 Lecture 15 of Pioneers of Science. We approach tonight perhaps the greatest, certainly the most conspicuous, triumphs of the theory of gravitation. The explanation by Newton of the observed facts of the motion of the moon, the way he accounted for procession and mutation and for the tides, the way in which Laplace explained every detail of the planetary motions. These achievements may seem to the professional astronomer equally, if not more, striking and wonderful. But of the facts to be explained in these cases, the general public are necessarily more or less ignorant, and so no beauty or thoroughness of treatment appeals to them, nor can excite their imaginations. But predict in the solitude of the study, with no weapons other than pen, ink, and paper, an unknown and enormously distant world, to calculate its orbit when as yet it had never been seen, and to be able to say to a practical astronomer, point your telescope in such a direction at such a time, and you will see a new planet hitherto unknown to man. This must always appeal to the imagination with dramatic intensity, and must always awaken some interest in almost the dullest. Prediction is no novelty in science, and an astronomy least of all is it a novelty. Thousands of years ago Thales, and others whose very names we have forgotten, could predict eclipses with some certainty, though with only rough accuracy. And many other phenomena were capable of prediction by accumulated experience. We have seen, for instance, coming to later times, how a gap between Mars and Jupiter caused a missing planet to be suspected and looked for, and to be found in a hundred pieces. We have seen, also, how the abnormal proper motion of Sirius suggested to Bessel the existence of an unseen companion, and these last instances seem to approach very near the same class of prediction as that of the discovery of Neptune. Wherein, then, lies the difference? How comes it that some classes of prediction, such as that if you put your finger in fire it will get burnt, are childishly easy and commonplace, while others excite in the keenest intellects the highest feelings of admiration? Mainly, the difference lies, first, in the grounds on which the prediction is based. Second, on the difficulty of the investigation whereby it is accomplished. Third, in the completeness and the accuracy with which it can be verified. In all these points, the discovery of Neptune stands out preeminently among the verified predictions of science, and the circumstances surrounding it are of singular interest. In 1781, Sir William Herschel discovered the planet Uranus. Now you know the three distinct observations suffice to determine the orbit of a planet completely, and that it is well to have the three observations as far apart as possible, so as to minimize the effects of minute but necessary errors of observation. Directly Uranus was found, therefore, old records of stellar observations were ransacked, with the object of discovering whether it had ever been unwittingly seen before. If seen, it had been thought of course to be a star, for it shines like a star of the sixth magnitude, and can therefore be just seen without a telescope if one knows precisely where to look for it, and if one has good sight. But if it had been seen and catalogued as a star, it would have moved from its place, and the catalog would, by that entry, be wrong. The thing to detect, therefore, was errors in the catalogues, to examine all entries and see if the stars entered actually existed, or were any of them missing. If a wrong entry were discovered, it might of course have been due to some clerical error, though that is hardly probable considering the care taken over these things. Or it might have been some tailless comet or other, or it might have been the newly found planet. So the next thing was to calculate backwards, and see if by any possibility the planet could have been in that place at that time. Examined in this way, the tabulated observations of Flamsteed showed that he had unwittingly observed Uranus five distinct times, the first time in 1690, nearly a century before Herschel discovered its true nature. But more remarkable still, Le Monnier of Paris, had observed it eight times in one month, cataloging it each time as a different star. If only he had reduced and compared his observations, he would have anticipated Herschel by twelve years. As it was, he missed it altogether. It was seen once by Bradley also, altogether it had been seen twenty times. These old observations of Flamsteed and those of Le Monnier, combined with those made after Herschel's discovery, were very useful in determining an exact orbit for the new planet, and its motion was considered thoroughly known. It was not an exact ellipse of course, none of the planets describe exact ellipses. Each perturbs all the rest, and the small perturbations must be taken into account, those of Jupiter and Saturn being by far the most important. For a time, Uranus seemed to travel regularly and as expected, in the orbit which had been calculated for it. But early in the present century, it began to be slightly refractory, and by 1820, its actual place showed quite a distinct discrepancy from its position as calculated, with the aid of the old observations. It was at first thought that this discrepancy must be due to inaccuracies in the older observations, and they were accordingly rejected, and tables prepared for the planet based on the newer and more accurate observations only. But by 1830, it became apparent that it would not accurately obey even these. The error amounted to some twenty seconds. By 1840, it was as much as ninety seconds, or a minute and a half. This discrepancy is quite distinct, but still it is very small, and had two objects been in the heavens at once, the actual Uranus and the theoretical Uranus. No unaided eye could possibly have distinguished them or detected that they were other than a single star. The diagram, figure 93, shows all the irregularities plotted in the light of our present knowledge, and to compare with their amounts, a few standard things are placed on the same scale, such as the smallest interval capable of being detected with the unaided eye, the distance of the component stars in Epsilon Liri, the constants of aberration, of nutation, and of stellar parallax. The errors of Uranus, therefore, though small, were enormously greater than things which had certainly been observed. There was an unmistakable discrepancy between theory and observation. Some cause was evidently at work on this distant planet, causing it to disagree with its motion as calculated according to the law of gravitation. Some thought that the exact law of gravitation did not apply to so distant a body. Others surmised the presence of some foreign and unknown body, some comet, or some still more distant planet perhaps, whose gravitative attraction for Uranus was the cause of the whole difficulty. Some perturbations, in fact, which had not been taken into account because of our ignorance of the existence of the body which caused them. But though such an idea was mentioned among astronomers, it was not regarded with any special favor, and was considered merely as one among a number of hypotheses which could be suggested as fairly probable. It is perfectly right not to attach much importance to un-elaborated guesses. Not until the consequences of an hypothesis have been laboriously worked out, not until it can be shown capable of producing the effect quantitatively does its statement rise above the level of a guess and attain the dignity of a theory. A later state still occurs when the theory has been actually and completely verified by agreement with observation. Now, the errors in the motion of Uranus, i.e. the discrepancy between its observed and calculated longitudes, all known disturbing causes, such as Jupiter and Saturn being allowed for, are as follows, as quoted by Dr. Houghton in Seconds of Arc. Ancient observations casually made as of a star. Flamsteed 1690 plus 61.2. Flamsteed 1712 plus 92.7. Flamsteed 1715 plus 73.8. Le Monnier 1750 minus 47.6. Bradley 1750 minus 39.5. Meyer 1756 minus 45.7. Le Monnier 1764 minus 34.9. Le Monnier 1769 minus 19.3. Le Monnier 1771 minus 2.3. Modern observations 1780 plus 3.46. 1783 plus 8.45. 1786 plus 12.36. 1789 plus 19.02. 1801 plus 22.21. 1810 plus 23.16. 1822 plus 20.97. 1825 plus 18.16. 1828 plus 10.82. 1831 minus 3.98. 1834 minus 20.80. 1837 minus 42.66. 1840 minus 66.64. These are the numbers plotted in the above diagram, Figure 93, where H marks the discovery of the planet and the beginning of its regular observation. Something was evidently the matter with the planet. If the law of gravitation held exactly at so great a distance from the sun, there must be some perturbing force acting on it besides all those known ones which had been fully taken into account. Could it be an outer planet? The question occurred to several, and one or two tried if they could solve the problem, but they were soon stopped by the tremendous difficulties of calculation. The ordinary problem of perturbation is difficult enough, given a disturbing planet in such and such a position to find the perturbations it produces. This problem it was that Laplace worked out in the Mechanic Celeste. But the inverse problem, given the perturbations to find the planet which causes them, such a problem had never yet been attacked, and by only a few had its possibility been conceived. Bessel made preparations for trying what he could do at it in 1840, but he was prevented by fatal illness. In 1841 the difficulties of the problem presented by these residual perturbations of Uranus excited the imagination of a young student, an undergraduate of St. John's College, Cambridge, John Couch Adams by name, and he determined to have a try at it as soon as he was through his tripos. In January 1843 he graduated a senior wrangler, and shortly afterwards he set to work. In less than two years he reached a definite conclusion, and in October 1845 he wrote to the astronomer royal at Greenwich, Professor Eyrie, saying that the perturbations of Uranus would be explained by assuming the existence of an outer planet, which he reckoned was now situated in a specified latitude and longitude. We know now that had the astronomer royal put sufficient faith in this result to point his big telescope to the spot indicated and commence sweeping for a planet, he would have detected it within one and three-quarter degrees of the place assigned to it by Mr. Adams. But anyone in the position of the astronomer royal knows that almost every post brings an absurd letter from some ambitious correspondent or other, some of them having just discovered perpetual motion, or squared the circle, or proved the earth flat, or discovered the constitution of the moon, or of ether, or of electricity. And out of this massive rubbish it requires great skill and patience to detect such gems of value as there may be. Now this letter of Mr. Adams' was indeed a jewel of the first water, and no doubt bore on its face a very different appearance from the chaff of which I've spoken. But still Mr. Adams was an unknown man. He'd graduated a senior wrangler it is true, but somebody must graduate a senior wrangler every year, and every year by no means produces a first rate mathematician. Those behind the scenes, as Professor Ari of course was, having been a senior wrangler himself, knew perfectly well that the labeling of a young man on taking his degree is much more worthless as a testimony to his genius and ability than the general public are apt to suppose. Was it likely that a young and unknown man should have successfully solved so extremely difficult a problem? It was altogether unlikely. Still he would test him. He would ask for further explanations concerning some of the perturbations which he himself had specially noticed, and see if Mr. Adams could explain these also by his hypothesis. If he could, there might be something in his theory. If he failed, well, there was an end of it. The questions were not difficult. They concerned the error of the radius vector. Mr. Adams could have answered them with perfect ease, but sad to say though a brilliant mathematician, he was not a man of business. He did not answer Professor Ari's letter. It may to many seem a pity that the Greenwich Equatorial was not pointed to the place just to see whether any foreign object did happen to be in that neighborhood, but it is no light matter to derange the work of an observatory and alter the work mapped out for the staff into a sudden sweep for a new planet on the strength of a mathematical investigation just received by post. If observatories were conducted on these unsystematic and spasmodic principles, they would not be the calm, accurate, satisfactory places they are. Of course, if anyone could have known that a new planet was to be had for the looking, any course would have been justified, but no one could know this. I do not suppose that Mr. Adams himself could feel all that confidence in his attempted prediction, so there the matter dropped. Mr. Adams' communication was pigeon-holed and remained in seclusion for eight or nine months. Meanwhile, and quite independently, something of the same sort was going on in France. A brilliant young mathematician born in Normandy in 1811 had accepted the post of astronomical professor at the École Polytechnique, then recently founded by Napoleon. His first published papers directed attention to his wonderful powers, and the official head of astronomy in France, the famous Aragot, suggested to him the unexplained perturbations of Uranus as a worthy object for his fresh and well-armed vigor. At once he set to work in a thorough and systematic way. He first considered whether the discrepancies could be due to errors in the tables or errors in the old observations. He discussed them with minute care and came to the conclusion that they were not thus to be explained away. This part of the work he published in November 1845. He then set to work to consider the perturbations produced by Jupiter and Saturn to see if they had been with perfect accuracy allowed for, or whether some minute improvements could be made sufficient to destroy the irregularities. He introduced several fresh terms into these perturbations, but none of them of sufficient magnitude to do more than slightly lessen the unexplained perturbations. He next examined the various hypotheses that had been suggested to account for them. Was it a failure in the law of gravitation? Was it due to the presence of a resisting medium? Was it due to some unseen but large satellite? Or was it due to a collision with some comet? All these he examined and dismissed for various reasons one after the other. It was due to some steady continuous cause, for instance some unknown planet. Could this planet be inside the orbit of Uranus? No. For then it would perturb Saturn and Jupiter also and they were not perturbed by it. It must therefore be some planet outside the orbit of Uranus and in all probability, according to Bodhi's empirical law, at nearly double the distance from the Sun that Uranus is. Lastly he proceeded to examine where this planet was and what its orbit must be to produce the observed disturbances. Not without failures and disheartening complications was this part of the process completed. This was after all the real tug of war. So many unknown quantities. Its mass, its distance, its eccentricity, the obliquity of its orbit, its position at any time. Nothing known in fact about the planet except the microscopic disturbance it caused in Uranus some thousand million miles away from it. Without going into further detail, suffice it to say that in June 1846 he published his last paper and in it announced to the world its theoretical position for the planet. Professor Airy received a copy of this paper before the end of the month and was astonished to find that Leverier's theoretical place for the planet was within one degree of the place Mr. Adams had assigned to it eight months before. So striking a coincidence seemed sufficient to justify a Herschelian sweep for a week or two. But a sweep for so distant a planet would be no easy matter. When seen in a large telescope it would still only look like a star and it would require considerable labor and watching to sift it out from the other stars surrounding it. We know that Uranus had been seen twenty times and thought to be a star before its true nature was by Herschel discovered. And Uranus is only about half as far away as Neptune is. Neither in Paris nor yet at Greenwich was any optical search undertaken. But Professor Airy wrote to ask Mr. Leverier the same old question as he had fruitlessly put to Mr. Adams. Did the new theory explain the errors of the radius vector or not? The reply of Leverier was both prompt and satisfactory. These errors were explained as well as all the others. The existence of the object was then for the first time officially believed in. The British Association met that year at South Ampton and Sir John Herschel was one of its sectional presidents. In his inaugural address on September 10th, 1846 he called attention to the researches of Leverier and Adams in these memorable words. The past year has given to us the new minor planet Astria. It has done more. It has given us the probable prospect of another. We see it as Columbus saw America from the shores of Spain. Its movements have been felt trembling along the far-reaching line of our analysis with a certainty hardly inferior to ocular observation. It was about time to begin to look for it. So the Astronomer Royal thought on reading Leverier's paper. But as the National Telescope at Greenwich was otherwise occupied, he wrote to Professor Chalice at Cambridge to know if he would permit a search to be made for it with the Northumberland Equatorial, the large telescope of Cambridge University presented to it by one of the dukes of Northumberland. Professor Chalice said he would conduct the search himself and shortly commenced the modified series of sweeps round about the place assigned by theory, cataloging all the stars which he observed, intending afterwards to sort out his observations, compare one with another, and find out whether any one star had changed its position. Because if it had, it must be the planet. He thus, without giving an excessive time to the business, accumulated a host of observations which he intended afterwards to reduce and sift at his leisure. The wretched man thus actually saw the planet twice on August 4th and August 12th, 1846, without knowing it. If only he had had a map of the heavens containing telescopic stars down to the tenth magnitude, and if he had compared his observations with this map as they were made, the process would have been easy and the discovery quick. But he had no such map. Nevertheless, one was in existence. It had just been completed in that country of enlightened method in industry, Germany. Dr. Bremaker had not completed his great work, a chart of the whole zodiac down to stars of the tenth magnitude, but portions of it were completed, and the special region where the new planet was expected happened to be among the portions already just done. But in England, this was not known. Meanwhile, Mr. Adams wrote to the Astronomer Royal several additional communications, making improvements in his theory and giving what he considered nearer and nearer approximations for the place of the planet. He also now answered satisfactorily, but too late, the question about the radius vector sent to him months before. Let us return to Le Verrier. This great man was likewise engaged in improving his theory and in considering how best the optical search could be conducted. Actuated, probably, by the knowledge that in such matters as cataloging and mapping, Germany was then, as now, far ahead of all the other nations of the world. He wrote in September, the same September as Sir John Herschel delivered his eloquent address at Southampton to Berlin. Le Verrier wrote, I say, to Dr. Gall, head of the Observatory at Berlin, saying to him, clearly and decidedly, that the new planet was now in or close to such and such a position, and that if he would point his telescope to that part of the heavens he would see it. And, moreover, that he would be able to tell it from a star by its having a sensible magnitude, or disk, instead of being a mere point. Gall got the letter on the twenty-third of September, eighteen forty-six. That same evening he did point his telescope to the place Le Verrier told him, and he saw the planet that very night. He recognized it first by its appearance. To his practiced eye it did seem to have a small disk, and not quite the same aspect as an ordinary star. He then consulted Bremaker's great star chart, the part just engraved and finished, and sure enough, on that chart there was no such star there. Undoubtedly, it was the planet. The news flashed over Europe at the maximum speed with which news could travel at that date, which was not very fast. And by the first of October Professor Chalice and Mr. Adams heard it at Cambridge, and had the pleasure of knowing that they were forestalled, and that England was out of the race. It was an unconscious race to all concerned, however. Those in France knew nothing of the search going on in England. Mr. Adams's papers had never been published, and very annoyed the French were when a claim was set up on his behalf to a share in this magnificent discovery. Controversies and recriminations, excuses and justifications followed, but the discussion has now settled down. All the world honors the bright genius and mathematical skill of Mr. Adams, and recognizes that he first solved the problem by calculation. All the world, too, perceives clearly the no less eminent mathematical talents of Mr. Le Verrier, but it recognizes in him something more than the mere mathematician, energy, decision, and character. End of lecture 15. Lecture number 16 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 John Thomas Kuz, John Thomas Kuz Smarski. Pioneers of Science by Sir Oliver Lodge. Lecture number 16. Comets and meteors. We have now considered the solar system in several aspects, and we have passed in review something of what is known about the stars. We have seen how each star is itself in all probability the center of another and distinct solar system, the constituents of which are too dark and far off to be visible to us, nothing visible here by the central sun and that only as a twinkling speck. But between our solar system and these other suns, between each of these suns and all the rest, there exist vast, empty spaces, apparently devoid of matter. We have now to ask, are these spaces really empty? Is there really nothing in space but the nebulae, the suns, their planets, and their satellites? Are all the bodies in space of this gigantic size? May there not be an infinitude of small bodies as well? The answer to this question is in the affirmative. There appears to be no special size suited to the vastness of space. We find, as a matter of fact, bodies of all manner of sizes, ranging by gradations from the most tremendous suns, like Sirius, down through ordinary suns to smaller ones, then to planets of all sizes. Satellites still smaller, then the asteroids, till we come to the smallest satellite of Mars, only about 10 miles in diameter, weighing only some billion tons, the smallest of the regular bodies belonging to the solar system known. But besides all these, there are found to occur other masses, not much bigger and some probably smaller and these we call comets when we see them. Below these, again, we find masses varying from a few tons in weight down to only a few pounds or ounces and these, when we see them, or does not often, we call meteors or shooting stars. And to the size of these meteorites, there would appear to be no limit. Some may be literal grains of dust, there seems to be a regular gradation of size, therefore ranging from Sirius to dust and apparently, we must regard all space as full of these cosmic particles, stray fragments, as it were, perhaps of some older world, perhaps going to help deform a new one someday. As Kepler said, there are more comets in the sky than fish in the sea, not that they are all crowded together, else they would make a cosmic case. The transparency of space shows that there must be an enormous proportion of clear space between each and they are probably much more concentrated near one of the big bodies than they are in interstellar space. Even during the furious hail of meteors in November 1866, it was estimated that their average distance apart in the thickest of the shower was 35 miles. Consider the nature of a meteor or shooting star, we ordinarily see them as a mere streak of light. Sometimes they leave a luminous tail behind them, occasionally they appear as an actual fireball, accompanied by an explosion, sometimes, but very seldom, they are seen to drop and may subsequently be dug up as a lump of iron or rock, showing signs of rough treatment by excoriation and heat. These glass are the meteorites, or ciderites, or aerolites, or bolides of our museums. They are popular-spoking of as thunderbolts, though they have nothing whatever to do with atmospheric electricity. They appear to be travelling rocky or metallic fragments which in their journey through space are caught in the Earth's atmosphere and instantaneously ignited by the friction, far away in the depths of space, one of these bodies felt the attracting power of the sun and began moving towards it. As it approached, its speed grew gradually quicker and quicker. Continually, until by the time it has approached to within the distance of the Earth, it whizzes past with the velocity of 26 miles a second. The Earth is moving on its own account 19 miles every second. If the two bodies happen to be moving in opposite directions, the combined speed would be terrific, and the faintest trace of atmosphere miles above the Earth's surface would exert a furious grinding action on the stone. A stream of particles would be torn off. If, of iron, they would burn like a shower of filing from a firework, thus forming a trail, and the mass itself would be dissipated, shattered to fragments in an instant. Even if the Earth were moving laterally, the same thing would occur. But if Earth and stone happened to be moving in the same direction, there would be only the differential velocity of 7 miles a second. And though this is in all conscience great enough, yet there might be a chance for a residue of the nucleus to escape entire destruction, though it would be scraped, heated, and superficially molten by the friction, but so much of its speed would be rubbed out of it that on striking the Earth it might bury itself only a few feet or yards in the soil so that it could be dug out. The number of those which thus reached the Earth is comparatively infinitesimal. Nearly all get ground up and dissipated by the atmosphere. And fortunately it is for us that they are so. This bombardment of the exposed face of the Moon must be something terrible. Thus, then, every shooting star we see and all the myriads that we do not and cannot see, because they occur in the daytime, all these bright flashes or streaks represent the death and burial of one of these flying stones. It had been careering on its own account through space for untold ages, till it meets a planet. It cannot strike the actual body of the planet, the atmosphere, is a sufficient screen. The tremendous friction reduced it to dust in an instant, and this dust, then quietly and leisurely, settles down on the surface. Evidence of the settlement of meteoric dust is not easy to obtain in such a place as England, where the dust which accumulates is seldom of a celestial character. But on the snow fields of Greenland or Himalayas, dust can be found. And by a committee of the British Association, distinct evidence of molten globules of iron and other materials appropriate to aerolites, has been obtained by the simple process of collecting, melting, and filtering long exposed snow. Volcanic ash may be mingled with it, but under the microscope, the volcanic and the meteoric constituents have each a distinctive character. The quantity of meteoric material which reaches the earth as dust must be immensely in excess of the minute quality which arrives in the form of lumps. Hundreds or thousands of tonnes per atom must be received, and the accretion must, one would think, in the course of ages, be able to exert some influence on the period of the earth's rotation, the length of the day. It is too small, however, to have been yet certainly detected. Possibly it is altogether negligible. It has been suggested that those stones which actually fall are not the true cosmic wanderers, but are actually fragments of our own earth, cast up by powerful volcanoes long ago when the igneous power of the earth was more vigorous than now, cast up with a speed of close upon seven miles a second, and now in these quiet times gradually being swept up by the earth and so returning once they came. I confess I am unable to draw a clear distinction between one set and the other. Some falling stars may have had an origin of this sort, but certainly others have not. And it would seem very unlikely that one set only should fall bodily upon the earth, while the others should always be rubbed to powder. Still, it is a possibility to be born in mind. We have spoken of these cosmic visitors as wandering masses of stone or iron, but we should be wrong if we associated with the term wandering any ideas of lawlessness and irregularity of path. These small lumps of matter are as obedient to the law of gravity as any large ones can be. They must all, therefore, have definite orbits, and these orbits will have reference to the main attracting power of our sun, that will in fact be nearly all careering around the sun. Each planet may, in truth, have a certain following of its own. Within the limited sphere of the earth's predominant attraction, for instance, extending some way beyond the moon, we may have a number of satellites that we never see, all revolving regularly in elliptical orbits round the earth. But comparatively speaking, these satellite meteorites are few. The great bulk of them will be of a planetary character. They will be attendant upon the sun. It may seem strange that such minute bodies should have regular orbits and obey Kepler's laws, but they must. All three laws must be as rigorously obeyed by them as by the planets themselves. There is nothing in the smallness of a particle to excuse it from implicit obedience to law. The only consequence of their smallness is their inability to perturb others. They cannot appreciably perturb either the planets they approach or each other. The attracting power of a lump, one million tons in weight, is very minute. A pound on the surface of such a body of the same density as the earth would be only pulled to it with a force equal to that with which the earth pulls a grain. So the perturbing power of such a mass in distant bodies is imperceptible. It is a good thing it is so. Accurate astronomy would be impossible if we had to take into account the perturbations caused by a crowd of invisible bodies. Astronomy would then approach in complexity some of the problems of physics. But though we may be convinced from the facts of gravitation that these meteoric stones and all other bodies flying through space near our solar system must be constrained by the sun to obey Kepler's laws and fly around it in some regular elliptic or hyperbolic orbit, what chance have we of determining that orbit? At first sight a very poor chance, for we never see them except for the instant when they splash into our atmosphere. And for them that instant is instant death. It is likely that any escape that ordeal, and even if they do their career in orbits are effectively changed. Hence forward they must become a tendence on the earth. They may drop onto its surface or they may duck out of our atmosphere again. And revolve round us unseen in the clear space between earth and moon. Nevertheless, although the problem of determining the original orbit of any given set of shooting stars before it struck us would seem nearly insoluble. It has been solved and solved with some approach to accuracy. Being done by the help of observations of certain other bodies, the bodies by whose help this difficult problem has been attacked and resolved are comets. What are comets? I must tell you that the scientific world is not entirely and completely decided on the structure of comets. There are many floating ideas on the subject and some certain knowledge, but the subject is still, in many respects, an open one. And the ideas I propose to advocate you will accept for no more than they are worth. These are thee as worthy to be compared with other and different views. Up to the time of Newton the nature of comets was entirely unknown. They were regarded with superstitious awe as fiery portents and were supposed to be connected with the death of some king or with some national catastrophe. Even so late as the first edition of the Principia the problem of comets was unsolved and their theory is not given. But between the first and second editions a large comet appeared in 1680 and Newton speculated on its appearance and behaviour. It rushed down very close to the sun spun half around him very quickly and then receded from him again. If it were a material substance to which the law of gravitation applied it must be moving an iconic section with the sun in one focus and its radius vector must sweep out equal areas in equal times. Examining the record of its positions made at observatories its observed path quite according to theory and the motion of comets was from that time understood. Up to that time no one had attempted to calculate an orbit for a comet. They had been thought irregular and lawless bodies. Well they were recognised as perfectly obedient to the law of gravitation and revolving around the sun like everything else as members in fact of our solar system though not necessarily permanent members. But the orbit of a comet is very different from a planetary one. The eccentricity of its orbit is enormous in other words it is either a very elongated ellipse or a parabola. The comet of 1680 Newton found to move in an orbit so nearly a parabola that the time of describing it must be reckoned in hundreds of years at the least. It is now thought possible that it may not be quite a parabola but an ellipse so elongated that it will not return till 2255 until that date arrives however uncertainty will prevail as to whether it is a periodic comet or one of those that only visit our system once. If it be periodic as suspected it is the same as appeared when Julius Caesar was killed and which likewise appeared in the years 531 and 1106 AD. Should it appear in 2055 our posterity will probably be regarded as a memorial of Newton. The next comet discussed in the light of the theory of gravitation was the famous one of Halley. You know something of the history of this its period is 75 and a half years. Hailey died in 1682 and predicted his return in 1758 or 1759 the first commentary prediction. Clair Haute calculated its return right within a month. It has been back months more in 1835 and this time its date was correctly predicted within three days because Uranus was now known. It was away at its furthest point in 1873 again in 1911. Coming to recent times we have the great comets of 1843 and of 1858. The history of neither being known quite possibly they arrived then for the first time. Possibly the second will appear again in 3808. But besides these great comets there are a multitude of telescopic ones which do not show the striking features and have no gigantic tail. Some have no tail at all. Others have at best a few insignificant streamers and others show a faint haze looking like a microscopic nebula. All these comets are of considerable extent. Some millions of miles thick usually and yet stars are clearly visible through them. Hence they must be matter of very small density. Their space can be nothing more dense than a filmy mist but their nucleus must be something more solid and substantial. I have said that comets arrive from the depths of space rushed towards and round the sun whizzing past the earth with a speed of 26 miles a second on round the sun with a far greater velocity than that and then rush off again. Now all the time they are away from the sun, they are invisible. It is only as they get near him that they begin to expand and throw off tails and other appendages. The sun's heat is evidently evaporating them and driving away a cloud of mist and volatile matter. This is when they can be seen. The comet is most gorgeous when it is near the sun and as soon as it gets a reasonable distance away from him it is perfectly invisible. The matter evaporated from the comet by the sun's heat does not return. It is lost to the comet and hence after a few such journeys its volatile matter gets appreciably diminished and so old established periodic comets have no tails to speak of. But the new visitants coming from the depths of space for the first time these have great supplies of volatile matter and these are they which show the most magnificent tails. The tail of a comet is always directed away from the sun as if it were repelled. To this rule there is no exception. It is suggested and held as most probable that the tail and sun are similarly electrified and that the repulsion of the tail is electrical repulsion. Some great forces obviously at work to account for the enormous distance to which the tail is shot in a few hours. The pressure of the sun's light can do something and is the force that must not be ignored when small particles are being dealt with. Now just think what analogies there are between comets and meteors. Both are bodies traveling in orbits around the sun and both are mostly visible but both become visible to us under certain circumstances. Meteors become visible when they plunge into the extreme limits of our atmosphere. Comets become visible when they approach the sun. Is it possible that comets are large meteors which dip into the solar atmosphere and are thus rendered conspicuously luminous? Certainly they do not dip into the actual main atmosphere of the sun. Else they would be utterly destroyed. But it is possible that the sun has a faint trace of atmosphere extending far beyond this. And into this perhaps these meteors dip and glow with the friction. The particles thrown off might be also by friction electrified and the vaporous tail might be thus accounted for. Let us make this hypothesis provisionally that comets are large meteors or a compact swarm of meteors from near the sun find a highly verified sort of atmosphere in which they get heated and partly vaporized just as ordinary meteorites do when they dip into the atmosphere on the Earth. And let us see whether any facts bear out the analogy and justify the hypothesis. I must tell you now the history of three bodies and you will see that some intimate connection between comets and meteors is proved. The three bodies are known as first, Anx comet, second Bayla's comet, third the November swarm of meteors. Anx comet one of those discovered by Miss Herschel is an insignificant looking telescopic comet of a small period the orbit of which was well known and which was carefully observed at each reappearance after Ankh had calculated its orbit it was the quickest of the comets returning every three and a half years. It was found however that its period was not quite constant. It kept on getting slightly shorter. The comet in fact returned to the sun slightly before its time. Now this effect is exactly what friction against a solar atmosphere would bring about. Every time it passed near the sun a little velocity would be rubbed out of it. But the velocity is that which carries it away hence it would not go quite so far and therefore would return a little sooner. Any revolving body subject to friction must revolve quicker and quicker and get nearer and nearer its central body until if the process goes on long enough it must drop upon its surface. This seems the kind of thing happening to Ankh's comet. The effect is very small and not thoroughly proved but so far as it goes the evidence points to a greatly extended rare solar atmosphere which rubbed some energy out of it at every perhalion passage. Next, Baila's Comet. This also was a well-known and carefully observed telescopic comet. With the period of six years in one of its distant excursions it calculated that it must pass very near Jupiter and much curiosity was excited as to what would happen to it in consequence of the perturbation it must experience. As I have said, comets are only visible as they approach the sun. And a watch was kept for about a point in time. It was late but it did ultimately arrive. The singular thing about it however was that it was now double. It had apparently separated into two. This was in 1846. It was looked for again in 1852 and this time the components were further separated. Sometimes one was brighter, sometimes the other. Next time it ought to have come round, no one could find either portion. The comet seemed to have wholly disappeared. It has never been seen since. It was then recorded and advertised as the missing comet. But now comes the interesting part of the story. The orbit of this Baila Comet was well known and it was found that on a certain night in 1872 the earth would cross the orbit and had some chance of encountering the comet. Not a very likely chance because it need not be that part of its orbit at that time. But it was suspected not to be far off if still existent. Well, the night arrived, the earth did cross the orbit and there was seen not the comet but a number of shooting stars. Not one body, nor yet two, but a multitude of bodies. In fact a swarm of meteors. Not a very great swarm, such as sometimes occurs, but still a quite noticeable one. And this shower of meteors is definitely recognized as flying along the track of Baila's Comet. They are known as the Andromedes. This observation has been generalized. Every cometary orbit is marked by a ring of meteoric stones traveling around it. And whenever a number of shooting stars are seen quickly, one after the other, it is evidence that we are crossing the track of some comet. But suppose instead of only crossing the track of a comet, we were to pass close to the comet itself. We should then expect to see an extraordinary swarm, a multitude of shooting stars. Such phenomena have occurred. The most famous are those known as the November meteors or Leonids. This is the third of those bodies whose history I had to tell you. Sir H. Newton of America by examining ancient records arrived at the conclusion that the Earth passed through a certain definite meteor shoal every 33 years. He found in fact that every 33 years an unusual flight of shooting stars was witnessed in November. The earliest record being 599 A.D. Their last appearance had been in 1833 and he therefore predicted their return in 1866 or 1867. Sure enough, in November 1866 they appeared and many must remember seeing that glorious display. Although their hail was almost continuous. It is estimated that their average distance apart was 35 miles. Their radiant point was and always is in the constellation Leo and hence their name Leonids. A parallel stream fixed in space necessarily exhibits a definite aspect with reference to the fixed stars. Its aspect with respect to the Earth will be very changeable because of the rotation and revolution of that body. But its position with respect to constellations will be steady. Hence each meteor swarm being a steady parallel stream rushing masses always strikes us from the same point in stellar space. And by this point or radiant it is identified and named. The paths do not appear to us to be parallel. Because of perspective they seem to radiate and spread in all directions from a fixed center like spokes. But all these diverging streaks are really parallel lines optically foreshortened by different amounts so as to produce the radiant impression. The annex diagram figure 105 clearly illustrates the fact that the radiant is the vanishing point of a number of parallel lines. This swarm is specially interesting to us from the fact that we cross its orbit every year. It's orbit and the Earth's intersect. Every November we go through it and hence every November we see a few stragglers of this immense swarm. The swarm itself takes 33 years on its revolution round the sun and hence we only encounter it every 33 years. The swarm is of immense size in breadth it is such that the Earth flying 19 miles a second takes 4 or 5 hours to cross it and this is therefore the time the display lasts. But in length it is far more enormous. The speed with which it travels is 25 miles a second for its orbit extends as far as Uranus although by no means parabolic and yet it takes more than a year to pass. Imagine a procession 200,000 miles broad every individual rushing along at the rate of 25 miles every second and the whole procession so long that it takes more than a year to pass. It's like a gigantic shawl of herrings swimming round and round the sun every 33 years and traveling past the Earth with that tremendous velocity of 25 miles a second the Earth dashes through the swarm and sweeps up myriads. Think of the countless numbers swept up by the whole Earth in crossing such a shawl as that but heaps more remain and probably the millions which are destroyed every 33 years have not yet made any very important difference to the numbers still remaining. The Earth never misses this swarm. Every 33 years it is bound to pass through some part of them for the shawl is so long that if the head is just missed one November the tail will be encountered next November. This is a plain and obvious result of its enormous length. It may be likened to a 2 foot length of sewing silk swimming round and round an oval 60 feet in circumference but you will say although the numbers are so great that destroying a few millions or so every 33 years makes but a little difference to them yet if this process has been going on from all eternity they ought to be all swept up. Granted and no doubt the most ancient swarms have already all or nearly all been swept up. The August meteors or Perseids are an example. Every August we cross their path and we have a small meteoric display radiating from the sword hand of Perseus but never specially more in one August than another it would seem as if the main shawl has disappeared and nothing is now left but the stragglers or perhaps it is that the shawl has gradually become uniformly distributed all along the path. Anyhow these August meteors are reckoned much more ancient members of the solar system than are the November meteors. The November meteors are believed to have entered the solar system in the year 126 AD. This may seem an extraordinary statement. It is not final but it is based on the calculations of Le Vierre. Confirmed recently by Mr. Adams a few moments will suffice to make the grounds of it clear. Le Vierre calculated the orbit of the November meteors and found them to be an oval extending beyond Uranus. It was perturbed by the outer planets near which it went so that in past times it must have moved in a slightly different orbit. Calculating back to their past positions it was found that in a certain year it must have gone very near to Uranus and that by the perturbation of this planet its path had been completely changed. Originally it had in all probability a comet flying in a parabolic orbit toward the sun like many others. This one encountering Uranus was pulled to pieces as it were and its orbit made elliptical as shown in figure 107. It was no longer free to escape and go away into the depths of space. It was enchained and made a member of the solar system. It also ceased to be a comet. It was degraded into a shawl of meteors. This is believed to be the past history of this splendid swarm. Since its introduction to the solar system it has made 52 revolutions. Its next return is due in November 1899 and I hope that it may occur in the English dusk and figure 97 in a cloudless after midnight sky as it did in 1866. End of lecture 16. Recording by John Thomas Cous, CousMarchie www.ValidateYourLife.com or JohnCous.com For more information or to volunteer please visit LibriVox.org Pioneers of Science by Sir Oliver Lodge Lecture 17 The Tides The tide generating force of one body on another is directly as the mass of the one body and inversely as the cube of the distance between them. Hence the moon is more effective in producing terrestrial tides than the sun. The tidal wave directly produced by the moon in the open ocean is about 5 feet high that produced by the sun is about 2 feet. Hence the average spring tide is to the average neap as about 7 to 3. The lunar tide varies between apogee and perigee from 4.3 to 5.9. The solar tide varies between apheleon and perihelion from 1.9 to 2.1. Hence the highest spring tide is to the lowest neap as 5.9 plus 2.1 is to 4.3 minus 2.1 or as 8 to 2.2. The semi-synchronous oscillation of the southern ocean raises the magnitude of oceanic tides somewhat above these directly generated values. Oceanic tides are true waves not currents. Coast tides are currents. The momentum of the water when the tidal wave breaks upon a continent and rushes up the channels raises coastal tides to a much greater height in some places up to 50 or 60 feet or even more. Early observed connections between moon and tides would be these. First spring tides at new and full moon. Second average interval between tide and tide is half a lunar not a solar day. A lunar day being the interval between two successive returns of the moon to the meridian 24 hours and 50 minutes. Third the tides of a given place at new and full moon occur always at the same time of day whatever the season of the year. Lecture 17 The Tides. Persons accustomed to make use of the mercy landing stages can hardly fail to have been struck by two obvious phenomena. One is that the gangways there too are sometimes almost level and at other times very steep. Another is that the water often rushes past the stage rather silently, sometimes south toward Garstyn, sometimes north towards the sea. They observe in fact that the water has two periodic motions one up and down the other to and fro a vertical and a horizontal motion. They may further observe if they take the trouble that a complete swing of the water up and down or to and fro takes place about every 12 and a half hours. Moreover that soon after high and low water there is no current. The water is stationary whereas about halfway between high and low it is rushing with maximum speed either up or down the river. To both these motions of the water the name tide is given and both are extremely important. Sailors usually pay most attention to the horizontal motion and on charge you find the tide races marked and the places where there is but a small horizontal rush of the water are labeled very little tide here. Landsmen are at any rate such of the more philosophic sort as pay any attention to the matter at all. Think most of the vertical motion of the water, its amount of rise and fall. Dwellers in some low-lying districts in London are compelled to pay attention to the extra high tides of the Thames because it is or was very liable to overflow its banks and inundate their basements. Sailors however on nearing a port are also greatly affected by the time and amount of high water there especially when they are in a big ship and we know well enough how frequently Atlantic liners after having accomplished their voyage with good speed have to hang around for hours waiting till there is enough water to lift them over the bar. That standing obstruction one feels inclined to say disgrace to the Liverpool harbour. To us in Liverpool the tides are of supreme importance upon them the very existence of the city depends for without them Liverpool would not be a port. It may be familiar to many of you how this is and yet it is a matter that cannot be passed over in silence. I will therefore call your attention to the ordnance survey of the estuaries of the Mercy and the D. You see first that there is a great tendency for sand banks to accumulate all about this coast from north Wales right away round to south port. You see next that the port of Chester has been practically silted up by the deposits of sand in the wide mouth D while the port of Liverpool remains open owing to the scouring action of the tide in its peculiarly shaped channel. Without the tides the Mercy would be a wretched dribble not much bigger than it is at Warrington with them this splendid basin is kept open and a channel is cut of such depth that the great eastern easily rode in it in all states of the water. The basin is filled with water every 12 hours through its narrow neck. The amount of water stored up in this basin at high tide I estimate a 60 million tons. All this quantity flows through the neck in six hours and flows out again in the next six scouring and cleansing and carrying mud and sand far out to sea just at present the current set strongest on the Birkenhead side of the river and accordingly a Pluckington bank unfortunately grows under the Liverpool stage. Should this tendency to silt up the gates of our docks increase land can be reclaimed on the other side of the river between Tranmere and Rockferry and an embankment made so as to deflect the water over Liverpool way and give us a fairer proportion of the current. After passing New Brighton the water spreads out again to the left its velocity forward diminishes and after a few miles it has no power to cut away that sand bank known as the bar. Should it be thought desirable to make it accomplish this and sweep the bar further out to sea into deeper water it is probable that a rude training wall say of old hulks or other partial obstruction on the west of Queen's Channel arranged so as to check the spreading out over all this useless area may be quite sufficient to retain the needed extra impetus in the water perhaps even without choking up the useful old rock channel through which smaller ships still find convenient exit. Now although the horizontal rush of the tide is necessary to our existence as a port it does not follow that the accompanying rise and fall of the water is an unmixed blessing. It is due the need for all the expensive arrangements of docks and gates wherewith to store up the high level water. Quebec and New York are cities on such magnificent rivers that the current required to keep open channel is supplied without any tidal action although Quebec is nearly 1,000 miles from the open ocean and accordingly Atlantic liners do not hover in mid-river and discharge passengers by tender but they proceed straight to the side of the keys lining the river in New York they dive into one of the pockets belonging to the company running the ship and there discharge passengers and cargo without further trouble and with no need for docks or gates. However rivers like the St. Lawrence and the Hudson are the natural property of a gigantic continent and we in England may be well contented with the possession of such tidal estuaries as the Mercy, the Thames, and the Humber. That by pertinacious dredging the citizens of Glasgow managed to get large ships right up their small river the Clyde to the keys of the town is a remarkable fact and redowns very highly to their credit. We will now proceed to consider the connection existing between the horizontal rush of water and its vertical elevation and ask which is cause and which is effect. Does the elevation of the ocean cause the tidal flow or does the tidal flow cause the elevation? The answer is two fold. Both statements are in some sense true. The prime cause of the tide is undoubtedly a vertical elevation of the ocean. A tidal wave or hump produced by the attraction of the moon. This hump as it passes the various channels opening into the ocean raises their level and causes water to flow up them. But this simple oceanic tide although the cause of all tide is itself but a small affair. It seldom rises above six or seven feet and tides on islands in mid ocean have about this value or less. But the tides on our coasts are far greater than this. They rise twenty or thirty feet or even fifty feet occasionally at some places as at Bristol. Why is this? The horizontal motion of the water gives it such an impetus or momentum that its motion far transcends that of the original impulse given to it. Just as a push given to a pendulum may cause it to swing over a much greater arc than that through which the force acts. The inrushing water flowing up the English Channel or the Bristol Channel or St. George's Channel has such an impetus that it propels itself some twenty or thirty feet high before it has exhausted its momentum and begins to descend. In the Bristol Channel the gradual narrowing of the opening so much assists this action that the tides often rise forty feet occasionally fifty feet and rush still further up the Severn in a precipitous and extraordinary rise and fall of water called the Boer. Some places are subject to considerable rise and fall of water with very little horizontal flow. Others possess strong tidal races but very little elevation and depression. The effect observed at any given place entirely depends on whether the place has a general character of a terminus or whether it lies en route to some great basin. You must understand then that all tide takes its rise in the free ocean under the action of the moon. No ordinary size sea like the North Sea or even the Mediterranean is big enough for more than a just appreciable tide to be generated in it. The Pacific the Atlantic and the Southern Oceans are the great tidal reservoirs and in them the tides of the earth are generated as low flat humps of gigantic area though only a few feet high oscillating up and down in the period of approximately twelve hours. The tides we and other coast-possessing nations experience are the overflow or backwash of these oceanic humps and I will now show you in what manner the great Atlantic tide wave reaches the British Isles twice a day. Big Ear 109 shows the contour lines of the great wave as it rolls in east from the Atlantic getting split by the land's end and by Ireland into three portions one of which rushes up the English Channel and through the Straits of Dover another rolls up the Irish Sea with the minor offshoot of the Bristol Channel and curling round Angusley flows along the North Wales Coast and fills Liverpool Bay and the Mercy. The third branch streams round the North Coast of Ireland past the Mull of Cantire and Rathland Island part fills up the Firth of Clyde while the rest flows south and swirling round the west side of the Isle of Man helps the southern current to fill the Bay of Liverpool. The rest of the Great Wave impinges on the coast of Scotland and curling round it fills up the North Sea right away to the Norway Coast and then flows down below Denmark joining the southern and earlier arriving stream. The diagram I show you is a rough chart of co-tidal lines which I made out of the information contained in Whitaker's Almanac. A place may thus be fed with tide by two distinct channels and many curious phenomena occur in certain places from this cause. Thus it may happen that one channel is six hours longer than the other in which case a flow will arrive by one at the same time as an ebb arrives by the other and the result will be that the place will have hardly any tide at all one tide interfering with and neutralizing the other. This is more markedly observed at other parts of the world than in the British Isles whenever a place is reached by two channels of different lengths its tides are sure to be peculiar and probably small. Another cause of all tide is the way the wave surges to and fro in a channel. The tidal wave surging up to English Channel for instance gets largely reflected by the constriction at Dover and so a crest surges back again as we may see waves reflected in the long trough or tilted bath. The result is that Southampton has two high tides rapidly succeeding one another and for three hours the high water level varies but slightly a fact of evident convenience to the port. Tides on a nodal line so to speak about the middle of the length of the channel have a minimum of rise and fall though the water rushes past them first violently up towards Dover where the rise is considerable and then back again towards the ocean. At Portland for instance the total rise and fall is very small it is practically on a node. Yarmouth again is near a less marked node in the North Sea where stationary waves likewise surge to and fro and accordingly the total rise and fall at Yarmouth is only about 5 feet varying from 4.5 to 6 whereas at London it is 20 or 30 feet and at Flamborough Head or Leith it is from 12 to 16 feet. It is generally supposed that water never flows uphill but in these cases of oscillation it flows uphill for 3 hours together. The water is rushing up the English Channel towards Dover long after it is highest at the Dover end. It goes on piling itself until its momentum is checked by the pressure and then it surges back. It behaves in fact very like the bop of a pendulum which rises against gravity at every quarter swing. To get a very large tide the place ought to be directly accessible by a long sweep of a channel to the open ocean and if it is situated on a gradually converging opening the ebb and flow may be enormous. The Severn is the best example of this on the British Isles but the largest tides in the world are found I believe in the Bay of Fundy on the coast of North America where they sometimes rise 120 feet. Excessive or extra tides may be produced occasionally in any place by the propelling force of a high wind driving the water towards the shore also by a low barometer that is by a local decrease in the pressure of the air. Well now leaving these topographical details concerning tides which we see to be due to great oceanic humps great area that is though small in height let us proceed to ask what causes these humps and if it be the moon that does it how does it do it. The statement that the moon causes the tides sounds at first rather an absurdity and a mere popular superstition Galileo chaffed Kepler for believing it who it was that discovered the connection between moon and tides we know not probably it is a thing which has been several times rediscovered by observant sailors or coast dwellers and it is certainly a very ancient piece of information. Probably the first connection observed was that about full moon and about new moon the tides are extra high being called spring tides whereas about half moon the tides are much less and are called knee tides. The word spring in this connection has no reference to the season of the year except that both words probably express the same idea of energetic uprising or upswinging while the word neep comes from nip which means pinched scanty nipped tide. The next connection likely to be observed would be that the interval between two day tides was not exactly a solar day of 24 hours but a lunar day of 55 minutes longer for by reason of the moon's monthly motion it lags behind the sun about 50 minutes a day and the tides do the same and so perpetually occur later and later about 50 minutes a day later or 12 hours and 25 minutes on the average between tide and tide. A third and more striking connection was also discovered by some of the ancient great navigators and philosophers namely that the time of high water at a given place at full moon is always the same or very nearly so. In other words the highest or spring tides always occur nearly at the same time of day at a given place. For instance at Liverpool this time is noon and midnight. London is about two hours and a half later. Each port has its own time for receiving a given tide and the time is called the establishment of the port. Look out a day when the moon is full and you will find the Liverpool high tide occurs at half past 11 or close upon it. The same happens when the moon is new. A day after full or new moon the spring tides rise to their highest and these extra high tides always occur in Liverpool at noon and at midnight whatever the season of the year. About the equinoxes they are liable to be extraordinarily high. The extra low tides here are therefore at 6am and 6pm and the 6pm low tide is a nuisance to the river steamers. The spring tides at London are highest about half past two. It is therefore quite clear that the moon has to do with the tides. It and the sun together are in fact the whole cause of them and the mode in which these bodies act by gravitative attraction was first made out and explained in remarkably full detail by Sir Isaac Newton. You will find his account of the tides in the second and third books of Principia and though the theory does not occupy more than a few pages of that immortal work he succeeds not only in explaining the local tidal peculiarities much as I have done tonight but also in calculating the approximate height of mid-ocean solar tide and from the observed lunar tide he shows how to determine the then quite unknown mass of the moon. This was quite an extraordinary achievement. The difficulty of which it is not easy for a person unused to similar discussions fully to appreciate. It is indeed but a small part of what Newton accomplished but by itself it is sufficient to confer immortality upon any ordinary philosopher and to place him in a front rank. To make intelligible Newton's theory of the tides I must not attempt to go into too great detail. I will consider only the salient points. First you know that every mass of matter attracts the other piece of matter. Second that the moon revolves around the earth or rather that the earth and moon revolve around their common center of gravity once a month. Third that the earth spins on its own axis once a day. Fourth that when a thing is world round it tends to fly out from the center and requires a force to hold it in. These are the principles involved. You can whirl a bucket full of water vertically round without spilling it. Make an elastic globe rotate and it bulges out into an oblate or orange shape as illustrated by the model shown in figure 110. This is exactly what the earth does and Newton calculated the bulging of it as 14 miles all around the equator. Make an elastic globe revolve around a fixed center outside itself and it gets pulled into a prolate or lemon shape. The simplest illustrative experiment is to attach a string to an elastic bag or football full of water and whirl it round and round. Its prolateness is readily visible. Now consider the earth and moon revolving round each other like a man whirling a child round. The child travels furthest but the man cannot merely rotate. He leans back and thus also describes a small circle. So does the earth. It revolves round the common center of gravity of earth and moon. This is a vital point in the comprehension of the tides. The earth's center is not at rest but is being world round by the moon in a circle about one eightieth as big as the circle which the moon describes because the earth weighs 80 times as much as the moon. The effect of the revolution is to make both bodies slightly protrude in the direction of the line joining them. They become slightly prolate as it is called. That is lemon shaped. Illustrating still by the man and the child, the child's legs fly outwards so that he is elongated in the direction of a radius. The man's coattails fly out too so that he too is similarly though less elongated. These elongations or protuberances constitute the tides. Figure 111 shows a model to illustrate the mechanism. A couple of cardboard discs to represent globes of course one four times the diameter of the other and each loaded so as to have about the correct earth-moon ratio of weights are fixed at either end of a long stick and they balance about a certain point which is their common center of gravity. For convenience this point is taken a trifle too far out from the center of the earth. That is just beyond its surface. Through the balancing point G a bridle is stuck and on that as a pivot the whole readily revolves. Now between the circular disc you see are four pieces of cart of appropriate shape which are able to slide out under proper forces. They are shown dotted in the figure and are lettered A B C D. The inner pair B and C are attached to each other by a bit of string which has to typify the attraction of gravitation. The outer pair A and D are not attached to anything but have a certain amount of play against friction in slots parallel to the length of the stick. The moon disc is also slotted so a small amount of motion is possible to it along the stick or bar. These things being so arranged and the protuberant pieces of cart being all pushed home so that they are hidden behind their respective disc the hole is spun rapidly round the center of gravity G. The result of a brief spin is to make A and D fly out by centrifugal force and show as in the figure while the moon flying out too in its slot tightens up the string which causes B and C to be pulled out too. Thus all four high tides are produced two on the earth and two on the moon. A and D being caused by centrifugal force B and C by the attraction of gravitation. Each disc has become prolate in the same sort of fashion as yielding globes do. Of course the fluid ocean takes this shape more easily and more completely than the solid earth can and so here are the very oceanic humps we have been talking about and about 3 feet high. Figure 112. If there were a C on the moon its humps would be a good deal bigger but there probably is no C there and if there were the earth tides are more interesting to us at any rate to begin with. The humps so far treated are always protruding in the earth moon line and our stationary but now we have to remember that the earth is spinning inside them. It is not easy to see what precise effect this spin will have upon the humps even if the world were covered with a uniform ocean but we can see at any rate that however much they may get displaced and they do get displaced a good deal possibly be carried round and round. The whole explanation we have given of their causes shows that they must maintain some steady aspect with respect to the moon. In other words they must remain stationary as the earth spins round. Not that the same identical water remain stationary for in that case it would have to be dragged over the earth equator at the rate of 1000 miles an hour but the hump or wave crest remain stationary. It is a true wave or form only and consists of continuously changing individual particles the same is true of all waves except breaking ones. Given then these stationary humps and the earth spinning on its axis we see that a given place on the earth will be carried round and round now past the hump and 6 hours later past the depression another 6 hours and it will be at the antipodal hump and so on thus every 6 hours we shall travel from the region in space where the water is high and where it is low and ignoring our own motion we shall say that the sea first rises and then falls and so with respect to the place it does. Thus the succession of high and low water and the two high tides every 24 hours are easily understood in their easiest and most elementary aspect. A more complete account of the matter it will be wisest not to attempt. Suffice it to say that the difficulties soon become formidable when the inertia of the water its natural time of oscillation the varying obliquity of the moon to the elliptic its varying distance and the disturbing action of the sun are taken into consideration. When all these things are included the problem becomes to ordinary minds overwhelming. A great many of these difficulties were successfully attacked by Laplace. Others remain for modern philosophers among whom are Sir George Airy, Sir William Thompson and Professor George Darwin. I may just mention that the main and simplest effect of including the inertia or momentum of the water is to dislocate the obvious and simple connection between high water and high moon. Inertia always tends to make an effect differ in phase by a quarter period from the cause producing it as may be illustrated by a swinging pendulum. Hence high water is not to be expected when the tide raising force is a maximum but six hours later so that considering inertia and neglecting friction there would be low water under the moon. Including friction something near the equilibrium state of things occurs. With sufficient friction the motion becomes deadbeat again. That is follows closely the force that causes it. Returning to the elementary discussion we see that the rotation of the earth with respect to the Humps will not be performed in exactly 24 hours. Because the Humps are traveling slowly after the moon and will complete a revolution in a month in the same direction as the earth is rotating. Hence a place on the earth has to catch them up. And so each high tide arrives later and later each day. Roughly speaking an hour later for each day tide. Not by any means a constant interval because of superimposed disturbances not here mentioned but on the average about 50 minutes. We see then that as a result of all this we get a pair of Humps traveling all over the surface of the earth about once a day. If the earth were all ocean and in the southern hemisphere it is nearly all ocean then they would go traveling across the earth tidal waves 3 feet high and constituting the mid ocean tides. But in the northern hemisphere they can only thus journey a little way without striking land. As the moon rises at a place on the east shores of the Atlantic for instance the waters begin to flow in towards this place or the tide begins to rise. This goes on till the moon is overhead and for some time afterwards when the tide is at its highest. The hump then follows the moon in its apparent journey across to America and there precipitates itself upon the coast rushing up all the channels and constituting the land tide. At the same time the water is dragged away from the east shores and so our tide is at its lowest. The same thing repeats itself in a little more than 12 hours again when the other hump passes over the Atlantic as the moon journeys beneath the earth and so on every day. In the free southern ocean where land obstruction is comparatively absent the water gets up a considerable swing by reason of its accumulated momentum and this modifies and increases the open ocean tides there. Also for some reason I suppose because of the natural time of swing of the water one of the humps is there usually much larger than the other and so places in the Indian and other offshoots of the southern ocean get their really high tide only once every 24 hours. These southern tides are in fact much more complicated than those the British Isles receive. Ours are singularly simple. No doubt some trace of the influence of the southern ocean is felt in the North Atlantic but any ocean extending over 90 degrees of longitude is big enough to have its own tides generated and I imagine that the main tides we feel are thus produced on the spot and that they are simple because the damping out being vigorous and accumulated effects small we feel the tide producing forces more directly but for authoritative statements on tides other books must be read I have thought and still think it best in an elementary exposition to begin by a consideration of the tide generating forces as if they acted on a non-rotating earth. It is the tide generating forces and not the tides themselves that are really represented in figures 112 and 114 the rotation of the earth then comes in as a disturbing cause a more complete exposition would begin with the rotating earth and would superpose the attraction of the moon as a disturbing cause treating it as a problem in planetary perturbation the ocean being a sort of satellite of the earth this treatment introducing inertia but ignoring friction and land obstruction gives low water in the line of pull and high water at right angles or where the pull is zero in the same sort of way as a pendulum bob is highest where most pulling it down and lowest where no force is acting on it for a clear treatment of the tides as due to the perturbing forces of sun and moon see a little book by Mr. TK Abbott of Trinity College Dublin if the moon were the only body that swung the earth round this is all that need be said in an elementary treatment but it is not the only one the moon swings the earth round once a month the sun swings it round once a year the circle of swing is bigger but the speed is so much slower that the protuberance produced is only one-third of that caused by the monthly world that is the simple solar tide in the open sea without taking momentum into account is but a little more than a foot high while the simple lunar tide is about three feet when the two agree we get a spring tide of four feet when they oppose each other we get a knee tide of only two feet they assist each other at full moon and at new moon at half moon they oppose each other so we have spring tides regularly once a fortnight with knee tides in between figure 114 gives the customary diagrams to illustrate these simple things you see that when the moon and sun act at right angles that is at every half moon the high tides of one coincide with the low tides of the other and so as a place is carried round by the earth's rotation it always finds either solar or else lunar high water only experiences the differences of their two effects whereas when the sun and moon act in the same line as they do at new and full moon their high and low tides coincide and a place feels their effects added together the tide then rises extra high and falls extra low utilizing these principles a very elementary form of tidal clock or tide predictor can be made and for an open co-station it really would not give the tide so very badly it consists of a sort of clock face with two hands one nearly three times as long as the other the shorthand C A should revolve round C once in 12 hours and the vertical height of its end A represents the height of the solar tide on the scale of horizontal lines ruled across the face of the clock the long hand A B should revolve round A once in 12 hours and 25 minutes and the height of its end B if A were fixed on the zero line would represent the lunar tide the two revolutions are made to occur together either by means of a link work parallelogram or what is better in practice by a string and pulleys as shown and the height of the end point B of the third side or resultant CB read off a scale of horizontal parallel lines behind represents the combination or actual tide at the place every fortnight the two will agree and you will get spring tides of maximum height C A plus A B every other fortnight the two will oppose and you will get knee tides of maximum height C A minus A B such a clock if set properly and driven in the ordinary way would then roughly indicate the state of the tide whenever you chose to look at it and read the height of its indicating point it would not indeed be very accurate especially for such an enclosed station as Liverpool is and that is probably why they are not made a great number of disturbances some astronomical some terrestrial have to be taken into account in the complete theory it is not an easy matter to do this but it can be and has been done and a tide predictor has not only been constructed but two of them are in regular work predicting the tides for years hence one the property of the Indian government for co-stations of India the other for various British and foreign stations wherever the necessary preliminary observations have been made these machines are the invention of Sir William Thompson the tide tables for Indian ports are now always made by means of them the first thing to be done by any port which wishes its tides to be predicted is to set up a tide gauge or automatic recorder and keep it working for a year or two the tide gauge is easy enough to understand it marks the height of the tide at every instant by an irregular curve line like a barometer chart figure 117 observational curves so obtained have next to be fed into a fearfully complex machine which it would take a whole lecture to make even partially intelligible but figure 118 shows its aspect it consists of 10 integrating machines in a row coupled up and working together this is the harmonic analyzer and the result of passing the curve through this machine is to give you all the constituents of which it is built up namely the lunar tide the solar tide and eight of the sub tides or disturbances these 10 values are then set off into a third machine the tide predictor proper the general mode of action of this machine is not difficult to understand it consists of a string wound over and under a set of pulleys which are each set on an eccentric so as to have an up and down motion these up and down motions are all different and there are 10 of these movable pulleys which by their respective excursions represent the lunar tide the solar tide and the eight disturbances already analyzed out of the tide gauge curve by the harmonic analyzer one end of the string is fixed the other carries a pencil which writes a trace on a revolving drum of paper a trace which represents the combined motion of all the pulleys and so predicts the exact height of the tide at the place at any future time you like the machine can be turned quite quickly so that a year's tides can be run off with every detail in about half an hour this is the easiest part of the operation nothing has to be done but to keep it supplied with paper and pencil and turn a handle as if it were a coffee mill instead of a tide mill figures 119 and 120 my subject is not half exhausted I might go on to discuss the question of tidal energy whether it can ever be utilized for industrial purposes and also the very interesting question once it comes tidal energy is almost the only terrestrial form of energy that does not directly or indirectly come from the sun the energy of tides is now known to be obtained at the expense of the earth's rotation and accordingly our day must be slowly very slowly lengthening the tides of past ages have destroyed the moon's rotation and so it always turns the same face to us there is every reason to believe that in geologic ages the moon was nearer to us than it is now and that accordingly the tides were then far more violent rising some hundreds of feet instead of 20 or 30 and sweeping every six hours right over the face of a country plowing down hills denuding rocks and producing a copious sedimentary deposit and thus discovering the probable violent tides of past ages astronomy has within the last few years presented geology with the most powerful denuding agent known and the study of the earth's past history failed to be greatly affected by the modern study of the intricate and refined conditions attending prolonged tidal action on incompletely rigid bodies read on this point the last chapter of Sir our balls story of the heavens I might also point out that the magnitude of our terrestrial tides enables us to answer the question as to the internal fluidity of the earth it used to be thought that the earth's crust was comparatively thin and that it contained molten interior we now know that this is not the case the interior of the earth is hot indeed but it is not fluid or at least if it be fluid the amount of fluid is but very small compared with the thickness of the unyielding crust all these and a number of other most interesting questions fringe the subject of the tides the theoretical study of which started by newton has developed and is destined in the future to further develop into one of the most gigantic and absorbing investigations having to do with the stability or instability of solar systems and with the construction and decay of universes these theories are the work of pioneers now living whose biographies it is therefore unsuitable for us to discuss nor shall I constantly mention their names but hemholz and Thompson are household words and you well know that in them and their disciples the race of pioneers maintains its ancient glory and of lecture 17