Lecture 11 of Pioneers of Science This is a LibriVox recording. All LibriVox recordings are in the public domain. For more information or to volunteer, please visit LibriVox.org. Pioneers of Science by Sir Oliver Lodge, Lecture 11 Notes to Lecture 11. Lagrangian Laplace, both tremendous mathematicians, worked very much in alliance and completed Newton's work. The mechanique celeste contains the higher intricacies of astronomy mathematically worked out according to the theory of gravitation. They proved the solar system to be stable, all its inequalities being periodic, not cumulative. And Laplace suggested the nebular hypothesis concerning the origin of sun and planets, a hypothesis previously suggested and to some extent elaborated by Kant. A list of some of the principal astronomical researches of Lagrangian Laplace. Liberation of the Moon, long inequality of Jupiter and Saturn, perturbations of Jupiter satellites, perturbation of comets, acceleration of the Moon's mean motion, improved lunar theory, improvements in the theory of the tides, periodic changes in the form and obliquity of the Earth's orbit, stability of the solar system considered as an assemblage of rigid bodies subject to gravity. The two equations which establish the stability of the solar system are, sum of M e squared times the square root of D equals constant, and sum M times tangent squared theta times square root of D equals constant. Where M is the mass of each planet, D its mean distance from the sun, E the eccentricity of its orbit, and theta the inclination of its plane. However, the expressions above formulated may change for individual planets. The sum of them for all the planets remains invariable. The period of the variations in eccentricity of the Earth's orbit is 86,000 years. The period of conical revolution of the Earth's axis is 25,800 years. About 18,000 years ago the eccentricity was at a maximum. Lecture 11. Laplace was the son of a small farmer or peasant of Normandy. His extraordinary ability was noticed by some wealthy neighbors, and by them he was sent to a good school. From that time his career was one brilliant success, until in the later years of his life his prominence brought him tangibly into contact with the deteriorating influence of politics. Perhaps one ought rather to say trying than deteriorating, for they seemed trying to a strong character, deteriorating to a weak one, and unfortunately Laplace must be classed in this latter category. It has always been the custom in France for its high scientific men to be conspicuous also in politics. It seems to be now becoming the fashion in this country also, I regret to say. The life of Laplace is not especially interesting, and I shall not go into it. His brilliant mathematical genius is unquestionable and almost unrivaled. He is in fact generally considered to come in this respect next afternoon. His talents were of a more popular order than those of a grunge, and accordingly he acquired fame and rank, and rose to the highest dignities. Nevertheless as a man and a politician he hardly commands our respect, and in time serving adjustability he is comparable to the redoubtable Vissar of Bray. The scientific insight and genius were, however, unquestionably of the very highest order, and his work has been invaluable to astronomy. I will give a short sketch of some of his investigations, so far as they can be made intelligible without over much labor. He worked very much in conjunction with Lagrange, a more solid though a less brilliant man, and it is both impossible and unnecessary for us to attempt to apportion respective shares of credit between these two scientific giants. The greatest scientific men that France ever produced. First comes a research into the liberation of the moon. This was discovered by Galileo in his old age at a set tree, just before his blindness. The moon, as everyone knows, keeps the same face to the earth as it revolves around it. In other words, it does not rotate with reference to the earth, though it does rotate with respect to outside bodies. Its liberation consists in a sort of oscillation, whereby it shows us now a little more on one side, now a little more on the other, so that altogether we are cognizant of more than one half of its surface, in fact, altogether about three-fifths. It is a simple and unimportant matter, easily explained. The motion of the moon may be analyzed into a rotation about its own axis combined with a revolution about the earth. The speed of the rotation is quite uniform, the speed of the revolution is not quite uniform, because the orbit is not circular, but elliptical, and the moon has to travel faster in perigee than in apogee, in accordance with Kepler's second law. The consequence of this is that we see a little too far around the body of the moon, first on one side, then on the other.  Its axis of rotation, too, is not precisely perpendicular to its plane of revolution, and therefore we sometimes see a few hundred miles beyond its north pole, sometimes a similar amount beyond itself. Lastly, there is a sort of parallax effect, owing to the fact that we see the rising moon from one point of view and the setting moon from a point 8,000 miles distant, and this baseline of the earth's diameter gives us again some extra glimpses. This diurnal, or parallactic liberation, is really more effective than the other two in extending our vision into the space-facing hemisphere of the moon. These simple matters may as well be understood, but there is nothing in them to dwell upon. The far side of the moon is probably, but little worth seeing. Its features are likely to be more blurred with accumulations of meteoric dust than are those of our side, but otherwise they are likely to be of the same general character. The thing of real interest is the fact that the moon does turn the same face towards us, that is, has ceased to rotate with respect to the earth, if ever it did so. The stability of this state of things was shown by Lagrange to depend on the shape of the moon. It must be slightly egg-shaped, or prolate, extended in the direction of the earth, its earth-grinning diameter being a few hundred feet longer than its visible diameter. It caused light enough, but nevertheless sufficient to maintain stability, except under the action of a distant disturbing cause. The prolate, or lemon-like shape, is caused by the gravitative pole of the earth, balanced by the centrifugal whirl. The two forces balance each other as regards motion, but between them they have strained the moon a trifle out of shape. The moon has yielded as if it were perfectly plastic in all probability it once was so. It may be interesting to note for a moment the correlative effect of this aspect of the moon. If we transfer ourselves to its surface in imagination and look at the earth, CF figure 41, the earth would be like a gigantic moon of four times our moon's diameter, and would go through its phases in regular order, but it would not rise or set. It would be fixed in the sky and subject only to a minute oscillation two and four once a month, for a reason of the liberation we have been speaking of. Its aspect, as seen by markings on its surface, would rapidly change, going through a cycle in 24 hours, but its permanent features would be usually masked by lawless accumulations of clouds, mainly aggregated in rude belts parallel to the equator, and these cloudy patches would be the most luminous, the whitest portions, for of course it would be their silver lining that we would then be looking on. Next among the investigations of Lagrange and Laplace, we will mention the long inequality of Jupiter and Saturn. Halley had found that Jupiter was continually lagging behind its true place as given by the theory of gravitation, and on the other hand, that Saturn was being accelerated. The lag on the part of Jupiter amounted to about 34 and a half minutes in a century. Overhauling ancient observations, however, Halley found signs of the opposite state of things, for when he got far enough back Jupiter was accelerated and Saturn was being retarded. Here was evidently a case of planetary perturbation, and the plos in the grunge undertook the working of it out. They attacked it as a case of the problem of three bodies, that is, the Sun, Jupiter, and Saturn, which are so enormously the biggest of the known bodies in the system that insignificant masses like the Earth, Mars, and the rest may be Halley neglected. They succeeded brilliantly after a long and complex investigation, succeeded not in the solving the problem of the three bodies, but by considering their mutual action as perturbations superposed on each other, in explaining the most conspicuous of the observed anomalies of their motion, and in laying the foundation of a general planetary theory. One of the facts that plays a large part in the result was known to the oldest astrologers, that is, that Jupiter and Saturn come into conjunction with a certain triangular symmetry, the whole scheme being called a trigon, and being mentioned several times by Kepler. It happens that five of Jupiter's years very nearly equal two of Saturn's, so that they get very nearly into conjunction three times in every five Jupiter years, but not exactly. The result of this close approach is that periodically one pulls the other on, and is itself pulled back, but since the three points progress, it is not always the same planet which gets pulled back. The complete theory shows that in the year 1560 there was no market perturbation. Before that it was in one direction, while afterwards it was in the other direction. In the period of the whole cycle of disturbances is 929 of our years. The solution of this long outstanding puzzle while the theory of gravitation was hailed with the greatest enthusiasm by astronomers, and it established the fame of the two French mathematicians. Next they attacked the complicated problem of the motions of Jupiter's satellites. They succeeded in obtaining a theory of their motions, which represented fact very nearly indeed, and they detected the following curious relationship between the The speed of the first satellite plus twice the speed of the second is equal to the speed of the third. They found this not empirically after the manner of Kepler, but as a deduction from the law of gravitation. For they go on to show that even if the satellites had not started with this relation, they would sooner or later, by mutual perturbation, get themselves into it. One singular consequence of this, and of another quite similar connection between their positions, is that all three satellites can never be eclipsed at once. The motion of the fourth satellite is less tractable. It does not so readily form an easy system with the others. After these great successes, the two astronomers naturally proceeded to study the mutual perturbations of all other bodies in the solar system, and one very remarkable discovery they made concerning the Earth and Moon, an account of which will be interesting, that the details and processes of calculation are quite beyond us in a course like this. Astronomical theory had become so nearly perfect by this time, an observation so accurate, that it was possible to calculate many astronomical events forwards or backwards, over even a thousand years or more, with admirable precision. Now, Haley had studied some records of ancient eclipses, and had calculated back by means of the lunar theory to see whether the calculation of the time they ought to occur would agree with the record of the time they did occur. To his surprise, he found a discrepancy, not a large one, but still one quite noticeable. To state it as we know it now, an eclipse a century ago happened 12 seconds later than it ought to have happened by theory. Two centuries back, the error amounted to 48 seconds. In three centuries, it would be 108 seconds, and so on. The lag depending on the square of the time. By research, and help from scholars, he succeeded in obtaining the records of some very ancient eclipses indeed. One in Egypt towards the end of the 10th century A.D., another in 201 A.D., another a little before Christ, and one, the oldest of all of which any authentic record has been preserved, observed by the Chaldean astronomers in Babylon in the reign of Hezekiah. Calculating back to the splendid old record of a solar eclipse over the intervening 2,400 years, the calculated and the observed time were found to disagree by nearly two hours. Pondering over an explanation of the discrepancy, Haley guessed that it must be because the moon's motion was not uniform. It must be going quicker and quicker, gaining 12 seconds each century on its previous gain. A discovery announced by him as, the acceleration of the moon's mean motion. The month was constantly getting shorter. What was the physical cause of this acceleration according to the theory of gravitation? Many attacked the question, but all failed. This was the problem Laplace set himself to work out. A singular and beautiful result rewarded his efforts. You know that the Earth describes an elliptic orbit round the Sun, and that an ellipse is a circle with a certain amount of flattening or eccentricity. Well, Laplace found that the eccentricity of the Earth's orbit must be changing, getting slightly less, and that this change of eccentricity would have an effect upon the length of the month. It would make the moon go quicker. One can almost see how it comes about. The decrease in eccentricity means an increase in the mean distance of the Earth from the Sun. This means to the moon, a less solar perturbation. Now one effect of the solar perturbation is to keep the moon's orbit extra large. If the size of its orbit diminishes, its velocity must increase according to Kepler's third law. Laplace calculated the amount of acceleration so resulting, and found it 10 seconds a century, very nearly what observation required. For though I have quoted observation as demanding 12 seconds per century, the facts were not then so distinctly and definitively ascertained. This calculation for a long time seemed thoroughly satisfactory, but it is not the last word on the subject. Quite lately, an error has been found in the working, which diminishes the theoretical gravitation acceleration to six seconds a century instead of 10, thus making it insufficient to agree exactly with fact. The theory of gravitation leaves an outstanding error. The point is now almost thoroughly understood and we shall return to it in lecture 18. But another question arises out of this discussion. I have spoken of the eccentricity of the Earth's orbit as decreasing. Was it always decreasing? And if so, how far back was it so eccentric that at perihelion, the Earth passed quite near the Sun? If it ever did thus pass near the Sun, the inference is manifest. The Earth must at one time have been thrown off or been separated off from the Sun. If a projectile could be fired so fast that it described an orbit round the Earth and the speed of fire to attain this lies between five and seven miles a second, not less than the one, nor more than the other, it would ever afterwards pass through its point of projection as one point of its elliptic orbit. And its periodic return through that point would be the sign of its origin. Similarly, if a satellite does not come near its central orb and can be shown never to have been near it, the natural inference is that it has not been born from it, but has originated in some other way. The question which presented itself in connection with the variable elliptic city of the Earth's orbit was the following. Had it always been decreasing, so that once it was eccentric enough just to graze the Sun at perihelion as a projected body would do? Into the problem thus presented, Lagrange threw himself, and he succeeded in showing that no such explanation of the origin of the Earth is possible. The eccentricity of the orbit, whether now decreasing, was not always decreasing. Ages ago, it was increasing. It passes through periodic changes. 18,000 years ago, its eccentricity was a maximum. Since then, it has been diminishing, and will continue to diminish for 25,000 years more, when it will be an almost perfect circle. It will then begin to increase again, and so on. The obliquity of the ecliptic is also changing periodically, but not greatly. The change is less than three degrees. This research has, or ought to have, the most transcendent interest for geologists and geographers. You know that geologists find traces of extraordinary variations of temperature on the surface of the Earth. England was at one time tropical, at another time glacial. Far away north, in Spitzbergen, evidence of the luxuriant vegetation of past ages has been found, and the explanation of these great climatic changes has long been a puzzle. Does not the secular variation in the eccentricity of Earth's orbit, combined with the procession of equinoxes, afford a key? And if a key at all, it will be an accurate key, and enable us to calculate back with some precision to the date of the glacial epoch, and again to the time when a tropical flora flourished in what is now Northern Europe, that is, to the date of the Carboniferous Era. This aspect of the subject has recently been talked with figure in success by Dr. Kroll in his book, Climate and Time. A brief and partial explanation of the matter may be given, because it is a point of some interest and is also one of fair simplicity. Everyone knows that the climatic conditions of winter and summer are inverted in the two hemispheres, and that at present the sun is nearest to us in our Northern winter. In other words, the Earth's axis is inclined so as to tilt its North Pole away from the sun at perihelion, or when the Earth is at the part of its elliptic orbit nearest the sun's focus, and to tilt it towards the sun at perihelion. The result of this present state of things is to diminish the intensity of the average Northern winter and of the average Northern summer, and on the other hand, to aggregate the extremes of temperature in the Southern Hemisphere, all other things being equal. Of course, other things are not equal, and the distribution of land and sea is a still more powerful climatic agent than is the 3 million miles or so extra nearness of the sun, but it is supposed that the Antarctic ice cap is larger than the Northern. An increased summer radiation with increased winter cold could account for this, but the present state of things did not always obtain. The conical movement of the Earth's axis, now known by a curious perversion of phrase as procession, will in the course of 13,000 years or so cause the tilt to be precisely opposite, and then we shall have the more extreme winters and summers instead of the Southern Hemisphere. If the change would occur now, it might not be overpowering because the eccentricity is moderate, but if it happened sometime back when the eccentricity was much greater, a decidedly different arrangement of climate may have resulted. There is no need to say if it happened sometime back, it did happen, and accordingly, an agent for affecting the distribution of mean temperature on the Earth is to hand. The weather it is sufficient to achieve all that has been observed by geologists is a matter of opinion. Once more, the whole diversity of the seasons depends on the tilt of the Earth's axis, the 23 degrees by which it is inclined to a perpendicular to the full orbital plane, and this obliquity or tilt is subject to slow fluctuations. Hence there will come errors when all causes combine to produce a maximum extremity of seasons in the Northern Hemisphere and other errors when it is the Southern Hemisphere which is subject to extremes. But a grander problem still awaited solution, nothing less than the fate of the whole solar system. Here are a number of bodies of various sizes circulating at various rates around one central body, all attracted by it, and all attracting each other, the whole abandoned to the free play of the force of gravitation. What will be the end of it all? Will they ultimately approach and fall into the Sun or will they recede further and further from Him into the cold of space? There is a third possible alternative. They may not alternately approach and recede from Him so as on the whole to maintain a fair approximation to their present distances, without great and violent extremes of temperature either way. If any one planet of the solar system were to fall into the Sun, more especially if it were a big one like Jupiter or Saturn, the heat produced would be so terrific that life on this Earth would be destroyed even at its present distance so that we are personally interested in the behavior of other planets as well as in the behavior of our own. The result of the potentially difficult and profoundly interesting investigation here sketched in the Barist Outline is that the solar system is stable. That is to say that if disturbed a little, it will oscillate and return to its old state. Whereas if it were unstable, the slightest disturbance would tend to accumulate and would sooner or later bring about a catastrophe. A hanging pendulum is stable and oscillates about a mean position. Its motion is periodic. A top heavy load bounced on a point is unstable. All the changes of the solar system are periodic. That is, they repeat themselves at regular intervals and they never exceed a certain moderate amount. The period is something enormous. They will not have gone through all of their changes until a period of two million years has elapsed. This is the period of the planetary oscillation, a great pendulum of eternity which beats ages as our pendulums beat seconds. Enormous it seems and yet we have reason to believe that the Earth has existed through many such periods. The two laws of stability discovered and stated by Lagrange and Laplace, I can state, though they may be difficult to understand, represent the masses of several planets by M1, M2, et cetera. Their mean distances from the Sun were radii vectors by R1, R2, et cetera. The eccentricities of their orbits by E1, E2, et cetera and the obliquity of the planes of these orbits reckon from a single plane of reference or invariable plane by theta one, theta two, et cetera. Then all these quantities, except M, are liable to fluctuate. But however much they change, an increase for one planet will be accompanied by a decrease for some others so that taking all the planets into account, the sum of a set of terms like these, M1 times E2 squared times square root R1 plus M2 times E2 squared times square root of R2 plus, et cetera, will remain always the same. This is summed up briefly in the following statement. Sum of M times E squared times square root of R equals constant. That is one law and the other is like it, both inclination of orbit instead of eccentricity, that is sum of M times theta squared times square root of R equals constant. The value of each of these two constants can at any time be calculated. At present their values are small. Hence they always were and always will be small, being in fact invariable. Hence neither E nor R nor theta can ever become infinite. Nor can their average value for the system ever become zero. The planets may share the given amount of total eccentricity and obliquity in various proportions between themselves. But even if it were all piled onto one planet, it would not be very excessive unless the planet were so small a one is Mercury. And it would be most improbable that one planet should ever have all the eccentricity of the solar system heaped upon itself. The Earth therefore never has been nor ever will be enormously nearer the sun than it is at present. Nor can it ever get very much further off. Its changes are small and are periodic. An increase is followed by a decrease like the swaying of a pendulum. The above two laws have been called the Magna Carta of the solar system. And we're long supposed to guarantee its absolute permanence. So far as the theory of gravitation carries us, they do guarantee its permanence, but something more remains to be said on the subject in a future lecture, 18. And now finally we come to a sublime speculation thrown out by a Laplace. Not as the result of profound calculation like the results Hitherto mentioned, not following certainly from the theory of gravitation or from any other known theory, and therefore not to be accepted as more than a brilliant hypothesis to be confirmed or rejected as our knowledge extends. The speculation is the nebular hypothesis. Since the time of Laplace, the nebular hypothesis has had ups and downs of credence, sometimes being largely believed in, sometimes being almost ignored. At the present time, it holds the field with perhaps greater probability of ultimate triumph than has ever before seemed to belong to it, far greater than belonged to it when first propounded. It had been previously stated clearly and well by the philosopher Kant, who was intensely interested in the starry heavens, as well as in the mind of man, and who shoot in connection with astronomy also a most surprising genius. The hypothesis ought by rights perhaps to be known rather by his name than by that of Laplace. The data on which it was founded are these. Every motion in the solar system known at that time took place in one direction and in one direction only. Thus the planets revolved around the sun, all going the same way around. Moons revolved around the planets, still maintaining the same direction of rotation, and all the bodies that were known to rotate on their own axis did so with still the same kind of spin. Moreover, all these motions take place in or near a single plane. The ancients knew that sun, moon, and planets all keep near to the ecliptic, within a belt known as the zodiac, none strays away into other parts of the sky. Satellites also, and rings, are arranged in or near the same plane, and the plane of diurnal spin, or equator of the different bodies, is but slightly tilted. Now all this could not be the result of chance. What could have caused it? Is there any connection or common ancestry possible to account for this strange family likeness? There is no connection now, but there may have been once. Must have been, we may almost say. It is as though they had once been parts of one great mass rotating as a whole. For if such a rotating mass broke up, its parts would retain its direction of rotation. But such a mass, filling all space as far as or beyond Saturn, although containing the materials of the whole solar system in itself must have been a very rare consistency. Occupying so much bulk it could not have been solid, no yet liquid, but it might have been gaseous. Are there any such gigantic rotating masses of gas in the heaven now? Certainly there are, there are nebulae. Some of the nebulae are now known to be gaseous, and some of them at least are in a state of rotation. Laplace could not have known this for certain, but he suspected it. The first distinctly spiral nebula was discovered by the telescope of Lord Ross, and quite recently a splendid photograph of the great Andromeda nebula by our townsman, Mr. Isaac Roberts, revealed what was quite unsuspected and makes it clear that this prodigious mass also is in a state of extensive and majestic swirl. Very well then, put this problem. A vast mass of rotating gas is left to itself to cool for ages and to condense as it cools. How will it behave? A difficult mathematical problem, worthy of being attacked today, not yet at all adequately treated. There are those who believe that by the complete treatment of such a problem, all the history of the solar system could be evolved. Laplace pictured to himself this mass shrinking and thereby whirling more and more rapidly. The spinning body shrinking in size or rotating its original amount of rotation, as it will unless a break is applied, must spin more and more rapidly as it shrinks. It has what mathematicians call a constant moment of momentum. And what it loses in leverage as it shrinks, it gains in speed. The masses held together by gravitation. Every particle attracting every other particle, but since all the particles are describing curved paths, they will all tend to fly off tangentially and only a small excess of the gravitation force over their centrifugal is left to pull the particles in and slowly to concentrate the nebula. The mutual gravitation of the parts is opposed by the centrifugal force of the whirl. At length a point is reached where the two forces balance. A portion outside a certain line will be in equilibrium. It will be left behind and the rest must contract without it. A ring is formed and away goes the inner nucleus contracting further and further towards the center. After a time, another ring will be left behind in the same way and so on. What happens to these rings? They rotate with the motion they possess when thrown or shrunk off. But will they remain rings? If perfectly regular, they may. If there be any irregularity, they are liable to break up. They will break into one or two or more large masses, which are ultimately very likely to collide and become one. The revolving body so formed is still a rotating gaseous mass and will go on shrinking and cooling and throwing off rings like the larger nucleus by which it has been abandoned. As any nucleus gets smaller, its rate of rotation increases and so the rings last thrown off will be spinning faster than those thrown off earliest. The final nucleus or residual central body will be rotating fastest of all. The nucleus of the whole original mass, we now see shrunk off into what we call the sun, which is spinning on its axis once every 25 days. The rings successively thrown off by it are now the planets, some large, some small. Those last thrown off rotating round him comparatively quickly, those outside much more slowly. The rings thrown off by the planetary gaseous masses as they contracted have now become satellites, except one ring which has remained without breaking up and is to be seen rotating round Saturn still. One other similar ring and a board of attempt at a planet is also left round the sun, the zone of asteroids. Such, crudely and baldly is the famous nebular hypothesis of Laplace. It was first dated as has been said above by the philosopher Kant, but it was elaborated into much fuller detail by the greatest of French mathematicians and astronomers. The contracting masses will condense and generate great quantities of heat by their own shrinkage. They will at a certain stage condense to liquid and after a time will begin to cool and congeal with a superficial crust, which will get thicker and thicker but for ages they will remain hot even after they have become thoroughly solid. The small ones will cool fastest, the big ones will retain their heat for an immense time. Bullets cool quickly, cannonballs take hours or days to cool, planets take millions of years. Our moon may be nearly cold, but the earth is still warm, indeed very hot inside. Jupiter is believed by some observers to still glow with a dull red heat and the high temperature of the much larger and still liquid mass of the sun is apparent to everybody. Not till it begins to scum over will it be perceptibly cooler. Many things are now known concerning heat, which were not known till the plus. In the above paragraph they are only hinted at. And these confirm and strengthen the general features of his hypothesis in a striking way. So do the most recent telescopic discoveries. But fresh possibilities have now occurred to us. Title phenomena are seen to have an influence then wholly unsuspected and it will be in a modified and amplified form that the philosopher of next century will still hold to the main features of this famous and old nebular hypothesis, respecting the origin of the sun and planets, the evolution of the solar system. End of lecture 11. Lecture 12 of the Pioneers of Science. This is a LibriVox recording. All LibriVox recordings are in the public domain. For more information or to volunteer, please visit LibriVox.org. Lecture 12, The Pioneers of Science by Sir Oliver Lodge. Notes to lecture 12. The subject of stellar astronomy was first opened up by Sir William Herschel, the greatest observing astronomer. Frederick William Herschel was born in Hanover in 1738 and brought up as a musician. Came to England in 1756. First saw a telescope in 1773. Made a great many himself and began a survey of the heavens. This is Sir Caroline, born in 1750, came to England in 1772 and became his devoted assistant to the end of his life. Uranus, discovered in 1781. Music finally abandoned next year and the 40-foot telescope begun. Discovered two moons of Saturn and two of Uranus, reviewed, described, and gauged all the visible heavens. Discovered and catalogued 2,500 nebulae and 806 double stars. Speculated concerning the Milky Way, the nebulosity of stars, the origin and growth of solar systems. Discovered that the stars were in motion, not fixed, and that the sun as one of them was journeying towards a point in the constellation Hercules. Died in 1822, 84 years old. Caroline Herschel discovered eight comets and lived on to the age of 98. Lecture 12, Herschel and the Motion of the Fixed Stars. We may admit, I think, that with a few notable exceptions, the work of the great men we have been recently considering was rather to complete and round off the work of Newton than to strike out new and original lines. This was the whole tendency of 18th century astronomy. It appeared to be getting into an adult and uninteresting stage, wherein everything could be calculated and predicted. Labor and ingenuity and a severe mathematical training were necessary to work out the remote consequences of known laws, but nothing fresh seemed likely to turn up. Consequently, men's minds began turning in other directions and we find chemistry and optics largely studied by some of the greatest minds instead of astronomy. But before the century closed, there was destined to arise one remarkable exception, a man who was comparatively ignorant of that which had been done before, a man unversed in mathematics and the intricacies of science, but who possessed such a real and genuine enthusiasm and love of nature that he overcame the force of adverse circumstances and entering the territory of astronomy by a by-path struck out a new line for himself and infused into the science a healthy spirit of fresh life and activity. This man was William Herschel. The rise of Herschel, says Ms. Clerk, is the one conspicuous anomaly in the otherwise somewhat quiet and prosy 18th century. It proved decisive of the course of events in the 19th. It was unexplained by anything that had gone before, yet all that came after hinged upon it. It gave a new direction to effort. It lent a fresh impulse to thought. It opened a channel for the widespread public interest which was gathering towards astronomical subjects to flow in. Herschel was born at Hanover in 1738, the son of an oboe player in a military regiment. The father was a good musician and a cultivated man. The mother was a German frau of the period, a strong, active, business-like woman, of strong character and profound ignorance. Herself unable to write, she set her face against learning in all new fangled notions. The education of the sons, she could not altogether control though she lamented over it. But the education of her two daughters, she strictly limited to cooking, sewing, and household management. These, however, she taught them well. It was a large family and William was the fourth child. We need only remember the names of his younger brother Alexander and of his much younger sister Caroline. They were all very musical. The youngest boy was once raised upon a table to play the violin at a public performance. The girls were forbidden to learn music by their mother but their father sometimes taught them a little on the sly. Alexander was besides an ingenious mecanition. At the age of 17, William became oboist to the Hanoverian guards, shortly before the regiment was ordered to England. Two years later, he removed himself from the regiment with the approval of his parents, though probably without the approbation or consent of the commanding officer, by whom such removal would be regarded as simple desertion, which indeed it was. And George III long afterwards handed him an official pardon for it. At the age of 19, he was thus launched in England with an outfit of some French, Latin, and English picked up by himself. Some skill in playing the hout boy, the violin and the organ, as taught by his father, and some good linen and clothing, and an immense stock of energy provided by his mother. He lived as musical instructor to one or two militia bands in Yorkshire, and for three years we hear no more than this of him. But, at the end of that time, a noted organist, Dr. Miller of Durham, who had heard his playing, proposed that he should come and live with him and play at concerts, which he was very glad to do. He next obtained the post of organist at Halifax, and some four or five years later he was invited to become organist at the Octagon Chapel in Bath, and soon led the musical life of that then very fashionable place. About this time, he went on a short visit to his family at Hanover, by all of whom he was very much beloved, especially by his young sister Caroline, who always regarded him as specially her own brother. It is rather pitiful, however, to find that her domestic occupation still unfairly repressed and blighted her life. She says, of the joys and pleasures which all felt at this long wished-for meeting with my, let me say my dearest brother, but a small portion could fall to my share for with my constant attendance at church and school, besides the time I was employed in doing the drudgery of the scullery, it was but seldom I could make one in the group when the family were assembled together. While at Bath he wrote many musical pieces, glies, anthems, chants, pieces for the harp, and an orchestral symphony. He taught a large number of pupils and lived a hard and successful life. After 14 hours or so spent in teaching and playing, he would retire at night to instruct his mind with a study of mathematics, optics, Italian, or Greek, in all of which he managed to make some progress. He also about this time fell in with some book on astronomy. In 1763, his father was struck with paralysis and two years later he died. William then proposed that Alexander should come over from Hanover and join him at Bath, which was done. Next they wanted to rescue their sister Caroline from her humdrum existence, but this was a more difficult matter. Caroline's journal gives an account of her life at this time that is instructive. Here are a few extracts from it. My father wished to give me something like a polished education, but my mother was particularly determined that it should be a rough, but at the same time a useful one, and nothing further she thought was necessary but to send me two or three months to a semestress to be taught to make household linen. My mother would not consent to my being taught French, so all my father could do for me was to indulge me and please himself, sometimes with a short lesson on the violin, when my mother was either in good humor or out of the way. She had cause for wishing me not to know more than was necessary for being useful in the family, for it was her certain belief that my brother William would have returned to his country and my eldest brother not have looked so high if they had had a little less learning. However, seven years after the death of their father, William went over to Germany and returned to England in triumph, bringing Caroline with him, she being then 22. So now began a busy life in Bath. For Caroline the work must have been tremendous. For besides having to learn singing, she had to learn English. She had more over to keep accounts and do the marketing. When the season at Bath was over, she hoped to get rather more of her brother William's society, but he was deep in optics and astronomy, used to sleep with the books under his pillow, read them during meals, and scarcely ever thought of anything else. He was determined to see for himself all the astronomical wonders and there being a small Gregorian reflector in one of the shops, he hired it. But he was not satisfied with this and contemplated making a telescope 20 feet long. He wrote to opticians inquiring the price of a mirror suitable, but found there were none so large and that even the smaller ones were beyond his means. Nothing daunted, he determined to make some for himself. Alexander entered into his plans. Tools, hones, polishers, and all sorts of rubbish were imported into the house to the sister's dismay, who says, And then to my sorrow, I saw almost every room turned into a workshop, a cabinet maker making a tube and stands of all descriptions in a handsomely furnished drawing room, Alex putting up a huge turning machine, which he had brought in the autumn from Bristol, where he used to spend the summer, in a bedroom for turning patterns, grinding glasses and turning eyepieces in company. At the same time, music durst not lie entirely dormant during the summer and my brother had frequent rehearsals at home. Finally in 1774, at the age of 36, he had made himself a five and a half foot telescope and began to view the heavens. So attached was he to the instrument that he would run from the concert room between parts and take a look at the stars. He soon began another telescope and then another. He must have made some dozen different telescopes, always trying to get them bigger and bigger. At last he got a seven foot and then a 10 foot instrument and began a systematic survey of the heavens. He also began to communicate his results to the Royal Society. He now took a larger house with more room for workshops and a grass plot for a 20 foot telescope. And still he went on grinding mirrors, literally hundreds of them. I read another extract from the diary of his sister who waited on him and obeyed him like a spaniel. My time was taken up with copying music and practicing, besides attendance on my brother when polishing, since by way of keeping him alive, I was constantly obliged to feed him by putting the victuals by bits into his mouth. This was once the case when, in order to finish a seven foot mirror, he had not taken his hands from it for 16 hours together. In general, he was never unemployed at meals but was always at those times contriving or making drawings of whatever came in his mind. Generally I was obliged to read to him whilst he was at the turning lathe or polishing mirrors. Don Quixote, Arabian Nights, Entertainments and the novels of Stern Fielding and Company, serving tea and supper without interrupting the work with which he was engaged and sometimes lending a hand. I became, in time, as useful a member of the workshop as a boy might be to his master in the first year of his apprenticeship. But as I was to take part the next year in the oratorios I had for a whole 12 month, two lessons per week from Miss Fleming, the celebrated dancing mistress, to drill me for a gentle woman. God knows how she succeeded. So we lived on without interruption. My brother Alex was absent from Bath for some months every summer but when at home he took much pleasure in executing some turning or clockmaker's work for his brother. The music and the astronomy and the making of telescopes all went on together, each at high pressure and enough done in each to satisfy any ordinary activity. But the Herschels knew no rest, grinding mirrors by day, concerts and oratorios in the evening, stargazing at night. It is strange his health could stand it. The stargazing, moreover, was no dilettante work. It was based on a serious system, a well thought out plan of observation. It was nothing less than this, to pass the whole heavens steadily and in order through the telescope, noting and describing and recording every object that should be visible, whether previously known or unknown. The operation is called sweeping but it is not a rapid passage from one object to the other as the term might suggest. It is a most tedious business and consists in following with the telescope a certain field of view for some minutes so as to be sure that nothing is missed then shifting it to the next overlapping field and watching again. And whatever object appears must be scrutinized anxiously to see what there is peculiar about it. If a star, it may be double or it may be colored or it may be nebulous or again it may be variable and so it's brightness must be estimated in order to compare with a subsequent observation. Four distinct times in his life did Herschel thus pass the whole visible heavens under review and each survey occupied him several years. He discovered double stars, variable stars, nebulae and comets and Mr. William Herschel of Bath, the amateur astronomer, was gradually emerging from his obscurity and becoming a known man. Tuesday, the 13th of March, 1781 is a date memorable in the annals of astronomy. On this night, he writes to the Royal Society in examining the small stars near Etta Geminorum, I perceived one visibly larger than the rest. Struck with its uncommon appearance I compared it to Etta Geminorum and another star and finding it so much larger than either I suspected it to be a comet. The comet was immediately observed by professional astronomers and its orbit was computed by some of them. It was thus found to move in nearly a circle instead of an elongated ellipse and to be nearly twice as far from the sun as Saturn. It was no comet, it was a new planet, more than 100 times as big as the Earth and nearly twice as far away as Saturn. It was presently christened Uranus. This was a most striking discovery in the news sped over Europe. To understand the interested excited, we must remember that such a discovery was unique. Since the most ancient times of which men had any knowledge, the planets Mercury, Venus, Mars, Jupiter, Saturn had been known and there had been no addition to their number. Galileo and others had discovered satellites indeed but a new primary planet was an entire and utterly unsuspected novelty. One of the most immediate consequences of the event was the discovery of Herschel himself. The Royal Society made him a fellow the same year. The University of Oxford dubbed him a doctor and the King sent for him to bring his telescope and show it at court. So to London and Windsor he went taking with him his best telescope. Masculine, the then astronomer Royal, compared it with the national one at Greenwich and found Herschel's homemade instrument far the better of the two. He had a stand made after Herschel's pattern but was so disgusted with his own instrument now that he scarcely thought it worthy of the stand when it was made. At Windsor, George III was very civil and Mr. Herschel was in great request to show the ladies of the court's Saturn and other objects of interest. Mr. Herschel exhibited a piece of worldly wisdom under these circumstances that recalls faintly the behavior of Tycho Brahe under similar circumstances. The evening when the exhibition was to take place threatened to become cloudy and wet. So Herschel rigged up an artificial Saturn constructed of card and tissue paper with a lamp behind it in the distant wall of a garden. And when the time came, his new titled friends were regaled with a view of this imitation Saturn through the telescope, the real one not being visible. They went away much pleased. He stayed hovering between Windsor and Greenwich and uncertain what was to be the outcome of all this regal patronizing. He writes to his sister that he would much rather be back grinding mirrors at Bath and she writes begging him to come for his musical pupils were getting impatient. They had to get the better of their impatience, however, for the king ultimately appointed him astronomer or rather telescope maker to himself. And so Caroline and the whole household were sent for and established in a small house at Datchett. From being a stargazing musician, Herschel thus became a practical astronomer. Henceforth he lived in his observatory. Only on wet and moonlit nights could he be torn away from it. The daytime he devoted to making his long contemplated 20-foot telescope. Not yet, however, were all their difficulties removed. The house at Datchett was a tumbledown barn of a place, chosen rather as a workshop and observatory than as a dwelling-house. And the salary allowed him by George III was scarcely a princely one. It was, as a matter of fact, 200 pounds a year. The idea was that he would earn his living by making telescopes, and so he did. He made altogether some hundreds, among others, four for the king. But this eternal making of telescopes for other people to use or play with was a weariness to the flesh. What he wanted was to observe, observe, observe. Sir William Watson, an old friend of his and of some influence at court, expressed his mind pretty plainly concerning Herschel's position. And as soon as the king got to understand that there was anything the matter, he immediately offered 2,000 pounds for a gigantic telescope to be made for Herschel's own use. Nothing better did he want in life. The whole army of carpenters and craftsmen, resident in Datchett, were pressed into the service. Furnaces for the speculum metal were built, stands erected, and the 40-foot telescope fairly begun. It cost 4,000 pounds before it was finished, but the king paid the whole. With it he discovered two more satellites to Saturn, five hitherto had been known, and two moons to his own planet, Uranus. These two are now known as Oberon and Titania. They were not seen again until some 40 years after when his son, Sir John Herschel, re-observed them. And in 1847, Mr. Lassel, at his house Starfield, near Liverpool, discovered two more called Aerial and Umbriel, making the number four as now known. Mr. Lassel also discovered with a telescope of his own making an eighth satellite of Saturn, Hyperion, and a satellite to Neptune. A letter from a foreign astronomer about this period describes Herschel and his sister's method of work. I spent the night of the 6th of January at Herschel's in Datchett, near Windsor, and had the good luck to hit on a fine evening. He has his 20-foot Newtonian telescope in the open air and mounted in his garden very simply and conveniently. It is moved by an assistant who stands below it. Near the instrument is a clock regulated to side real time. In the room near it sits Herschel's sister and she has Flamsteed's Atlas open before her. As he gives her the word, she writes down the declination and right ascension and the other circumstances of the observation. In this way Herschel examines the whole sky without omitting the least part. He commonly observes with a magnifying power of 150 and is sure that after four or five years he will have passed in review every object above our horizon. He showed me the book in which his observations up to this time are written and I am astonished at the great number of them. Each sweep covers two degrees 15 minutes in declination and he lets each star pass at least three times through the field of his telescope so that it is impossible that anything can escape him. He has already found about 900 double stars and almost as many nebulae. I went to bed about one o'clock and up to that time he had found that night four or five new nebulae. The thermometer in the garden stood at 13 degrees Fahrenheit but in spite of this, Herschel observes the whole night through except that he stops every three or four hours and goes into the room for a few moments. For some years Herschel has observed the heavens every hour when the weather is clear and this always in the open air because he says that the telescope only performs well when it is at the same temperature as the air. He protects himself against the weather by putting on more clothing. He has an excellent constitution and thinks about nothing else in the world but the celestial bodies. He has promised me in the most cordial way entirely in the service of astronomy and without thinking of his own interests to see to the telescopes I have ordered for European observatories and he will himself attend to the preparation of the mirrors. In 1783 Herschel married an estimable lady who sympathized with his pursuits. She was the only daughter of a city magnet so his pecuniary difficulties, such as they were, they were never very troublesome to him, came to an end. They move now into a more commodious house at slow. Their one son, afterwards the famous Sir John Herschel, was born some nine years later but the marriage was rather a blow to his devoted sister. Henceforth she lived in lodgings and went over at night time to help him observe. For it must be remarked that this family literally turned night in today. Whatever sleep they got was in the daytime. Every fine night without exception was spent in observing and the quite incredible fierceness of the pursuit is illustrated as strongly as can be by the following sentence out of Caroline's diary at the time of the move from dachet to slow. The last night at dachet was spent in sweeping till daylight and by the next evening the telescope stood ready for observation at slow. Caroline was now often allowed to sweep with a small telescope on her own account. In this way she picked up a good many nebulae in the course of her life and eight comets four of which were quite new and one of which, known since his angst comet has become very famous. The work they got through between them is something astonishing. He made with his own hands 430 parabolic mirrors for reflecting telescopes besides a great number of complete instruments. He was 42 when he began contributing to the Royal Society yet before he died he had sent them 69 long and elaborate treatises. One of these memoirs is a catalog of 1000 nebulae. 15 years after he sends in another 1000 and some years later another 500. He also discovered 806 double stars which he proved were really corrected from the fact they revolved around each other. He lived to see some of them perform half a revolution. For him the stars were not fixed they moved slowly among themselves. He detected their proper motions. He passed the whole northern firmament in review four distinct times and counted the stars in 3400 gauge fields and estimated the brightness of hundreds of stars. He also measured as accurately as he could their proper motions devising for this purpose the method which still to this day remains in use. And what is the outcome of it all? It is not Uranus nor the satellites nor even the double stars in the nebulae considered as mere objects. It is the beginning of a science of the stars. Hitherto the stars had only been observed for nautical and practical purposes. Their times of rising and salving and setting had been noted. They had been treated as a clock or piece of dead mechanism and as fixed points of reference. All the energies of astronomers had gone out towards the solar system. It was the planets that had been observed. Tycho had observed and tabulated their positions. Kepler had found out some laws of their motion. Galileo had discovered their peculiarities and attendance. Newton and Laplace had perceived every detail of their laws. But for the stars, the old Ptolemaic system might still have been true. They might still be mere dots in a vast crystalline sphere all set at about one distance and subservient to the uses of the earth. Herschel changed this. Instead of sameness, he found variety. Instead of uniformity of distance, limitless and utterly limitless fields and boundless distances. Instead of rest and quiescence, motion and activity, instead of stagnation, life. Yes, that is what Herschel discovered, the life and activity of the whole visible universe. No longer was our little solar system to be the one object of regard. No longer were its phenomena to be alone interesting to man. With Herschel, every star was a solar system. And more than that, he found suns revolving round suns at distances such as the mind reels at, still obeying the same law of gravitation as poles and apple from a tree. He tried hard to estimate the distance of the stars from the earth, but there he failed. It was too hopeless a problem. It was solved sometime after his death by Bessel and the distances of many stars are now known, but these distances are awful and unspeakable. Our distance from the sun shrinks up into a mirror spec. The whole solar system into a mirror unit of measurement to be repeated hundreds of thousands of times before we reach the stars. Yet their motion is visible. Yes, to very accurate measurement, quite plain. One star known as 61 Cygni was then and is now rushing along at the rate of 100 miles every second. Not that you must imagine that this makes any obvious and apparent change in its position. No, for all ordinary and practical purposes, they are still fixed stars. Thousands of years will show us no obvious change. Adam saw precisely the same constellations as we do. It is only by refined micrometric measurement with high magnifying power that their flight can be detected. But the sun is one of the stars. Not by any means, especially large or bright one. Serious, we now know to be 20 times as big as the sun. The sun is one of the stars. Then is it at rest? Herschel asked this question and endeavored to answer it. He succeeded in the most astonishing manner. It is perhaps his most remarkable discovery and savers of intuition. This is how it happened. Within perfect optical means and his own eyesight to guide him, he considered and pondered over the proper motion of the stars as he had observed it till he discovered a kind of uniformity running through it all. Mixed up with irregularities and individualities, he found that in a certain part of the heavens the stars were on the whole opening out, separating slowly from each other. On the opposite side of the heavens, they were on the average closing up, getting slightly nearer to each other. While in directions at right angles to this, they were fairly preserving their customary distances asunder. Now, what is the moral to be drawn from such uniformity of behavior among unconnected bodies? Surely that this part of their motion is only apparent, that it is we who are moving. Traveling over a prairie bounded by a belt of trees, we should see the trees in our line of advance opening out and those behind closing up. We should see, in fact, the same kind of apparent motion as Herschel was able to detect among the stars, the opening out being most marked near the constellation Hercules. The conclusion is obvious. The sun, with all its planets, must be steadily moving towards a point in the constellation Hercules. The most accurate modern research has been hardly able to improve upon this statement of Herschel's. Possibly the solar system may ultimately be found to revolve around some other body, but what that is, no one knows. All one can tell us the present direction of the majestic motion, since it was discovered it has continued unchanged and will probably so continue for thousands of years. And finally, concerning the nebulae. These mysterious objects exercised a strong fascination for Herschel and many are the speculation he indulges in concerning them. At one time he regards them all as clusters of stars and the Milky Way as our cluster. The other he regards as other universes almost infinitely distant and he proceeds to gauge and estimate the shape of our own universe or galaxy of suns, the Milky Way. Later on, however, he pictures to himself the nebulae as nascent suns, solar systems before they are formed. Some he thinks have begun to aggregate while some are still glowing gas. He likens the heavens to a garden in which there are plants growing in all manner of different stages. Some shooting, some in leafs, some in flower, some bearing seed, some decaying. And thus at one inspection we have before us the whole life history of the plant. Just so he thinks the heavens contain worlds, some old, some dead, some young and vigorous and some in the act of being formed. The nebulae are these latter and the nebulous stars are a further stage in the condensation towards a sun. And thus by simple observation he has led towards something very like the nebular hypothesis of Laplace and his position, whether it be true or false, is substantially the same as is held today. We know now that many of the nebulae consist of innumerable isolated particles and may be spoken of as gas. We know that some are in a state of whirling motion. We know also that such gas left to itself will slowly as it cools, condense and shrink, so as to form a central solid nucleus. And also if it were in whirling motion that it would send off rings from itself and that these rings could break up into planets. In two familiar cases the ring has not yet thus aggregated into planet or satellite the zone of asteroids and Saturn's ring. The whole of this could not have been asserted in Herschel's time. But for further information the world had to wait. These are the problems of modern astronomy. These and many others, which are the growth of this century, I, and the growth of the last thirty or forty, and indeed of the last ten years. Even as I write new and very confirmatory discoveries are being announced. The Milky Way does seem to have some affinity with our sun, and the chief stars of the constellation of Orion constitute another family, but are enveloped in the great nebula, now by photography perceived to be far greater than had ever been imagined. What is to be the outcome of it all? I know not, but I am sure of this. That the largest views of the universe were that we are able to frame and the grandest manner of its construction that we can conceive are certain to pale and shrink and become inadequate when confronted with the truth. End of lecture twelve. Recording by Kathleen Nelson, Austin, Texas, May twenty-ten. Lecture thirteen of Pioneers of Science. This is a LibriVox recording. All LibriVox recordings are in the public domain. For more information or to volunteer, please visit LibriVox.org. Pioneers of Science by Sir Oliver Lodge. Lecture thirteen. Notes to lecture thirteen. Bode's Law. Write down the series zero, three, six, twelve, twenty-four, forty-eight, et cetera. Add four to each and divide by ten. You get the series point four. Mercury, point seven. Venus, one point zero. Earth, one point six. Mars, two point eight. Five point two. Jupiter, ten point zero. Saturn, nineteen point six. Uranus, thirty-eight point eight. Numbers which very fairly represent the distances of the then-known planets from the Sun in the order specified. Series was discovered on the first of January, 1801 by Piazzi. Palace in March, 1802 by Olbers. Juno in 1804 by Harding. And Vesta in 1807 by Olbers. No more asteroids were discovered till 1845, but there are now several hundreds known. Their diameters range from 500 to 20 miles. Neptune was discovered from the perturbations of Uranus by sheer calculation, carried on simultaneously and independently by Leveret in Paris and Adams in Cambridge. It was first knowingly seen by Gall of Berlin on the 23rd of September, 1846. Lecture 13, The Discovery of the Asteroids. Up to the time of Herschel, astronomical interest centered on the solar system. Since that time, it has been divided and a great part of our attention has been given to the more distant celestial bodies. The solar system has by no means lost its interest. It has indeed gained an interest continually as we gain in knowledge concerning it. But in order to follow the course of science, it will be necessary for us to oscillate to and fro, sometimes attending to the solar system, the planets and their satellites, sometimes extending our vision to the enormously more distant stellar spaces. Those who have read the third lecture in part one will remember the speculation in which Kepler indulged respecting the arrangements of the planets, the order in which they succeeded one another in space, and the law of their respective distances from the sun, and his fanciful guess about the five regular solids inscribed and circumscribed about their orbits. The rude coincidences were, however, accidental, and he failed to discover any true law. No thoroughly satisfactory law is known at the present day. And yet, if the nebular hypothesis or anything like it be true, there must be some law to be discovered hereafter, though it may be a very complicated one. An empirical relation is, however, known. It was suggested by Tejas and published by Bodhi of Berlin in 1772. It is always known as Bodhi's law. Bodhi's law asserts that the distance of each planet is approximately double the distance of the inner adjacent planet from the sun, but that the rate of increase is distinctly slower than this for the inner ones. Consequently, a better approximation will be obtained by adding a constant to each term of an appropriate geometrical progression. Thus, form a doubling series like this. One and one-half, three, six, 12, 24, et cetera. Doubling each time. Then add four to each, and you get a series which expresses very fairly the relative distances of the successive planets from the sun, except that the number for Mercury is rather erroneous, and we now know that at the other extreme, the number for Neptune is erroneous too. I have stated it in the notes preceding this lecture in a form calculated to give the law every chance and a form that was probably fashionable after the discovery of Uranus. But to call the first term of the doubling series zero is evidently not quite fair, though it puts Mercury's distance right. Neptune's distance, however, turns out to be more nearly 30 times the Earth's distance than 38.8. The others are very nearly right. Compare the mean distances from the sun in the table in the summary of facts for lecture three with the numbers in the notes preceding this lecture. The discovery of Uranus a few years afterwards in 1781 at 19.2 times the Earth's distance from the sun lent great ecla to the law and seemed to establish its right to be regarded as at least a close approximation to the truth. The gap between Mars and Jupiter, which had often been noticed, and which Kepler filled with a hypothetical planet too small to see, comes into great prominence by this law of Bodhi. So much so that towards the end of last century, an enthusiastic German, von Sach, after some search himself for the expected planet, arranged a committee of observing astronomers, or as he termed it, a body of astronomical detective police to begin a systematic search for this missing subject of the sun. In 1800 the preliminaries were settled. The heavens near the zodiac were divided into 24 regions, each of which was entrusted to one observer to be swept. Meanwhile, however, quite independently of these arrangements in Germany and entirely unknown to this committee, a quiet astronomer in Sicily, Piazzi, was engaged in making a catalogue of the stars. His attention was directed to a certain region in Taurus by an error in a previous catalogue, which contained a star really non-existent. In the course of his scrutiny, on the 1st of January, 1801, he noticed a small star which next evening appeared to have shifted. He watched it anxiously for successive evenings, and by the 24th of January, he was quite sure he had got hold of some moving body, not a star. Probably, he thought, a comet. It was very small, only of the eighth magnitude, and he wrote to two astronomers, one of them Bodhi himself, saying what he had observed. He continued to observe till the 11th of February when he was attacked by illness and compelled to cease. His letters did not reach their destination till the end of March. Directly Bodhi opened his letter, he jumped to the conclusion that this must be the missing planet. But unfortunately, he was unable to verify the guess for the object, whatever it was, had now got too near the sun to be seen. It would not be likely to be out again before September, and by that time, it would be hopelessly lost again and have just as much to be rediscovered as if it had never been seen. Mathematical astronomers tried to calculate a possible orbit for the body from the observations of Piazzi, but the observed places were so desperately few and close together. It was like having to determine a curve from three points close together. Three observations ought to serve, but if they are taken with insufficient interval between them, it is extremely difficult to construct the whole circumstances of the orbit from them. All the calculations gave different results and none were of the slightest use. The difficulty, as it turned out, was most fortunate. It resulted in the discovery of one of the greatest mathematicians, perhaps the greatest, that Germany has ever produced, Gauss. He was then a young man of 25, eking out a living by tuition. He had invented, but not published, several powerful mathematical methods, one of them now known as the method of least squares, and he applied them to Piazzi's observations. He was thus able to calculate an orbit and to predict a place where, by the end of the year, the planet should be visible. On the 31st of December of that same year, very near the place predicted by Gauss, von Sach rediscovered it, and Ulbers discovered it also the next evening. Piazzi called it Ceres, after the tutelary goddess of Sicily. Its distance from the sun as determined by Gauss was 2.767 times the Earth's distance. Bodhi's law made it 2.8. It was undoubtedly the missing planet, but it was only 150 or 200 miles in diameter, the smallest heavenly body known at the time of its discovery. It revolves the same way as other planets, but the plane of its orbit is tilted 10 degrees to the plane of the ecliptic, which was an exceptionally large amount. Very soon, a more surprising discovery followed. Ulbers, while searching for Ceres, had carefully mapped the part of the heavens where it was expected, and in March 1802, he saw in this place a star he had not previously noticed. In two hours he detected its motion, and in a month he sent his observations to Gauss, who returned his answer the calculated orbit. It was distant 2.67, like Ceres, and was a little smaller, but it had a very eccentric orbit, its plane being tilted 34.5 degrees, an extraordinary inclination. This was called Pallas. Ulbers at once surmised that these two planets were fragments of a larger one, and kept an eager look out for other fragments. In two years another was seen, in the course of charting the region of the heavens traversed by Ceres and Pallas. It was smaller than either, and was called Juno. In 1807, the persevering search of Ulbers resulted in the discovery of another, with a very oblique orbit, which Gauss named Vesta. Vesta is bigger than any of the others, being 500 miles in diameter, and shines like a star of the sixth magnitude. Gauss by this time had become so practised in the difficult computations that he worked out the complete orbit of Vesta within 10 hours of receiving the observational data from Ulbers. For many weary years, Ulbers kept up a patient and undermitting search for more of these small bodies or fragments of the large planet as he thought them. But his patience went unrewarded and he died in 1840 without seeing or knowing of any more. In 1845 another was found, however, in Germany, and a few weeks later, two others by Mr. Heind in England. Since then, there seems no end to them. Numbers have been discovered in America, where professors Peters and Watson have made a specialty of them and have themselves found something like a hundred. Vesta is the largest, its area being about the same as that of central Europe without Russia or Spain, and the smallest known is about 20 miles in diameter or with a surface about the size of Kent. The whole of them together do not nearly equal the Earth in bulk. The main interest of these bodies to us lies in the question, what is their history? Can they have been once a single planet broken up? Or are they rather an abortive attempt at a planet never yet formed into one? The question is not entirely settled, but I can tell you which way opinion strongly tends at the present time. Imagine a shell travelling in an elliptic orbit around the Earth to suddenly explode. The center of gravity of all its fragments would continue moving along precisely the same path as had been traversed by the center of the shell before explosion and would complete its orbit quite undisturbed. Each fragment would describe an orbit of its own because it would be affected by a different initial velocity. But every orbit would be a simple ellipse and consequently every piece would in time return through its starting point, namely the place at which the explosion occurred. If the zone of asteroids had a common point through which they all successively passed, they could be unhesitatingly asserted to be the remains of an exploded planet. But they have nothing of the kind. Their orbits are scattered within a certain broad zone, a zone everywhere as broad as the Earth's distance from the Sun, 92 million miles, with no sort of law indicating an origin of this kind. It must be admitted, however, that the fragments of our supposed shell might in the course of ages, if left to themselves, mutually perturb each other into a different arrangement of orbits from that with which they began. But their perturbations would be very minute and, moreover, on Laplace's theory, would only result in periodic changes provided each mass were rigid. It is probable that the asteroids were at one time not rigid and hence it is difficult to say what may have happened to them. But there is not the least reason to believe that their present arrangement is derivable in any way from an explosion, and it is certain that an enormous time must have elapsed since such an event, if it ever occurred. It is far more probable that they never constituted one body at all, but are the remains of a cloudy ring thrown off by the solar system in shrinking past that point. A small ring after the immense effort which produced Jupiter and his satellites, a ring which is aggregated into a multitude of little lumps instead of a few big ones. Such an event is not unique in the solar system. There is a similar ring round Saturn. At first sight, and to ordinary careful inspection, this differs from the zone of asteroids in being a solid lump of matter, like a quite. But it is easy to show from the theory of gravitation that a solid ring could not possibly be stable but would before long get precipitated eccentrically upon the body of the planet. Devices have been invented, such as artfully distributed irregularities calculated to active satellites and maintain stability. But none of these things really work. Nor will it do to imagine the ring's fluid.  The mechanical behavior of a system of rings on different hypotheses as to their constitution has been worked out with consummate skill by clerk Maxwell, who finds that the only possible constitution for Saturn's assemblage of rings is a multitude of discrete particles each pursuing its independent orbit. Saturn's ring is, in fact, a very concentrated zone of minor asteroids, and there is every reason to conclude that the origin of the solar asteroids cannot be very unlike the origin of the Saturnian ones. The nebular hypothesis lends itself readily to both. The interlockings and motions of the particles in Saturn's rings are most beautiful and have been worked out and stated by Maxwell with marvelous completeness. His paper constituted what is called the Adam's Prize Essay for 1856. Sir George Airey, one of the adjudicators, recently astronomer Royal, characterized it as one of the most remarkable applications of mathematics to physics that I have ever seen. There are several distinct constituent rings in the entire Saturnian zone and each perturbs the other with the result that they ripple and pulse in concord. The waves, thus formed, absorb the effect of the mutual perturbations and prevent an accumulation which would be dangerous to the persistence of the whole. The only effect of gravitational perturbation and of collisions is gradually to broaden out the whole ring, enlarging its outer and diminishing its inner diameter. But if there were any frictional resistance in the medium through which the rings spin, then other effects would slowly occur which ought to be looked for with interest. So complete and intimate is the way Maxwell works out and describes the whole circumstances of the motion of such an assemblage of particles and so cogent his argument as to the necessity that they must move precisely so and no otherwise. Else the rings would not be stable that it was a Cambridge joke concerning him that he paid a visit to Saturn one evening and made his observations on the spot. End of lecture 13. Lecture 14 of Pioneers of Science. This is a LibriVox recording. All LibriVox recordings are in the public domain. For more information or to volunteer, please visit LibriVox.org. Recording by Avae in August 2010. Pioneers of Science by Sir Oliver Lodge. Lecture 14. Notes to lecture 14. The total number of stars in the heavens visible to a good eye is about 5,000. The total number at present seen by a telescope is about 50 million. The number able to impress a photographic plate has not yet been estimated, but it is enormously greater still. Of those which we can see in these latitudes, about 14 are of the first magnitude, 48 of the second, 152 of the third, 313 of the fourth, 854 of the fifth, and 2010 of the sixth. Total, 3391. The quickest moving stars known are a double star of the sixth magnitude called 61 Cygni and one of the seventh magnitude called Groom Bridge 1830. The velocity of the latter is 200 miles a second. The nearest known stars are 61 Cygni and Alpha Centauri. The distance of these from us is about 400,000 times the distance of the sun. Their parallax is accordingly half a second of arc. Sirius is more than a million times further from us than our sun is and 20 times as big. Many of the brightest stars are at more than double this distance. The distance of Arcturus is too great to measure even now. Stella parallax was first securely detected in 1838 by Bessel for 61 Cygni. Bessel was born in 1784 and died in 1846, shortly before the discovery of Neptune. The stars are suns and are most likely surrounded by planets. One planet belonging to Sirius has been discovered. It was predicted by Bessel, its position calculated by Peters and seen by Elvin Clark in 1862. Another predicted one belonging to Procyon has not yet been seen. A velocity of five miles a second could carry a projectile right round the earth. A velocity of seven miles a second would carry it away from the earth and round the sun. A velocity of 27 miles a second would carry a projectile right out of the solar system, never to return. Lecture 14, Bessel, the distances of the stars and the discovery of stellar planets. We will now leave the solar system for a time and hastily sketch the history of stellar astronomy from the time of Sir William Herschel. You remember how greatly Herschel had changed the aspect of the heavens for man, how he had found that none of the stars were really fixed but were moving in all manner of ways. Some of this motion owned the apparent, much of it real. Nevertheless, so enormously distant are they that if we could be transported back to the days of the old Chaldean astronomers or to the days of Noah, we should still see the heavens with precisely the same aspect as they are now. Only by refined apparatus could any change be discoverable in all those centuries. For all practical purposes, therefore, the stars may still be well-called fixed. Another thing one may notice is showing their enormous distances is that from every planet of the solar system the aspect of the heavens will be precisely the same. Inhabitants of Mars or Jupiter or Saturn or Uranus will see exactly the same constellations as we do. The whole dimensions of the solar system shrink up into a speck when so contemplated. And from the stars, none of the planetary orbs of our system are visible at all. Nothing but the sun is visible and that merely as a twinkling star, brighter than some but fainter than many others. The sun and the stars are one. Try to realize this distinctly and keep it in mind. I find it often difficult to drive this idea home. After some talk on the subject, the friendly auditor will report, quote, the lecturer then described the stars, including that greatest and most magnificent of all stars, the sun, end quote. It would be difficult more completely to misapprehend the entire statement. When I say the sun is one of the stars, I mean one among the others. We are a long way from them. They are a long way from each other. They need be no more closely packed among each other than we are closely packed among them, except that some of them are double or multiple and we are not double. It is highly desirable to acquire an intimate knowledge of the constellations and a nodding acquaintance with the principal stars. A description of their peculiarities is dull and uninteresting, unless they are at least familiar by name. A little viva voce help to begin with. Supplemented by patient night scrutiny with a celestial globe or star maps under a tent or shed is perhaps the easiest way. A very convenient instrument for the purpose of learning the constellations is the form of map called a planisphere, because it can be made to show all the constellations visible at a given time, at a given date, and no others. The Greek alphabet also is a thing that should be learned by everybody. The increased difficulty in teaching science owing to the modern ignorance of even a smattering of Greek is becoming grotesque. The stars are named from their ancient grouping into constellations and by the prefix of a Greek letter to the larger ones and of numerals to the smaller ones. The biggest of all have special Arabic names as well. The brightest stars are called of the first magnitude, the next are of the second magnitude, and so on. But this arrangement into magnitudes has become technical and precise and intermediate or fractional magnitudes are inserted. Those brighter than the ordinary first magnitude are therefore now spoken of as of magnitude one-half, for instance, or 0.6, which is rather confusing. Small telescopic stars are often only named by their numbers in some specified catalogue, a dull but sufficient method. Here is a list of the stars visible from these latitudes, which are popularly considered as of the first magnitude. All of them should be familiarly recognized in the heavens whenever seen. Sirius in constellation Canis meia. Procyon in constellation Canis minor. Rigel in constellation Orion. Betelgeuse in constellation Orion. Castor in constellation Gemini. Pollux in constellation Gemini. Aldebaran in constellation Taurus. Arcturus in constellation Bootes. Viga in constellation Lyra. Capella in constellation Auriga. Regulus in constellation Leo. Altair in constellation Aquila. Formal Halt in constellation Southern Fish. Spica in constellation Virgo. Alpha Cygni is a little below the first magnitude. So perhaps is Castor. In the southern heavens, Canopus and Alpha Centauri rank next after Sirius in brightness. The distances of the fixed stars had, we know, been a perennial problem, and many had been the attempts to solve it. All the methods of any precision have depended on the Copernican fact that the Earth in June was 184 million miles away from its position in December, and that accordingly the grouping and aspect of the heavens should be somewhat different when seen from so different a point of view. An apparent change of this sword is called generally parallax. The parallax of a star being technically defined as the angle subtended at the star by the radius of the Earth's orbit. That is to say the angle is Sigma S, where E is the Earth, S the Sun, and Sigma a star. Plainly, the further off Sigma is, the more nearly parallel will the two lines to it become. And the difficulty of determining the parallax was just this, that the more accurately the observations were made, the more nearly parallel did those lines become. The angle was in fact just as likely to turn out negative as positive, an absurd result of course, to be attributed to unavoidable very minute inaccuracies. For a long time, absolute methods of determining parallax were attempted. For instance, by observing the position of the star with respect to the zenith at different seasons of the year. And many of these determinations appear to result in success. Hook fancied he had measured a parallax for Vega in this way, amounting to 30 seconds of arc. Flamestead obtained 40 seconds for gamma draconis. Röma made a serious attempt by comparing observations of Vega and Sirius, stars almost the antipodes of each other in the celestial world, hoping to detect some effect due to the size of the Earth's orbit, which should apparently displace them with the season of the year. All these fancied results, however, were shown to be spurious and their real cause assigned by the great discovery of the aberration of light by Bradley. After this discovery, it was possible to watch for still outstanding very minute discrepancies. And so the problem of stellar parallax was attacked with fresh vigor by Piazzi, by Brinkley and by Struve. But when results were obtained, they were traced after long discussion to age and gradual wear of the instrument or to some other minute inaccuracy. The more carefully the observation was made, the more nearly zero became the parallax, the more nearly infinite the distance of the stars. The brightest stars were the ones commonly chosen for the investigation and Vega was a favorite, because going near the zenith, it was far removed from the fluctuating and entire some disturbances of atmospheric refraction. The reason bright stars were chosen was because they were presumably nearer than the others. And indeed, a rough guess at a probable distance was made by supposing them to be of the same size as the sun and estimating the light in comparison with sunlight. By this confessively unsatisfactory method, it had been estimated that Sirius must be 140,000 times further away than the sun is if he be equally big. We now know that Sirius is much further off than this and accordingly that he is much brighter, perhaps 60 times as bright, though not necessarily 60 times as big as our sun. But even supposing him of the same light giving power as the sun, his parallax was estimated as 1.8 second, a quantity very difficult to be sure of in any absolute determination. Relative methods were, however, also employed and the advantages of one of these, which seems to have been suggested by Galileo, so impressed themselves upon William Herschel that he made a serious attempt to compass the problem by its means. The method was to take two stars in the same telescopic field and carefully to estimate their apparent angular distance from each other at different seasons of the year. All such disturbances as precession, aberration, nutation, refraction and the like would affect them both equally and could thus be eliminated. If they were at the same distance from the solar system, relative parallax would indeed also be eliminated, but if, as was probable, they were at different distances, then they would apparently shift relatively to one another and the amount of shift, if it could be observed, would measure not indeed the distance of either from the Earth, but their distance from each other. And this, at any rate, would be a step. It might be completed by similarly treating other stars in the same field, taking them in pairs together. A bright and a faint star would naturally be suitable because their distances were likely to be unequal, and so Herschel fixed upon a number of doublets which he knew of, containing one bright and one faint component. For up to that time it had been supposed that such grouping in occasional pairs or triplets was trans coincidence, the two being optically foreshortened together but having no real connection or proximity. Herschel failed in what he was looking for, but instead of that he discovered the real connection of a number of these doublets, for he found that they were slowly revolving around each other. There are a certain number of merely optical or accidental doublets, but the majority of them are real pairs of suns revolving round each other. This relative method of mapping micrometrically a field of neighboring stars and comparing their configuration now and six months hence was, however, the method ultimately destined to succeed, and it is, I believe, the only method which has succeeded down to the present day. Certainly it is the method regularly employed at Danzig at the Cape of Good Hope and everywhere else where stellar parallax is part of the work. Between 1830 and 1840, the question was ripe for settlement and as frequently happens with a long matured difficulty, it gave way in three places at once. Bessel, Henderson, and Struve almost simultaneously announced the stellar parallax which could reasonably be accepted. Bessel was a little the earliest and by far the most accurate. His indeed was the result which commanded confidence and to him the palm must be awarded. He was largely a self-taught student having begun life in a counting house and having abandoned business for astronomy. But notwithstanding these disadvantages, he became a highly competent mathematician as well as a skillful practical astronomer. He was appointed to superintend the construction of Germany's first great astronomical observatory that of Königsberg, which by his system, Zeal and Genius, he rapidly made a place of the first importance. Struve at Dorpat, Bessel at Königsberg, and Henderson at the Cape of Good Hope, all of them at newly equipped observatories were severely engaged at the same problem. But the Russian and German observers had the advantage of the work of one of the most brilliant opticians, as opposed the most brilliant that has yet appeared, Fraunhofer of Munich. An orphan lad apprenticed to a maker of looking glasses and subject to hard struggles and privations in early life, he struggled upwards and ultimately became head of the optical department of a Munich firm of telescope makers. Here he constructed the famous Dorpat Refractor for Struve, which is still at work and designed the Königsberg Heliometer for Bessel. He also made a long and most skillful research into the solar spectrum, which has immortalized his name. But his health was broken by early trials and he died at the age of 39 while planning new and still more important optical achievements.  It consists of an equatorial telescope with object glass cut right across and each half movable by a sliding movement, one past the other, the amount by which the two halves are dislocated being read off by a refined method. And the whole instrument having a multitude of appendages conducive to convenience and accuracy. Its use is to act as a micrometer or measure of small distances. Each half of the object glass gives a distinct image which may be allowed to coincide or may be separated as occasion requires. If it be the components of a double star that are being examined, each component will in general be seen double so that four images will be seen all together. But by careful adjustment, it will be possible to arrange that one image of each pair shall be superposed on or coincide with each other in which case only three images are visible. The amount of dislocation of the halves of the object glass necessary to accomplish this is what is read off. The adjustment is one that can be performed with extreme accuracy and by performing it again and again with all possible modifications, an extremely accurate determination of the angular distance between the two components is obtained. Bessel determined to apply this beautiful instrument to the problem of stellar parallax and he began by considering carefully the kind of star for which success was most likely. Hitherto the brightest had been most attended to but Bessel thought that quickness of proper motion would be a still better test of nearness. Not that either criterion is conclusive as to distance but there was a presumption in favor of either a very bright or an obviously moving star being nearer than a faint or a stationary one and as the bright criterion had already been often applied without result, he decided to try the other. He had already called attention to a record by Piazzi in 1792 of a double star in Cygnus whose proper motion was five seconds of arc every year, a motion which caused this telescopic object, six one Cygni, to be known as the flying star. Its motion is not really very perceptible for it will only have traversed one third of a lunar diameter in the course of a century. Still, it was the quickest moving star then known. The position of this interesting double he compared with two other stars which was seen simultaneously in the field of the heliometer by the method I have described throughout the whole year 1838. And in the last month of that year he was able to announce with confidence a distinct though very small parallax, substantiating it with a mass of detailed evidence which commanded the ascent of astronomers. The amount of it he gave is one third of a second. We know now that he was very nearly right, though modern research makes it more like half a second. Soon afterwards, Struve announced a quarter of a second as the parallax of Viga, but that is distinctly too great. And Henderson announced for Alpha Centauri, then thought to be a double, a parallax of one second, which, if correct, would make it quite the nearest of all the stars, but the result is now believed to be about twice too big. Knowing the distance of 6'1's Cygni, we can at once tell its real rate of travel, at least its rate across our line of sight. It is rather over 3 million miles a day. Now just consider the smallness of the half second of arc. Thus triumphantly, though only approximately measured. It is the angle subtended by 26 feet at a distance of 2,000 miles. If a telescope planted at New York could be directed to a house in England and then be turned so as to set its cross-wire first on one end of an ordinary room and then on the other end of the same room, it would have turned through half a second, the angle of greatest stellar parallax. Or, putting it another way, if the star were as near us as New York is, the sun on the same scale would be nine paces off. As 26 feet is to the distance of New York, so is 92 million miles to the distance of the nearest fixed star. Suppose you could arrange some sort of telegraphic vehicle able to carry you from here to New York in the 10th part of a second. That is, in the time required to drop two inches. Such a vehicle would carry you to the moon in 12 seconds to the sun in an hour and a quarter. Traveling thus continually, in 24 hours, you would leave the last member of the solar system behind you and begin your plunge into the depths of space. How long would it be before you encountered another object?  At these awful distances from one another, the stars are scattered in space, and where they not brilliantly self-luminous and glowing like our sun, they would be hopelessly invisible. I have spoken of 6-1 Cygni as a flying star, but there is another which goes still quicker, a faint star, 1-830 in Groombridge's catalogue. Its distance is far greater than that of 6-1 Cygni, and yet it is seen to move almost as quickly. Its actual speed is about 200 miles a second, greater than the whole visible firmament of 50 million stars can control, and unless the universe is immensely larger than anything we can see with the most powerful telescopes, or unless there are crowds of invisible, non-luminous stars mixed up with the others, it can only be a temporary visitor to this frame of things. It is rushing from an infinite distance to an infinite distance. It is passing through our visible universe for the first and only time it will never return. But so gigantic is the extent of visible space that even with its amazing speed of 200 miles every second, this star will take two or three million years to get out of sight of our present telescopes and several thousand years before it gets perceptibly fainter than it is now. Have we any reason for supposing that the stars we see are all there are? In other words, have we any reason for supposing all celestial objects to be sufficiently luminous to be visible? We have every ground for believing the contrary. Everybody in the solar system is dull and dark except the sun, though probably Jupiter is still red hot. Why may not some of the stars be dark too? The genius of Bessel surmised this and consistently upheld the doctrine that the astronomy of the future would have to concern itself with dark and invisible bodies. He preached an astronomy of the invisible. Moreover, he predicted a presence of two such dark bodies, one a companion of Sirius, the other of Prussian. He noticed certain irregularities in the motions of these stars which he asserted must be caused by their revolving round other bodies in a period of half a century. He announced in 1844 that both Sirius and Prussian were double stars, but that their companions, though large, were dark and therefore invisible. No one accepted this view till Peters in America found in 1851 that the hypothesis accurately explained the anomalous motion of Sirius and, in fact, indicated an exact place where the companion ought to be. And the obscure companion of Sirius became now a recognized celestial object, although it had never been seen, and it was held to revolve round Sirius in 50 years and to be about half as big. In 1862, the firm of Alvin Clark and Sons of New York were completing a magnificent 18-inch refractor, and the younger Clark was trying it on Sirius when he said, Why, Father, the star has a companion. The elder Clark also looked, and sure enough there was a faint companion due east of the bright star and in just the position required by theory. Not that the Clarks knew anything about the theory. They were keen-sighted and most skillful instrument makers, and they made a discovery by accident. After it had once been seen, it was found that several of the large telescopes of the world were able to show it. It is half as big, but it only gives one-thousandth part of the light that Sirius gives. No doubt it shines partly with the borrowed light and partly with the dull heat of its own. It is a real planet, but is yet too hot to live on. It will cool down in time as our earth has cooled and its Jupiter is cooling, and no doubt become habitable enough. It does revolve round Sirius in a period of 49.4 years, almost exactly what Bessel assigned to it. But Bessel also assigned a dark companion to Procyon. It and its luminous neighbor are considered to revolve round each other in a period of 40 years, and astronomers feel perfectly assured of its existence. Though at presence, it has not been seen by man. End of lecture 14