"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[Pg 160]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[Pg 161]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."
"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[Pg 160]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[Pg 161]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, andHerschel'sexplanation 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?
Herschelassumed 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.
Herschelendeavored, 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 theeye) 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. Asectionof 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 acombination 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 ofHerschelare 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 ofHerschel(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 thedepth of the systemin any direction, as theclustering power or tendencyof 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, onHerschel'sfirst hypothesis, rigorously interpreted, it would be necessary to suppose a spike-shaped protuberance directed from the earth, in order to explainthe 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 ofHerschelbreaks 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,Herschelpublished 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[Pg 166]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 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[Pg 166]of the difference in the apparent magnitudes of the stars to a difference in their relative distances from us. On account of the great number of stars in each class, we must also allow that the stars of each succeeding magnitude, beginning with the first, are, one with another, further from us than those of the magnitude immediately preceding. The relative magnitudes give only relative distances, and can afford no information as to the real distances at which the stars are placed.
"A standard of reference for the arrangement of the stars may be had by comparing their distribution to a certain properly modified equality of scattering. The equality which I propose does not require that the stars should be at equal distances from each other, nor is it necessary that all those of the same nominal magnitude should be equally distant from us."
It consisted in allotting a certain equal portion of space to every star, so that, on the whole, each equal portion of space within the stellar system contains an equal number of stars. The space about each star can be considered spherical. Suppose such a sphere to surround our own sun. Its radius will not differ greatly from the distance of the nearest fixed star, and this is taken as the unit of distance.
Suppose a series of larger spheres, all drawn around our sun as a centre, and having the radii 3, 5, 7, 9, etc. The contents of the spheres being as the cubes of their diameters, the first sphere will have 3 × 3 × 3 = 27 times the volume of the unit sphere, and will therefore be large enough to contain 27 stars; the second will have 125 times the volume, and will therefore contain 125 stars, and so on with the successive spheres. For instance, the sphere of radius 7 has room for 343 stars, but of this space 125 parts belong to the spheres inside of it; there is, therefore, room for 218 stars between the spheres of radii 5 and 7.
Herscheldesignates 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:
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 byHerschel, 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 tomake it shine like a star of the sixth magnitude.
On the scheme here laid down,Herschelsubsequently assigned theorderof 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 whichHerschelwould assign to the seventh, eighth, ninth, tenth, eleventh, twelfth, and thirteenth magnitudes. However this may be, the fact remains that it is fromHerschel'sgroundwork that future investigators must build. He found the whole subjectin utter confusion. By his observations, data for the solution of some of the most general questions were accumulated, and in his memoirs, whichStruvewell 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 aresupposedall 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 ofSirius, 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. Starsat thedistancestwo, three, four, etc.,Herschelcalled of the second, third, and fourth magnitudes.
By a series of experiments, the details of which cannot be given here,Herscheldetermined 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 ofSirius(1,344 = 7 × 192). If, further, we suppose that the visibility of a star is strictly proportional to the total intensity of the light from it which strikes the eye, then a condensed cluster of 25,000 stars of the 1,344th magnitude could still be seen in the forty-foot at a distance where each star would have become 25,000 times fainter, that is, at about 158 times the distance ofSirius(158 × 158 = 24,964). The light from the nearest star requires some three years to reach the earth. From a star 1,344 times farther it would require about 4,000 years, and for such a cluster as we have imagined no less than 600,000 years are needed. That is, the light by which we see such a group has not just now left it. On the contrary, it has been travelling through space for centuries and centuries since it first darted forth. It is the ancient history of such groups that we are studying now, and it was thus thatHerscheldeclared that telescopes penetrated into time as well as into space.
Other more exact researches on the relative light of stars were made byHerschel. 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 equalin every respect, were chosen and placed side by side. Pairs of stars which wereexactly equal, were selected by means of them. By diminishing the aperture of one telescopedirected 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 oflimiting 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 ustwelvetimes 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 asbright in itself as some of our first-magnitude stars. The smallest telescope of the set showed a large number of stars; these must, then, betwiceas far from us, on the average, as the stars just visible to the naked eye. But first-magnitude stars, likeSirius,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 asArcturus, for example.
"At least," asHerschelsays, "we are certain that if stars of the size and lustre ofSirius,Arcturus, etc., were removed into the profundity of space I have mentioned, they would then appear like the stars which I saw." With the next telescope, which collected nine times more light than the eye, and brought into view objects three times more distant, other and new stars appeared, which were then (3 × 12) thirty-six times farther from us thanArcturus. In the same way, the seven-foot reflector showed stars 204 times, the ten-foot 344times, 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).
ButHerschelwas 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 ofArcturus, 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 byHerschel. 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 whichHerschelobtained be diminished. But for every star of which his hypothesis is true, we may assert that his conclusions are true, and no onecan 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 wordveryby a numerical ratio.
Themethodstruck out byHerschelwas 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 weknowthe stars to be all at the same distance from us.
Researches on Light and Heat, Etc.
Frequently in the course of his astronomical work,Herschelfound himself confronted by questions of physics which couldnot 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,Herschelgave an expression for thespace-penetrating powerof 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 theeyein 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 theareaof the pupil is one-hundredth theareaof 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 eyealone,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'sargument 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 thespace-penetrating powerof 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)Herscheldetermined 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 lightmust be so lost was evident, but no data existed for determining the loss.Herschelwas 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 conclusionsHerschelhad an almost unlimited amount of experimental data in the records of his observations, of which he made effective use.
By far the most important ofHerschel'swork 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 stellaruniverse, 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 towhether 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[Pg 183]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 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[Pg 183]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,Herscheldescribes the experiments which led to the conclusion given above. This paper contains a remarkably interesting passage which admirably illustratesHerschel'sphilosophic 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."
"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 conclusionhere 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 thePhilosophical 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 principlewhich belongs to a later period of intellectual development than that ofHerschel'sown time.
Herschelmade 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 theonus probandiought 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."
"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 theonus probandiought 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.Herschelthus 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 ofHerschel, 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 adoptedbyHerschelon 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 byHerschel, 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 differentbodies, 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 stateHerschel'sclaims clearly, as his work has been neglected by those who should first have done him justice. In his "History of Physics,"Poggendorffhas no reference toHerschel. In the collected works ofVerdet, long bibliographical notes are appended to each chapter, with the intention of exhibiting the progress and order of discovery. But all ofHerschel'swork 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 ofHelmholtzon physiological optics,Herschel'slabors are not taken account of.
It is easy to account for this seemingly strange neglect.Herschelis 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 highrank 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 ofHerschel'sresearches in physics which interested him to the greatest degree, was the investigation of the optical phenomena known asNewton'srings. In 1792 he obtained the two object-glasses ofHuyghens, which were in the possession of the Royal Society, for the purpose of repeatingNewton'sexperiments, and in 1810 he read the last of his three papers on the subject.
SirIsaac Newtonhad 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 planepolished 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 beforeNewton, these rings have, ever since the publication of his remarkable work, been known by his name.
To explain the phenomena,Newtonwas 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 toHerscheltoo artificial and improbable for ready acceptance, and his effort was to supply a more probable explanation.
The developments of optical science have justifiedHerschelin 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 thathis position was distinctly less advanced than that ofNewton. That great philosopher announced the true law governing the relation between the color and the thickness of the film.Herscheldid not recognize such a relation.Newtonshowed exactly how the phenomenon depended upon the obliquity at which it was viewed.Herschelfound no place in his theory for this evident variation.
In the series of experiments described in the first paper on this subject,Herschelmistook 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 thatNewton'sconception 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 polishedmetal as one of the surfaces limiting the thin plate of air. Observing the so-called "blue bow" ofNewtonat 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.
Herschelexamined 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,Herschelfound 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 criterioncame in the first years of this century, with the discovery of three small planets having orbits lying between those ofMarsandJupiter.Herschelgave the nameAsteroidsto these bodies. As the appropriateness of this term had been violently assailed, the discovery ofJuno, 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,Herschelfound that ifJunosubtended 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 theydeserved, and they only became an object of especial interest to students of physics when they were again studied by the famous German opticianFraunhofer, a generation later.
Incidentally the experiments are of interest, as yielding us a measure of the excellence ofHerschel'stelescopes, 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 thePhilosophical Transactionsfor 1790, pp. 468 and 475, whereHerschelgives observations of bothEnceladusandMimasseen in contact with the ball ofSaturn. 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 bySecchito the study of the spectra of the fixed starsvisible 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 ortypes. His results have been verified and extended by other astronomers, and his classification has been generally accepted. According toSecchi, the lucid stars may be separated into three groups, distinguished by marked differences in their spectra.Secchi'sType I. contains stars whose spectra are like those ofSirius,Procyon, and αLyræ; his Type II. stars likeArcturusandAldebaran; his Type III. stars like αOrionis.
Herschelalso made some trials in this direction. In thePhilosophical Transactionsfor 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 ofSiriusconsists of red, orange, yellow, green, blue,[Pg 197]purple, and violet. αOrioniscontains the same colors, but the red is more intense, and the orange and yellow are less copious in proportion than they are inSirius.Procyoncontains all the colors, but proportionately more blue and purple thanSirius.Arcturuscontains more red and orange, and less yellow in proportion thanSirius.Aldebarancontains much orange and very little yellow. αLyræcontains much yellow, green, blue, and purple."
"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 ofSiriusconsists of red, orange, yellow, green, blue,[Pg 197]purple, and violet. αOrioniscontains the same colors, but the red is more intense, and the orange and yellow are less copious in proportion than they are inSirius.Procyoncontains all the colors, but proportionately more blue and purple thanSirius.Arcturuscontains more red and orange, and less yellow in proportion thanSirius.Aldebarancontains much orange and very little yellow. αLyræcontains much yellow, green, blue, and purple."
Here the essential peculiarities of the spectrum of each of the stars investigated byHerschelis pointed out, and if we were to use his observations alone to classify these stars into types, we should putSiriusandProcyoninto one type of stars which have "all the colors" in their spectra;ArcturusandAldebaranwould represent another group of stars, with a deficiency of yellow and an excess of orange and red in the spectrum; and αOrioniswould stand as a type of those stars with an excess of red and a deficiency of orange. αLyræwould represent a sub-group of the first class.
Herschel'simmediate object was not classification, and his observations are only recorded in a passing way. But the fact remainsthat 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 ofArcturusandAldebaran, for instance, is as different from the light ofSiriusandCapellaas that ofMarsandSaturnis from the light ofVenusandJupiter."
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 thatHerschelwas 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 conditionedthe 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 beforeHerschelhad 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.
AlthoughHerschelsaw the advantages of using the whole aperture of a telescope insuch 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,Herschelturned 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 toHerschel. That phenomenon is the frequent occurrence of a darker central shade or kernel in large spots, discovered byDawesabout 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 observerSchwabe. The probable importance of such a period in its relation to terrestrial meteorology was not only clearly pointed out byHerschel, 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. ButHerschel'sfertile mind, though it couldnot 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 inHerschel'shands on account of the paucity of solar statistics; but it has since proved of value, and has taken its place as a recognized method of research.
Researches on Nebulæ and Clusters.
WhenHerschelfirst began to observe the nebulæ in 1774, there were very few of these objects known. The nebulæ ofOrionandAndromedahad been known in Europe only a little over a hundred years.
In 1784Messierpublished a list of sixty-eight such objects which he had found in his searches for comets, and twenty-eight nebulæ had been found byLacaillein his observations at the Cape of Good Hope. In themere discovery of these objectsHerschelquickly surpassed all others. In 1786 he published a catalogue of one thousand new nebulæ, in 1789 a catalogue of a second thousand, and in 1802 one of five hundred. In all he discovered and described two thousand five hundred and eight new nebulæ and clusters. This branch of astronomy may almost be said to be proper to theHerschels, father and son. SirJohn Herschelre-observed all his father's nebulæ in the northern hemisphere, and added many new ones, and in his astronomical expedition to the Cape of Good Hope he recorded almost an equal number in the southern sky.
Of the six thousand two hundred nebulæ now known theHerschelsdiscovered at least eight-tenths. The mere discovery of twenty-five hundred nebulæ would have been a brilliant addition to our knowledge of celestial statistics.
Herscheldid more than merely point out the existence and position of these new bodies. Each observation was accompanied by a careful and minute description of theobject viewed, and with sketches and diagrams which gave the position of the small stars in it and near it.[36]
As the nebulæ and clusters were discovered they were placed in classes, each class covering those nebulæ which resembled each other in their general features. Even at the telescopeHerschel'sobject was not discovery merely, but to know the inner constitutionof the heavens. His classes were arranged with this end, and they are to-day adopted. They were:
The lists of these classes were the storehouses of rich material from whichHerscheldrew the examples by which his later opinions on the physical conditions of nebulous matter were enforced.
As the nebulæ were discovered and classifiedthey were placed upon a star-map in their proper positions (1786), and, as the discoveries went on, the real laws of the distribution of the nebulæ and of the clusters over the surface of the sky showed themselves more and more plainly. It was by this means thatHerschelwas led to the announcement of the law that the spaces richest in nebulæ are distant from the Milky Way, etc. By no other means could he have detected this, and I believe this to have been the first example of the use of the graphical method, now become common in treating large masses of statistics.
It is still in his capacity of an observer—an acute and wise one—thatHerschelis considered. But this was the least of his gifts. This vast mass of material was not left in this state: it served him for a stepping-stone to larger views of the nature and extent of the nebulous matter itself.
His views on the nature of nebulæ underwent successive changes. At first he supposed all nebulæ to be but aggregations of stars. The logic was simple. To the nakedeye there are many groups of stars which appear nebulous.Praesepeis, perhaps, the best example. The slightest telescopic power applied to such groups alters the nebulous appearance, and shows that it comes from the combined and confused light of discrete stars. Other groups which remain nebulous in a seven-foot telescope, become stellar in a ten-foot. The nebulosity of the ten-foot can be resolved into stars by the twenty-foot, and so on. The nebulæ which remained still unresolved, it was reasonable to conclude, would yield to higher power, and generally a nebula was but a group of stars removed to a great distance. An increase of telescopic power was alone necessary to demonstrate this.[37]