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. 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 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.
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 Nebulae and Clusters.
When HERSCHEL first began to observe the nebulae in 1774, there were very few of these objects known. The nebulae 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 nebulae 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 nebulae, 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 nebulae 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 nebulae 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 nebulae now known the HERSCHELS discovered at least eight-tenths. The mere discovery of twenty-five hundred nebulae 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.
As the nebulae and clusters were discovered they were placed in classes, each class covering those nebulae 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 nebulae (288 in all). II. "Faint nebulae (909 in all). III. "Very faint nebulae (984 in all). IV. "Planetary nebulae, stars with burs, with milky chevelure, with short rays, remarkable shapes, etc. (79 in all). V. "Very large nebulae (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 nebulae 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 nebulae 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 nebulae 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 nebulae underwent successive changes. At first he supposed all nebulae 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 nebulae 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.
"Nebulae 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 nebulae, 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. Nebulae 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." 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 nebulae have had such an origin. When nebulae 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 nebulae 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 nebulae (and clusters) which are most perfect in the globular form, have been longest exposed to central forces. The planetary nebulae are the oldest in our system. They must have a rotatory motion on their axes.
By progressive condensation planetary nebulae may be successively converted into bright stellar nebulae, 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, nebulae 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.
 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.
 At least one of these telescopes had the principal mirror made of glass instead of metal.—Philosophical Transactions, 1803.
 The following extract from FOURIER'S Eloge of HERSCHEL is of interest in this connection. The sum first appropriated by the king was L2,000. This was afterwards raised to L4,000, and a sum of L200 yearly was given for maintenance.
"L'histoire doit conserver a jamais la reponse de ce prince a un etranger celebre [LALANDE?] qui le remerciait des sommes considerables accordees pour les progres de l'astronomie. 'Je fais les depenses de la guerre,' dit le roi, 'parcequ'elles sont necessaires; quant a celles des sciences, il m'est agreable des les ordonner; leur objet ne coute point des larmes, et honore l'humanite.'"
LALANDE'S own account is a little different. He says the king exclaimed: "Ne vaut-il pas mieux employer son argent a cela qu'a faire tuer des hommes?"
 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.
 HERSCHEL accepted, as did all his cotemporaries, the Newtonian or corpuscular theory of light.
 Thus the position of small stars critically situated in the centre, or on the edges of the nebulae was always noted. Many of the descriptions are given in the published papers, but the publication of the diagrams would be an immense help to this branch of astronomy. D'ARREST in his reduction of HERSCHEL'S nebula observations (1856) writes: "Gewiss waere es vom hoechsten Interesse fuer die Entwickelung, welche hoffentlich auch dieser Zweig der beobachtenden Astronomie zukuenftig erhalten wird, wenn die HERSCHEL'Schen Beobachtungen in der Ausfuehrlichkeit in welcher sie, verschiedenen Andeutungen zufolge, handschriftlich vorhanden sind, veroeffentlicht wuerden. Es schliesst sich dieser Wunsch in Betreff der Nebelflecken lebhaft an den an, welcher, schon vor einem Jahrzehnt nach Veroeffentlichung der 400 noch unedirten star-gauges von gewichtigerer Seite her geaeussert wurde." In this all must agree who have a knowledge of the direction in which we must look for advances in the difficult and important questions of the distance, the motions, and the changes of the nebulae. Almost the only aid to be looked for from the older observations must come from such diagrams, and we may safely say that the publication of this priceless material, just as it stands, would carry our exact data back from 1833 to 1786, or no less than forty-seven years.
 Long after HERSCHEL had abandoned this idea, it continued current among astronomers. The successes of Lord ROSSE'S telescope perpetuated to the middle of the nineteenth century an erroneous view which HERSCHEL had given up in 1791.
 These have never been re-observed. They should be sought for with a powerful refractor, taking special precautions against the illumination of the field of view from neighboring bright stars. HERSCHEL'S reflectors were specially open to illusions produced in this way. His observations probably will remain untested until some large telescope is used in the way he adopted, i. e., in sweeping.
I.—LIST OF THE PUBLISHED WRITINGS OF WILLIAM HERSCHEL ON ASTRONOMICAL SUBJECTS.
[In chronological order.]
N.B.—In general, translations and abstracts of those which appeared in periodicals are not noticed here. I have made exceptions in the more important cases.
[Solution of a prize question. See this book, page 46.] Ladies' Diary, 1779.
Astronomical observations on the periodical star in Collo Ceti. Phil. Trans., 1780, p. 338.
Astronomical observations relating to the mountains of the moon. Phil. Trans., 1780, p. 507.
Astronomical observations on the rotation of the planets round their axes, made with a view to determine whether the earth's diurnal motion is perfectly equable. Phil. Trans., 1781, p. 115.
Account of a comet. [Dated 13th March, 1781. This was Uranus.] Phil. Trans., 1781, p. 492.
On the parallax of the fixed stars. Phil. Trans., 1782, p. 82.
Catalogue of double stars. Phil. Trans., 1782, p. 112: translation in Bode's Jahrbuch, 1786, p. 187.
Description of a lamp micrometer and the method of using it. Phil. Trans., 1782, p. 163.
A paper to obviate some doubts concerning the great magnifying powers used. Phil. Trans., 1782, p. 173.
A letter from WILLIAM HERSCHEL, Esq., F.R.S., to Sir JOSEPH BANKS, Bart., P.R.S. Phil. Trans., 1783, p. 1.
Aus einem Schreiben des Hrn. HERSCHEL an mich [BODE], datirt London, den 13ten August, 1783. [This is a letter forwarding HERSCHEL'S memoir on the Parallax of the Fixed Stars, etc.] Bode's Jahrbuch, 1786, p. 258.
On the diameter and magnitude of the Georgium Sidus, with a description of the dark and lucid disk and periphery micrometers. Phil. Trans., 1783, p. 4.
On the proper motion of the sun and solar system, with an account of several changes that have happened among the fixed stars since the time of Mr. FLAMSTEED. Phil. Trans., 1783, p. 247. Bode's Jahrbuch, 1787, p. 194, p. 224.
Astronomische Nachrichten und Entdeckungen, aus einem franzoesischen Schreiben desselben an mich [BODE], datirt Datchet, nahe bey Windsor, den 18. Mai, 1784.
[This letter is on the subject of the use of high magnifying powers, and gives a resume of his recent papers.] Bode's Jahrbuch, 1787, p. 211.
On the remarkable appearances at the polar regions of the planet Mars, the inclination of its axis, the position of its poles and its spheroidical figure; with a few hints relating to its real diameter and atmosphere. Phil. Trans., 1784, p. 233.
Account of some observations tending to investigate the construction of the heavens. Phil. Trans., 1784, p. 437.
[Bode's Jahrbuch, 1788, p. 246, has a summary of this paper by Baron VON ZACH. See, also, Bode's Jahrbuch, 1794, p. 213.]
Catalogue of double stars. Phil. Trans., 1785, p. 40.
On the construction of the heavens. Phil. Trans., 1785, p. 213. Bode's Jahrbuch, 1788, p. 238. See, also, same, 1787, p. 213, and 1794, p. 213.
Aus einem Schreiben des Hrn. HERSCHEL an mich [BODE], datirt Clay Hall, nahe bey Windsor, den 20. Jul., 1785. [This is a letter forwarding two memoirs, and giving the prices of telescopes] Bode's Jahrbuch, 1788, p. 254.
Catalogue of one thousand new nebulae and clusters of stars. Phil. Trans., 1786, p. 457. Bode's Jahrbuch, 1791, p. 157, and same, 1794, p. 213.
Investigation of the cause of that indistinctness of vision which has been ascribed to the smallness of the optic pencil. Phil. Trans., 1786, p. 500.
Remarks on the new comet [1786, II.]. Phil. Trans., 1787, p. 4.
[Letter from HERSCHEL to BODE on the discovery of two satellites to Uranus, dated Slough, 1787, Feb. 11.] Bode's Jahrbuch, 1790, p. 253.
An account of the discovery of two satellites revolving round the Georgian planet. Phil. Trans., 1787, p. 125. Bode's Jahrbuch, 1791, p. 255.
An account of three volcanoes in the moon. Phil. Trans., 1787, p. 229. Bode's Jahrbuch, 1791, p. 255.
Note on M. MECHAIN'S comet. [1787, I.] [Added to preceding paper.] Phil. Trans., 1787, p. 232.
On the Georgian planet and its satellites. Phil. Trans., 1788, p. 364. Bode's Jahrbuch, 1793, p. 104.
Observations on a comet [1788, II.]. Phil. Trans., 1789, p. 151.
Catalogue of a second thousand of new nebulae and clusters of stars, with a few introductory remarks on the construction of the heavens. Phil. Trans., 1789, p. 212. Bode's Jahrbuch, 1793, p. 104. Also, same, 1794, p. 150.
Account of the discovery of a sixth and seventh satellite of the planet Saturn, with remarks on the construction of its ring, its atmosphere, its rotation on an axis, and its spheroidical figure. Phil. Trans., 1790, p. 1. Bode's Jahrbuch, 1793, p. 239; same, 1796, p. 88; 1797, p. 249.
On the satellites of the planet Saturn, and the rotation of its ring on an axis. Phil. Trans., 1790, p. 427.
On nebulous stars properly so called. Phil. Trans., 1791, p. 71. Bode's Jahrbuch, 1801, p. 128.
On the ring of Saturn and the rotation of the fifth satellite upon its axis. Phil. Trans., 1792, p. 1. Bode's Jahrbuch, 1796, p. 88.
[Account of a comet], p. 23 [1792, I.].
[On the periodical appearance of omicron Ceti], p. 24.
[On the disappearance of the 55th Herculis], p. 26.
[Remarkable phenomenon in an eclipse of the moon], p. 27. Phil. Trans., 1792, p. 23.
Observations on the planet Venus. Phil. Trans., 1793, p. 201.
Observations of a quintuple belt on the planet Saturn. Phil. Trans., 1794, p. 28. Bode's Jahrbuch, 1798, p. 90.
Account of some particulars observed during the late eclipse of the sun. [1793, September 5th.] Phil. Trans., 1794, p. 39.
On the rotation of the planet Saturn upon its axis. Phil. Trans., 1794, p. 48. Bode's Jahrbuch, 1798, p. 74.
On the nature and construction of the sun and fixed stars. Phil. Trans., 1795, p. 46. Bode's Jahrbuch, II. Suppl. Band, p. 65.
Description of a forty-foot reflecting telescope. Phil. Trans., 1795, p. 347. Bode's Jahrbuch, III. Suppl. Band, p. 238.
Additional observations on the comet. [1796, I.] Phil. Trans., 1796, p. 131.
On the method of observing the changes that happen to the fixed stars; with some remarks on the stability of the light of our sun. To which is added a catalogue of comparative brightness for ascertaining the permanency of the lustre of stars. Phil. Trans., 1796, p. 166. Bode's Jahrbuch, 1809, p. 201.
On the periodical star [alpha] Herculis; with remarks tending to establish the rotatory motion of the stars on their axes; to which is added a second catalogue of the comparative brightness of the stars. Phil. Trans., 1796, p. 452. Bode's Jahrbuch, 1809, p. 201.
A third catalogue of the comparative brightness of the stars, with an introductory account of an index to Mr. FLAMSTEED'S observations of the fixed stars, contained in the second volume of the Historia Coelestis. To which are added several useful results derived from that index. Phil. Trans., 1797, p. 293. Bode's Jahrbuch, 1810, p. 143.
Observations of the changeable brightness of the satellites of Jupiter, and of the variation in their apparent magnitudes, with a determination of the time of their rotatory motions on their axes. To which is added a measure of the diameter of the second satellite, and an estimate of the comparative size of all the four. Phil. Trans., 1797, p. 332. Bode's Jahrbuch, 1801, p. 103.
On the discovery of four additional satellites of the Georgium Sidus. The retrograde motion of its old satellites announced, and the cause of their disappearance at certain distances from the planet explained. Phil. Trans., 1798, p. 47. Bode's Jahrbuch, 1801, p. 231.
A fourth catalogue of the comparative brightness of the stars. Phil. Trans., 1799, p. 121. Bode's Jahrbuch, 1810, p. 143.
On the power of penetrating into space by telescopes, with a comparative determination of the extent of that power in natural vision, and in telescopes of various sizes and constructions, illustrated by select observations. Phil. Trans., 1800, pp. 49-85. Bode's Jahrbuch, 1804, p. 231.
Investigation of the powers of the prismatic colors to heat and illuminate objects, with remarks that prove the different refrangibility of radiant heat. To which is added an inquiry into the method of viewing the sun advantageously with telescopes of large apertures and high magnifying powers. Phil. Trans., 1800, pp. 255-283. Bode's Jahrbuch, 1804, p. 89.
Experiments on the refrangibility of the invisible rays of the sun. Phil. Trans., 1800, pp. 284-292. Bode's Jahrbuch, 1804, p. 89.
Experiments on the solar and on the terrestrial rays that occasion heat, with a comparative view of the laws by which light and heat, or rather the rays that occasion them, are subject, in order to determine whether they are the same or different. Phil. Trans., 1800, pp. 293-326, 437-538. Gilbert Annal., X. (1802), pp. 68-78; same, XII. (1803), pp. 521-546.
Observations tending to investigate the nature of the sun, in order to find the causes or symptoms of its variable emission of light and heat, with remarks on the use that may possibly be drawn from solar observations. Phil. Trans., 1801, pp. 265-318. Bode's Jahrbuch, 1805, p. 218, and 1806, p. 113.
Ueber den 7 Nebelfleck der 1sten classe des Herschel'schen Verzeichniss, und ueber Ceres und Pallas, vom Herrn Doctor HERSCHEL, aus zwey Briefen desselben. Bode's Jahrbuch, 1805, p. 211.
Additional observations tending to investigate the symptoms of the variable emission of the light and heat of the sun, with trials to set aside darkening glasses by transmitting the solar rays through liquids, and a few remarks to remove objections that might be made against some of the arguments contained in the former paper. Phil. Trans., 1801, pp. 354-362.
Observations on the two lately discovered celestial bodies [Ceres and Pallas]. Phil. Trans., 1802, pp. 213-232. Nicholson Journal, IV. (1808), pp. 120-130, 142-148.
Catalogue of five hundred new nebulae, nebulous stars, planetary nebulae, and clusters of stars, with remarks on the construction of the heavens. Phil. Trans., 1802, pp. 477-528. Bode's Jahrbuch, 1807, p. 113.
Observations of the transit of Mercury over the sun's disk, to which is added an investigation of the causes which often prevent the proper action of mirrors. Phil. Trans., 1803, pp. 214-232.
Account of the changes which have happened during the last twenty-five years in the relative situation of double stars, with an investigation of the cause to which they are owing. Phil. Trans., 1803, pp. 339-382. Bode's Jahrbuch, 1808, pp. 154-178.
Continuation of the account of the changes that have happened in the relative situation of double stars. Phil. Trans., 1804, pp. 353-384. Bode's Jahrbuch, 1808, p. 226.
Aus einem Schreiben des Herrn Doctor HERSCHEL, datirt Slough, bey Windsor, den 31. May, 1804.
[Relates to his theory of the relation between the solar radiation and the price of wheat.] Bode's Jahrbuch, 1808, p. 226.
Experiments for ascertaining how far telescopes will enable us to determine very small angles, and to distinguish the real from the spurious diameters of celestial and terrestrial objects, with an application of the results of those experiments to a series of observations on the nature and magnitude of Mr. HARDING'S lately discovered star [Juno (1804),]. Phil. Trans., 1805, pp. 31-70.
On the direction and velocity of the motion of the sun and solar system. Phil. Trans., 1805, pp. 233-256. Bode's Jahrbuch, IV. Suppl. Band, p. 67.
Observations on the singular figure of the planet Saturn. Phil. Trans., 1805, pp. 272-280. Bode's Jahrbuch, 1809, p. 197.
On the quantity and velocity of solar motion. Phil. Trans., 1806, pp. 205-237. Bode's Jahrbuch, 1811, p. 224.
Observations and remarks on the figure, climate, and atmosphere of Saturn and its ring. Phil. Trans., 1806, pp. 455-467. Gilbert Annal., XXXIV. (1810), pp. 82-105. Bode's Jahrbuch, 1810, p. 228.
Experiments for investigating the cause of the colored concentric rings discovered by Sir I. NEWTON between two object-glasses laid one upon another. Phil. Trans., 1807, pp. 180-233. Annal. de Chimie, LXX., 1809, pp. 154-181, 293-321; same, LXXI., 1809, pp. 5-40.
Observations on the nature of the new celestial body [Vesta] discovered by Dr. OLBERS, and of the comet which was expected to appear last January in its return from the sun. [1806, II.] Phil. Trans., 1807, pp. 260-266.
Observations of a comet [1807, I.] made with a view to investigate its magnitude and the nature of its illumination, to which is added an account of a new irregularity lately perceived in the apparent figure of the planet Saturn. Phil. Trans., 1808, pp. 145-163. Gilbert Annal., XXXVI. (1810), pp. 389-393. Zach, Monat. Corresp., XX. (1809), pp. 512-514.