some of his most vigorous efforts to the

study of the phenomena of interference of light, which are exemplified

in the colors of thin and of thick plates. The colors of thin plates are

most conveniently studied in the regular form which they present when

produced by a thin plate of air, limited on one side by a plane

polished surface, and on the other by a spherical surface of long

radius, such as the exterior surface of a convex lens, for example.

The colors are then arranged in concentric circles, and, though others

had so produced them before NEWTON, these rings have, ever since the

publication of his remarkable work, been known by his name.

To explain the phenomena, NEWTON was obliged to supplement his theory of

the corpuscular nature of light, by supposing that the inconceivably

minute particles constituting light are not always equally susceptible

of reflection, but that they have periodically recurring "fits of easy

reflection" and of "easy transmission." This conception, though by no

means unphilosophical, seemed to HERSCHEL too artificial and improbable

for ready acceptance, and his effort was to supply a more probable

explanation.

The developments of optical science have justified HERSCHEL in his

objections, but we cannot accord to him must any considerable part in

making clear the true nature of the phenomenon. Indeed, it must be

recognized that his position was distinctly less advanced than that of

NEWTON. That great philosopher announced the true law governing the

relation between the color and the thickness of the film. HERSCHEL did

not recognize such a relation. NEWTON showed exactly how the phenomenon

depended upon the obliquity at which it was viewed. HERSCHEL found no

place in his theory for this evident variation.

In the series of experiments described in the first paper on this

subject, HERSCHEL mistook the locus of a certain set of rings which he

was observing. This mistake, though so slight as hardly to be detected

without the guidance of the definite knowledge acquired in later times,

not only vitiated the conclusion from the experiments, but gave an

erroneous direction to the whole investigation. To him these experiments

proved that NEWTON'S conception of a periodic phenomenon was untenable.

Thus cut loose from all hypothesis, his fertility in ideas and ingenuity

in experimentation are as striking as ever. He tried the effect of

having a polished metal as one of the surfaces limiting the thin plate

of air. Observing the so-called "blue bow" of NEWTON at the limit of

total reflection in a prism, he was led to the discovery of its

complement, the "red bow" by refraction. Here he thought he had found

the solution of his problem, and attributed the rings to the reflection

of the light which passed through in the red bow. Though mistaken, he

had presented to the world of science two experiments which have since

played very prominent parts in the undulatory theory of light, namely,

the rings formed upon polished metal, and the bands produced by a thin

plate near the critical angle.

As in his later researches upon the nature of radiant heat, he was wrong

in his conclusions, and perhaps with less excuse. His experiments were

skilfully devised and most ingenious. His philosophizing was distinctly

faulty. We can see not only that he was wrong, but exactly where he

began to go wrong. Yet these papers are full of interest to the

physicist, and by no means deserve the neglect into which they have

fallen.

_Researches on the Dimensions of the Stars._

HERSCHEL examined a number of bright stars, using extremely high

magnifying powers, in order to determine whether the stars have sensible

dimensions. In a good telescope stars present round and pretty uniformly

illuminated disks. If these disks really represent the angular diameter

of the stars, they should admit of magnifying, like other objects; but,

instead of this, HERSCHEL found that they appeared smaller as the

telescopic power was increased. He accordingly called the disk of light

seen in the telescope a spurious disk. This singular phenomenon gave its

discoverer a ready criterion for determining whether a small bright body

has an appreciable size, or only impresses the sense of sight by virtue

of its intrinsic brightness. If the first were the case, the apparent

size would increase with increased magnifying power, while, if the

angular dimensions were inappreciable, the apparent size would, on the

contrary, diminish with additional magnifying. An occasion for using

this criterion came in the first years of this century, with the

discovery of three small planets having orbits lying between those of

_Mars_ and _Jupiter_. HERSCHEL gave the name _Asteroids_ to these

bodies. As the appropriateness of this term had been violently assailed,

the discovery of _Juno_, in 1804, the third one of the group, led to a

careful experimental study of the defining power of the telescope used,

and of the laws governing the phenomena of spurious disks.

With a telescope of about nine inches in aperture, HERSCHEL found that

if _Juno_ subtended an angle greater than a quarter of a second of arc,

a certain indication of the fact would have shown itself in the course

of the experiments. This conclusion was a justification of the name

Asteroid, since the appearance of the new planet was strictly stellar.

On other grounds, a better name might have been selected.

In the paper giving the results of the experiments, the phenomena of the

spurious disks are very completely described; but they did not attract

the attention which they deserved, and they only became an object of

especial interest to students of physics when they were again studied by

the famous German optician FRAUNHOFER, a generation later.

Incidentally the experiments are of interest, as yielding us a measure

of the excellence of HERSCHEL'S telescopes, and a measure which is quite

independent of the keenness of his vision. From them we may be sure that

the efficiency of the nine-inch mirror used was not sensibly less than

that of the highest theoretically attainable excellence. In this

connection, too, we may refer to the _Philosophical Transactions_ for

1790, pp. 468 and 475, where HERSCHEL gives observations of both

_Enceladus_ and _Mimas_ seen in contact with the ball of _Saturn_.

I have never seen so good definition, telescopic and atmospheric, as he

must have had on these occasions.

_Researches on the Spectra of the Fixed Stars._

The spectroscope was applied by SECCHI to the study of the spectra of

the fixed stars visible to the naked eye in the years 1863 to 1866.

He examined the nature of the spectrum of each of the larger stars,

and found that these stars could be arranged in three general classes or

_types_. His results have been verified and extended by other

astronomers, and his classification has been generally accepted.

According to SECCHI, the lucid stars may be separated into three groups,

distinguished by marked differences in their spectra. SECCHI'S Type I.

contains stars whose spectra are like those of _Sirius_, _Procyon_, and

_[alpha] Lyrae_; his Type II. stars like _Arcturus_ and _Aldebaran_;

his Type III. stars like _[alpha] Orionis_.

HERSCHEL also made some trials in this direction. In the _Philosophical

Transactions_ for 1814 (p. 264), he says:

"By some experiments on the light of a few of the stars of the first

magnitude, made in 1798, by a prism applied to the eye-glasses of my

reflectors, adjustable to any angle and to any direction, I had the

following analyses:

"The light of _Sirius_ consists of red, orange, yellow, green, blue,

purple, and violet. _[alpha] Orionis_ contains the same colors,

but the red is more intense, and the orange and yellow are less

copious in proportion than they are in _Sirius_. _Procyon_ contains

all the colors, but proportionately more blue and purple than

_Sirius_. _Arcturus_ contains more red and orange, and less yellow

in proportion than _Sirius_. _Aldebaran_ contains much orange and

very little yellow. _[alpha] Lyrae_ contains much yellow, green,

blue, and purple."

Here the essential peculiarities of the spectrum of each of the stars

investigated by HERSCHEL is pointed out, and if we were to use his

observations alone to classify these stars into types, we should put

_Sirius_ and _Procyon_ into one type of stars which have "all the

colors" in their spectra; _Arcturus_ and _Aldebaran_ would represent

another group of stars, with a deficiency of yellow and an excess of

orange and red in the spectrum; and _[alpha] Orionis_ would stand as

a type of those stars with an excess of red and a deficiency of orange.

_[alpha] Lyrae_ would represent a sub-group of the first class.

HERSCHEL'S immediate object was not classification, and his observations

are only recorded in a passing way. But the fact remains that he

clearly distinguished the essential differences of the spectra of these

stars, and that he made these observations in support of his statement

that the fixed stars, "like the planets, also shine with differently

colored light. That of _Arcturus_ and _Aldebaran_, for instance, is as

different from the light of _Sirius_ and _Capella_ as that of _Mars_ and

_Saturn_ is from the light of _Venus_ and _Jupiter_."

Of course, no special discovery can be claimed for him on these few

instances. We can see, however, a good example of the manner in which he

examined a subject from every side, and used the most remote evidence

exactly in its proper place and time.

_Researches on the Variable Emission of Light

and Heat from the Sun._

It is certainly a remarkable fact that HERSCHEL was the first observer

to recognize the real importance of the aperture or diameter of a

telescope. Before his time it was generally assumed that this element

only conditioned the amount of light transmitted to the eye, or, in

other words, merely determined the brightness of the image. Hence the

conclusion that if an object is sufficiently bright, the telescope may

be made as small as desired without loss of power. Thus, in observing

the sun, astronomers before HERSCHEL had been accustomed to reduce the

aperture of their telescopes, in order to moderate the heat and light

transmitted. SCHEINER, it is true, nearly two centuries before the time

we are considering, had invented a method for observing the sun without

danger, still employing the full aperture. This was by projecting the

image of the sun on a white screen beyond the eye-piece, the telescope

being slightly lengthened. For special purposes this ingenious method

has even been found useful in modern times, though for sharpness of

definition it bears much the same relation to the more usual manner of

observing, that a photographic picture does to direct vision.

Although HERSCHEL saw the advantages of using the whole aperture of a

telescope in such observations, the practical difficulties in the way

were very great. We have noted his attempts to find screens which would

effectively cut off a large portion of the heat and light without

impairing vision, and have considered, somewhat in detail, the

remarkable discoveries in radiant heat to which these attempts led him.

His efforts were not unsuccessful. A green glass smoked, and a glass

cell containing a solution of black writing ink in water--were found to

work admirably.