Chapter IV (2)

"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 × 3 × 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 × 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 × 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 × 2, 3 × 3, 4 × 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 × 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 × 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] Lyræ_; 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] Lyræ_ 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] Lyræ_ 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.

Thus provided with more powerful instrumental means than had ever been applied to the purpose, HERSCHEL turned his attention to the sun. In a very short time he exhausted nearly all there was to be discovered, so that since the publication of his last paper on this subject, in 1801, until the present time, there has been but a single telescopic phenomenon, connected with the physical appearance of the sun, which was unknown to HERSCHEL. That phenomenon is the frequent occurrence of a darker central shade or kernel in large spots, discovered by DAWES about 1858.

HERSCHEL, though observing a hundred and ninety years after the earliest discovery of sun spots, seems to have been the first to suspect their periodic character. To establish this as a fact, and to measure the period, was left for our own times and for the indefatigable observer SCHWABE. The probable importance of such a period in its relation to terrestrial meteorology was not only clearly pointed out by HERSCHEL, but he even attempted to demonstrate, from such data as were obtainable, the character of this influence.

Perhaps no one thing which this great philosopher has done better exhibits the catholic character of his mind than this research. When the possible connection of solar and terrestrial phenomena occurred to him as a question to be tested, there were no available meteorological records, and he could find but four or five short series of observations, widely separated in time. To an ordinary thinker the task would have seemed hopeless until more data had been collected. But HERSCHEL'S fertile mind, though it could not recall lost opportunities for solar observations, did find a substitute for meteorological records in the statistics of the prices of grain during the various epochs. It is clear that the price of wheat must have depended upon the supply, and the supply, in turn, largely upon the character of the season. The method, as ingenious as it is, failed in HERSCHEL'S hands on account of the paucity of solar statistics; but it has since proved of value, and has taken its place as a recognized method of research.

_Researches on Nebulæ and Clusters._

When HERSCHEL first began to observe the nebulæ in 1774, there were very few of these objects known. The nebulæ of _Orion_ and _Andromeda_ had been known in Europe only a little over a hundred years.

In 1784 MESSIER published a list of sixty-eight such objects which he had found in his searches for comets, and twenty-eight nebulæ had been found by LACAILLE in his observations at the Cape of Good Hope. In the mere discovery of these objects HERSCHEL quickly surpassed all others. In 1786 he published a catalogue of one thousand new nebulæ, in 1789 a catalogue of a second thousand, and in 1802 one of five hundred. In all he discovered and described two thousand five hundred and eight new nebulæ and clusters. This branch of astronomy may almost be said to be proper to the HERSCHELS, father and son. Sir JOHN HERSCHEL re-observed all his father's nebulæ in the northern hemisphere, and added many new ones, and in his astronomical expedition to the Cape of Good Hope he recorded almost an equal number in the southern sky.

Of the six thousand two hundred nebulæ now known the HERSCHELS discovered at least eight-tenths. The mere discovery of twenty-five hundred nebulæ would have been a brilliant addition to our knowledge of celestial statistics.

HERSCHEL did more than merely point out the existence and position of these new bodies. Each observation was accompanied by a careful and minute description of the object viewed, and with sketches and diagrams which gave the position of the small stars in it and near it.[36]

As the nebulæ and clusters were discovered they were placed in classes, each class covering those nebulæ which resembled each other in their general features. Even at the telescope HERSCHEL'S object was not discovery merely, but to know the inner constitution of the heavens. His classes were arranged with this end, and they are to-day adopted. They were:

CLASS I. "Bright nebulæ (288 in all).
II. "Faint nebulæ (909 in all).
III. "Very faint nebulæ (984 in all).
IV. "Planetary nebulæ, stars with burs, with milky chevelure,
with short rays, remarkable shapes, etc. (79 in all).
V. "Very large nebulæ (52 in all).
VI. "Very compressed and rich clusters of stars (42 in all).
VII. "Pretty much compressed clusters (67 in all).
VIII. "Coarsely scattered clusters of stars" (88 in all).

The lists of these classes were the storehouses of rich material from which HERSCHEL drew the examples by which his later opinions on the physical conditions of nebulous matter were enforced.

As the nebulæ were discovered and classified they were placed upon a star-map in their proper positions (1786), and, as the discoveries went on, the real laws of the distribution of the nebulæ and of the clusters over the surface of the sky showed themselves more and more plainly. It was by this means that HERSCHEL was led to the announcement of the law that the spaces richest in nebulæ are distant from the Milky Way, etc. By no other means could he have detected this, and I believe this to have been the first example of the use of the graphical method, now become common in treating large masses of statistics.

It is still in his capacity of an observer--an acute and wise one--that HERSCHEL is considered. But this was the least of his gifts. This vast mass of material was not left in this state: it served him for a stepping-stone to larger views of the nature and extent of the nebulous matter itself.

His views on the nature of nebulæ underwent successive changes. At first he supposed all nebulæ to be but aggregations of stars. The logic was simple. To the naked eye there are many groups of stars which appear nebulous. _Praesepe_ is, perhaps, the best example. The slightest telescopic power applied to such groups alters the nebulous appearance, and shows that it comes from the combined and confused light of discrete stars. Other groups which remain nebulous in a seven-foot telescope, become stellar in a ten-foot. The nebulosity of the ten-foot can be resolved into stars by the twenty-foot, and so on. The nebulæ which remained still unresolved, it was reasonable to conclude, would yield to higher power, and generally a nebula was but a group of stars removed to a great distance. An increase of telescopic power was alone necessary to demonstrate this.[37]

"Nebulæ can be selected so that an insensible gradation shall take
place from a coarse cluster like the _Pleiades_ down to a milky
nebulosity like that in _Orion_, every intermediate step being
represented. This tends to confirm the hypothesis that all are
composed of stars more or less remote."

So, at first, HERSCHEL believed that his twenty-foot telescope was of power sufficient to fathom the Milky Way, that is, to see through it and beyond it, and to reduce all its nebulosities to true groups of stars.

In 1791 he published a memoir on _Nebulous Stars_, in which his views were completely changed. He had found a nebulous star, the sixty-ninth of his Class IV., to which his reasons would not apply. In the centre of it was a bright star; around the star was a halo gradually diminishing in brightness from the star outward, and perfectly circular. It was clear the two parts, star and nebula, were connected, and thus at the same distance from us.

There were two possible solutions only. Either the whole mass was, _first_, composed of stars, in which case the nucleus would be enormously larger than the other stars of its stellar magnitude elsewhere in the sky, or the stars which made up the halo indefinitely small; or, _second_, the central nucleus was indeed a star, but a star surrounded with "a shining fluid, of a nature totally unknown to us."

The long strata of nebulæ, which he had before described under the name of "telescopic Milky Ways," might well be accounted for by masses of this fluid lying beyond the regions of the seventh-magnitude stars. This fluid might exist independently of stars. If it is self-luminous, it seems more fit to produce a star by its condensation, than to depend upon the star for its own existence. Such were a few of the theorems to which his discovery of this nebula led him. The hypothesis of an elastic _shining fluid_ existing in space, sometimes in connection with stars, sometimes distinct from them, was adopted and never abandoned. How well the spectroscope has confirmed this idea it is not necessary to say. We know the shining fluid does exist, and in late years we have seen the reverse of the process imagined by HERSCHEL. A star has actually, under our eyes, become a planetary nebula, and the cycle of which he gave the first terms is complete.

In five separate memoirs (1802, 1811, 1814, 1817, and 1818) HERSCHEL elaborated his views of the sidereal system. The whole extent of his views must be gained from the extended memoirs themselves. Here only the merest outline can be given.

In 1802 there is a marshaling of the various objects beyond our solar system. The stars themselves may be _insulated_, or may belong to _binary_ or _multiple_ systems, to _clusters_ and groups, or to grand groups like the Milky Way. Nebulæ may have any of the forms which have been described; and, in 1811, he gives examples of immense spaces in the sky covered with diffused and very faint nebulosity. "Its abundance exceeds all imagination."[38] These masses of nebular matter are the seats of attracting forces, and these forces must produce condensation. When a nebula has more than one preponderating seat of attracting matter, it may in time be divided, and the double nebulæ have had such an origin. When nebulæ appear to us as round masses, they are in reality globular in form, and this form is at once the effect and the proof of a gravitating cause.

The central brightness of nebulæ points out the seat of the attraction; and the completeness of the approximation to a spherical form points out the length of time that the gravitating forces have been at work. Those nebulæ (and clusters) which are most perfect in the globular form, have been longest exposed to central forces. The planetary nebulæ are the oldest in our system. They must have a rotatory motion on their axes.

By progressive condensation planetary nebulæ may be successively converted into bright stellar nebulæ, or into nebulous stars, and these again, by the effects of the same cause, into insulated or double stars. This chain of theorems, laid down in the memoir of 1811, is enforced in 1814 with examples which show how the nebulous appearance may grow into the sidereal. HERSCHEL selects from the hundreds of instances in his note-books, nebulæ in every stage of progress, and traces the effect of condensation and of clustering power through all its course, even to the final breaking up of the Milky Way itself.

The memoirs of 1817 and 1818 add little to the general view of the physical constitution of the heavens. They are attempts to gain a scale of celestial measures by which we may judge of the distances of the stars and clusters in which these changes are going on.

There is little to change in HERSCHEL'S statement of the general construction of the heavens. It is the groundwork upon which we have still to build. Every astronomical discovery and every physical fact well observed is material for the elaboration of its details or for the correction of some of its minor points. As a scientific conception it is perhaps the grandest that has ever entered into the human mind. As a study of the height to which the efforts of one man may go, it is almost without a parallel. The philosopher who will add to it to-day, will have his facts and his methods ready to his hands. HERSCHEL presents the almost unique example of an eager observer marshaling the multitude of single instances, which he himself has laboriously gathered, into a compact and philosophic whole. In spite of minor errors and defects, his ideas of the nature of the sidereal universe have prevailed, and are to-day the unacknowledged basis of our every thought upon it. Some of its most secret processes have been worked out by him, and the paths which he pointed out are those along which our advances must be made.

In concluding this condensed account of HERSCHEL'S scientific labors, it behoves us to remember that there was nothing due to accident in his long life. He was born with the faculties which fitted him for the gigantic labors which he undertook, and he had the firm basis of energy and principle which kept him steadily to his work.

As a practical astronomer he remains without an equal. In profound philosophy he has few superiors. By a kindly chance he can be claimed as the citizen of no one country. In very truth his is one of the few names which belong to the whole world.

FOOTNOTES:

[31] JAMES SHORT, F.R.S. (1710-1768), and JOHN DOLLOND, F.R.S. (1706-1761), were the most celebrated makers of telescopes of their day. The six-foot Newtonian reflectors of SHORT (aperture 9.4 inches), and the forty-six-inch achromatics of DOLLOND (aperture 3.6 inches), were highly esteemed. The Royal Observatory of Greenwich possessed, in 1765, one of each class. In a comparative trial of SHORT'S telescope, at Greenwich, and one of HERSCHEL'S first telescopes, the latter was adjudged greatly superior.

[32] At least _one_ of these telescopes had the principal mirror made of glass instead of metal.--_Philosophical Transactions_, 1803.

[33] The following extract from FOURIER'S _Éloge_ of HERSCHEL is of interest in this connection. The sum first appropriated by the king was £2,000. This was afterwards raised to £4,000, and a sum of £200 yearly was given for maintenance.

"L'histoire doit conserver à jamais la réponse de ce prince à un étranger célèbre [LALANDE?] qui le remerciait des sommes considérables accordées pour les progrès de l'astronomie. 'Je fais les dépenses de la guerre,' dit le roi, 'parcequ'elles sont nécessaires; quant à celles des sciences, il m'est agréable des les ordonner; leur objet ne coûte point des larmes, et honore l'humanité.'"

LALANDE'S own account is a little different. He says the king exclaimed: "Ne vaut-il pas mieux employer son argent à cela qu'à faire tuer des hommes?"

[34] The memoirs on the parallaxes of stars, written by various astronomers from 1750 to 1800, were mainly directed to the improvement of the methods, or to the discovery of the parallax of some particular star. For example, LACAILLE'S observations of _Sirius_, at the Cape of Good Hope, had resulted in a parallax of 9" for that star--a quantity over forty times too large.

[35] HERSCHEL accepted, as did all his cotemporaries, the Newtonian or corpuscular theory of light.