Sir William Herschel: His Life and Works Part 11

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 s.p.a.ce. 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 a.s.sumption that the stars were nearly equably distributed in s.p.a.ce. 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 ma.s.s 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 s.p.a.ce is nearly uniformly filled with stars. Without it is empty s.p.a.ce. 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 a.s.sumption of HERSCHEL (equable distribution), no other conclusion can be drawn from his statistics but the one laid down by him.

This a.s.sumption 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 _cl.u.s.tering 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 cla.s.s, 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 s.p.a.ce to every star, so that, on the whole, each equal portion of s.p.a.ce within the stellar system contains an equal number of stars. The s.p.a.ce 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 s.p.a.ce 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 a.s.sume 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 a.s.signed the _order_ of distance of various objects, mostly star-cl.u.s.ters, and his estimates of these distances are still quoted. They rest on the fundamental hypothesis which has been explained, and the error in the a.s.sumption 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 a.s.sign 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 acc.u.mulated, 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 s.p.a.ce-penetrating power of each of his telescopes. The twenty-foot would penetrate into s.p.a.ce 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 cl.u.s.ter 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 cl.u.s.ter 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 s.p.a.ce 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 s.p.a.ce.

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 l.u.s.tre of _Sirius_, _Arcturus_, etc., were removed into the profundity of s.p.a.ce 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 a.s.sert 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 s.p.a.ce. 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 cl.u.s.ters 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 una.s.sisted 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 _s.p.a.ce-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 a.s.sisted 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-gla.s.s 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-gla.s.s. 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 a.s.sisted 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 s.p.a.ce 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 _s.p.a.ce-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 s.p.a.ce-penetrating power of his twenty-foot telescope, with which he made his star-gauges, was sixty-one times that of the una.s.sisted eye, while the s.p.a.ce-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 s.p.a.ce-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-gla.s.ses 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 gla.s.ses permitted very little light to pa.s.s, but transmitted so much heat that they could not be used; while, on the other hand, different combinations and differently colored gla.s.ses would stop nearly all the heat, but allow an inconveniently great amount of light to pa.s.s. 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 pa.s.sage which admirably ill.u.s.trates 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 quant.i.tative 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 quant.i.tative 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.