 Lecture 9 of Pioneers of Science. This is LibriVox Recording. All LibriVox recordings are in the public domain. To learn more about LibriVox or to volunteer, visit LibriVox.org. Recording by John Thomas Kuzmursky. Pioneers of Science by Sir Oliver Lodge. Lecture number 9. Notes for lecture 9. The Principia published 1687. Newton died 1727. The law of gravitation. Every particle of matter attracts every other particle of matter with a force proportional to the mass of each and the inverse square of the distance between them. Some of Newton's deductions. One, Kepler's second law. Equal description of areas proves that each planet is acted on by a force directed towards the sun as a center of force. Two, Kepler's first law proves that this central force diminishes in the same proportion as the square of the distance increases. Three, Kepler's third law proves that all the planets are acted on by the same kind of force of an intensity depending on the mass of the sun. Four, so by knowing the length of year and distance of any planet from the sun, the sun's mass can be calculated in terms of that of the earth. Five, for the satellites, the force acting depends on their mass and their central body, a planet. Hence, the mass of any planet possessing a satellite becomes known. Six, the force constraining the moon in her orbit is the same gravity as gives terrestrial bodies their weight and regulates the motion of projectiles. Because, while a stone drops 16 feet in a second, the moon, which is 60 times as far from the center of the earth, drops 16 feet in a minute. Seven, the moon is attracted not only by the earth but also by the sun. Hence, its orbit is perturbed and Newton calculated out the chief of these perturbations. These are the equation of the center discovered by Hipparchus. A, the eviction discovered by Hipparchus and Ptolemy. B, the variation discovered by Tycho Brahe. Seven, the annual equation discovered by Tycho Brahe. D, the retroaggression of the nodes then being observed at Greenwich by Flamsteed. E, the variation of inclination then being observed at Greenwich by Flamsteed. F, the progression of the apsees with an air of one half. G, the inequality of apogee previously unknown. H, the inequality of nodes previously unknown. Eight, each planet is attracted not only by the sun but by the other planets. Hence, their orbits are slightly affected by each other. Newton began the theory of planetary perturbations. He recognized the comments as members of the solar system, obedient to the same law of gravity and moving in very elongated ellipses so their return could be predicted. Example, Haley's Comet. Ten, applying the idea of centrifugal force to the earth considered as a rotating body, he perceived that it could not be a true sphere and calculated its oblateness, obtaining 28 miles greater equatorial than polar diameter. Eleven, conversely, from the observed shape of Jupiter or any planet the length of its day could be estimated. Twelve, the so calculated shape of the earth in combination with centrifugal force causes the weight of bodies to vary with latitude and Newton calculated the amount of this variation, 194 pounds, at pole balance 195 pounds at equator. Thirteen, a homogenous sphere attracts as if its mass were concentrated at its center. For any other figure, such as an oblate spheroid, this is not exactly true. A hollow concentric spherical shell exerts no force on small bodies inside it. Fourteen, the earth's equatorial protuberance being acted on by the attraction of the sun and moon must disturb its axis of rotation in a calculated manner and thus is produced the procession of the equinoxes. The attraction of the planets on the same protuberance causes a smaller and rather different kind of procession. Fifteen, the waters of the ocean are attracted towards the sun and moon on one side and world a little further away than the solid earth on the other side, hence Newton explained all the main phenomena of the tides. Sixteen, the sun's mass being known, he calculated the height of the solar tide. Seventeen, from the observed heights of spring and deep tides, he determined the lunar tide and thence made an estimate of the mass of the moon. Reference table of numerical data, masses in solar systems, Mercury 0.065, Venus 0.885, Earth 1, Mars 0.108, Jupiter 300.8, Saturn 89.7, the sun 316,000, the moon about 0.012, height dropped by a stone in first second. Mercury 7 feet, Venus 15.8 feet, Earth 16.1 Mars 6.2 feet, Jupiter 45.0 feet, Saturn 18.4 feet, the sun 436.0 feet, the moon 3.7 feet, length of day or time of rotation. Mercury 24 hours, Venus 23.5 hours, Earth 24 hours, Mars 24.5 hours, Jupiter 10 hours, Saturn 10.5 hours, the sun 608 hours, the moon 702 hours, the mass of the Earth taken above as unity is 6,000 trillion tons. Observatories. Uraniburg flourished from 1576 to 1597. The Observatory of Paris was founded in 1667, Greenwich Observatory in 1675. Astronomers Royale, Flamsteed, Haley, Bradley, Bliss, Maskeline, Pond, Airy, Christie. Lecture number nine, Newton's Principia. The law of gravitation above enunciated in conjunction with the laws of motion rehearsed at the end of the preliminary notes of lecture seven, now supersedes the laws of Kepler and includes them as special cases. The more comprehensive law enables us to criticize Kepler's laws from a higher standpoint to see how far they are exact and how far they are only approximations. They are, in fact, not precisely accurate, but the reason for every discrepancy now becomes abundantly clear and can be worked out by the theory of gravitation. We may treat Kepler's laws either as immediate consequences of the law of gravitation or as the known facts upon which that law was founded. Historically, the latter is the more natural plan and it is thus that they are created in the first three statements of the above notes, but each proposition may be worked inversely and we might state them thus. One, the fact that the force acting on each planet is directed to the sun necessitates the equitable description of areas. Two, the fact that the force varies as the inverse square of the distance necessitates motion in an ellipse or some other conic section with the sun in one focus. Three, the fact that one attracting body acts on all the planets with an inverse square law causes the cubes of their mean distances to be proportional to the squares of their periodic times. Not only these, but a multitude of other deductions follow rigorously from the simple datum that every particle of matter attracts every other particle with a force directly proportional to the mass of each and to the inverse square of their mutual distance. Those dealt with in the Principia are summarized above and it will be convenient to run over them in order with the object of giving some idea of the general meaning of each without attempting anything to intricate to be readily intelligible. Number one, Kepler's second law, equitable description of areas, proves that each planet is acted on by a force directed toward the sun as a center of force. The equitable description of areas about a center of force has already been fully though briefly established. It is undoubtedly of fundamental importance and is the earliest instance of the serious discussion of central forces i.e. of forces directed always to a fixed center. We may put it afresh thus. O A has been the motion of a particle in a unit of time. At A it receives a knock towards C, whereby in the next unit it travels along A D instead of A B. Now the area of the triangle C A D swept out by the radius vector in the unit time is one half B H, one half base time site, H being the perpendicular height of the triangle from the base A C. Now the blow at A being along the base has no effect upon H and consequently the area remains just what it would have been without the blow. A blow directly to any point other than C would at once alter the area of the triangle. One interesting deduction may at once be drawn. If gravity were a radiant force emitted from the sun with a velocity like that of light the moving planet would encounter it at a certain apparent angle, aberration, and the force experienced would come from a point a little in advance of the sun. The rate of description of areas would thus tend to increase, whereas in reality it is constant. Hence the force of gravity, if it travel at all, does so with a speed far greater than that of light. It appears to be practically instantaneous. CF modern views of electricity, 126 end of chapter 12. Again anything like a retarding effect of the medium through which the planets move would constitute a tangential force entirely undirected towards the sun. Hence no such frictional or retarding force can appreciably exist. It is however conceivable that both these effects might occur and just neutralize each other. The neutralization is unlikely to be exact for all the planets and the fact is that no trace of either effect has yet been discovered. The planets are however subject to focuses not directed towards the sun vis-a-vis their attractions for each other and these perturbing forces do produce a slight discrepancy from Kepler's second law, but a discrepancy which is completely subject to calculation. Number two, Kepler's first law proves that this central force diminishes in the same proportion as the square of the distance increases. To prove the connection between the inverse square law of distance and the traveling in a conic section with the center of force in one focus the other focus being empty is not so simple. It obviously involves some geometry and must therefore be left to properly armed students. It may be useful to state that the inverse square law of distance although the simplest possible law for force emanating from a point or sphere is not to be regarded as self-evident or as needing no demonstration. The force of a magnetic pole on a magnetized steel scrap for instance varies as the inverse cube of the distance and the curve described by such a particle would be quite different from a conic section. It would be a definite class of spiral called Coates's spiral again on an iron filing the force of a single pole might vary more nearly as the inverse fifth power and so on. Even when the thing concerned is radiant in straight lines like light the law of inverse squares is not universally true its truth assumes first that the source is a point or sphere next that there is no reflection or refraction of any kind and lastly that the medium is perfectly transparent the law of inverse squares by no means holds from a prairie fire for instance or from a lighthouse or from a street lamp in a fog. Mutual perturbations especially the pole of Jupiter prevent the path of a planet from being really and truly an ellipse or indeed from being any simple re-entrant curve moreover when a planet possesses a satellite it is not the center of the planet whichever attempts to describe the Kaplerian ellipse but it is the common center of gravity of the two bodies thus in the case of the earth and moon the point which really does describe a close attempt to an ellipse is a point displaced about 3000 miles from the center of the earth towards the moon and is therefore only 1000 miles beneath the surface. Number three Kapler's third law proves that all the planets are acted on by the same kind of force of an intensity depending on the mass of the sun the third law of Kapler although it requires geometry to state and establish it for elliptic motion for which it holds just as well as it does for circular motion is very easy to establish for circular motion by anyone who knows about centrifugal force if m is the mass of a planet v its velocity or the radius of its orbit and t the time of describing it 2 pi r equals the t and the centripetal force needed to hold it in its orbit is m v squared over r or 4 pi squared m r over t squared now the force of gravitative attraction between the planet and the sun is gamma ms over r squared where gamma is a fixed quantity called the gravitation constant to be determined if possible by experiment once for all now expressing the fact that the force of gravitation is the force holding the planet in we write 4 pi squared m r over t squared equals gamma ms over r squared whence by the simplest algebra r cubed m r over t squared equals gamma s over 4 pi squared the mass of the planet has been cancelled out the mass of the sun remains multiplied by the gravitation constant and is seen to be proportional to the cube of the distance divided by the square of the periodic time a ratio which is therefore the same for all planets controlled by the sun hence knowing r and t for any single planet the value of gamma s is known number four so by knowing the length of year and distance of any planet from the sun the sun's mass can be calculated in terms of that of the earth number five for the satellites the force acting depends on the mass of their central body a planet hence the mass of any planet possessing a satellite becomes known the same argument holds for any other system controlled by a central body for instance for the satellites of jupiter only instead of s it will be natural to write j as meaning the mass of jupiter hence knowing r and t for any one satellite of jupiter the value of gamma j is known apply the argument also to the case of moon and earth knowing the distance and time revolution of our moon the value of gamma e is at once determined e being the mass of the earth hence s and j and in fact the mass of any central body possessing a visible satellite are now known in terms of e the mass of the earth or what is practically the same thing in terms of gamma the gravitation constant observe that so far none of these qualities are known absolutely their relative values are known and are tabulated at the end of the notes above but the finding of their absolute values is another matter which we must defer but it may be asked if kepler's third law only gives us the mass of a central body how is the mass of a satellite to be known well it is not easy the mass of no satellite is known with much accuracy their mutual perturbations give us some data in the case of the satellites of jupiter but to our own moon this method is of course inapplicable our moon perturbs at first sight nothing and accordingly its mass is not even yet known with exactness the mass of comets again is quite unknown all that we can be sure of is that they are smaller than a certain limit else they would perturb the planets they pass near nothing of this sort has ever been detected they are themselves perturbed plentifully but they perturb nothing hence we learn that their mass is small the mass of a comet may indeed be a few million or even billion tons but is quite small in astronomy but now it may be asked surely the moon perturbs the earth swinging it around their common center of gravity and really describing its own orbit about this point instead of about the earth's center yes that is so and the more precise consideration of kepler's third law enables us to make a fair approximation to the position of this common center of gravity and thus practically to weigh the moon i.e to compare its mass with that of the earth for their masses will be inversely as their respective distances from the common center of gravity or balancing point on the simple steel yard principle hitherto we have not troubled ourselves about the precise point about which the revolution occurs but kepler's third law is not precisely accurate unless it is attended to the bigger the revolving body the greater is the discrepancy and we see in the table preceding lecture three on page 57 that jupiter exhibits an error which though very slight is greater than that of any of the other planets when the sun is considered the fixed center let the common center of gravity of earth and moon be displaced a distance x from the center of the earth then the moon's distance from the real center of revolution is not r but r minus x and the revolution of centrifugal force to gravitative attraction is strictly four pi squared over t squared times r minus x equals gamma e over r squared instead of what is in the text above and this gives a slightly modified third law from this equation if we have any distinct method of determining gamma e and the next section gives such a method we can calculate x and thus roughly weigh the moon since r minus x over r equals e over e plus m but to get anything like a reasonable result the data must be very precise number six the force constraining the moon in her orbit is the same gravity as gives terrestrial bodies their weight and regulates the motion of projectiles here we come to the newtonian verification already several times mentioned but because of its importance i will repeat it in other words the hypothesis to verify is that the force acting on the moon is the same kind of force as acts on bodies we can handle and weigh and which gives them their weight now the weight of a mass m is commonly written mg where g is the intensity of terrestrial gravity a thing easily measured being indeed numerically equal to twice the distance of a stone drops in the first second of freefall see table page 205 hence expressing the weight of a body is due to gravity and remembering that the center of the earth's attraction is distant from us by one earth's radius r we can write mg equals gamma me over r squared or gamma e equals gr squared equals 95522 cubic miles per second per second but we already know gamma e in terms of the moon's motion as for pi squared r cubed over r squared approximately more accurately see proceeding note this quantity is gamma parentheses e plus m and parentheses and bracket hence we can easily see if the two determinations of this quantity agree all the deductions are fundamental and may be considered as the foundation of the principia it was these that flashed upon newton during that moment of excitement when he learned the real size of the earth and discovered his speculations to be true the next all elaborations and amplifications of the theory such as in ordinary times are left for subsequent generations of theorists to discover and work out newton did not work out these remote or consequences of his theory completely by any means the astronomical and mathematical world has been working them out ever since but he carried the theory a great way and here it is that his marvel's power is most conspicuous it is this treatment of number seven the perturbations of the moon that perhaps most especially has struck all future mathematicians with amazement number seven number fourteen number fifteen these are the most inspired of the whole number seven the moon is attracted not only by the earth but by the sun also hence its orbit is perturbed and newton calculated out the chief of these perturbations now running through the perturbations page two or three in order the first is in parentheses because it is near eccentricity it is not a true perturbation at all and more properly belongs to kepler a the first true perturbation is what told me called the eviction the principal part of which is a periodic change in the ellipticity or eccentricity of the moon's orbit owing to the pull of the sun it is a complicated matter and newton only partially solved it i shall not attempt to give an account of it be the next the variation is a much simpler affair it is caused by the fact that as the moon revolves around the earth it is half the time nearer to the sun than the earth is and so gets pulled more than the average while for the other fortnight it is further from the sun than the earth is and so gets pulled less for the week during which it is changing from a decreasing half to a new moon it is moving in the direction of the extra pull and hence becomes new sooner than would have been expected all next week it is moving against the same extra pull and so arrives at quadrature half moon somewhat late for the next fortnight it is in the region of to lick a pull the earth gets pulled more than it does the effect of this is to hurry it up for the third week so that the full moon occurs a little early and to retard it for the fourth week so that the decreasing half moon like the increasing half occurs behind time again thus each scissors g as new and full or technically called is too early each quadrature is too late the maximum hurrying and slackening force being felt at the octance or intermediate 45 degree points see the annual equation is a fluctuation introduced into the other perturbations by reason of the varying distance of the disturbing body the sun at different seasons of the year its magnitude plainly depends simply on the eccentricity of the earth's orbit both these perturbations b and c newton worked out completely d and e next come the retrogression of the nodes and the variation of the inclination which at the time were being observed at rinich by flamsteed from whom newton frequently but vainly begged for data that he might complete their theory while he had his mind upon it fortunately hallie succeeded flamsteed as astronomer royal c list at end of notes above and then newton would have no difficulty in gaining such information as the national observatory could give the inclination meant is the angle between the plane of the moon's orbit and that of the earth the plane of the earth's orbit round the sun is called the elliptic the plane of the moon's orbit round the earth is inclined to it at a certain angle which is slowly changing though in a periodic manner imagine a curtain ring bisected by a sheet of paper and tilted to a certain angle it may be likened to the moon's orbit cutting the plane of the elliptic the two points at which the plane is cut by the ring are called nodes and these nodes are not stationary but are slowly regressing i.e. traveling in a direction opposite to that of the moon itself also the angle of tilt is varying slowly oscillating up and down in the course of centuries f the two points in the moon's elliptical orbit where it comes nearest to or farthest from the earth i.e. the points at the extremity of the long axis of the ellipse are called separately perigee and apogee or together the apces now the pull of the sun causes the whole orbit to slowly revolve in its own plane and consequently these apces progress so that the true path is not quite a closed curve but a sort of spiral with elliptic loops but here comes in a striking circumstance newton states with reference to this perturbation that theory only counts for one and a half degrees per annum whereas observation gives three degrees or just twice as much this is published in the principia as a fact without comment it was for long regarded as a very curious thing and many great mathematicians afterwards tried to find an air in the working de limberre clareau and others attacked the problem but were led to just the same result it constituted the great outstanding difficulty in the way of accepting theory of gravitation it was suggested that perhaps the inverse square law was only a first approximation that perhaps a more complete expression such as a over r squared plus b over r to the fourth must be given for it and so on ultimately clareau took into account a whole series of neglected terms and it came out correct thus verifying the theory but the strangest part of this tale is to come for only a few years ago professor adams of cambridge nettoon adams as he is called was editing various old papers of newtons now in the possession of the duke of portland and he found manuscripts bearing on this very point and discovered that newton had reworked out the calculations himself had found the cause of the error had taken into account the terms hitherto neglected and so 50 years before clareau had completely though not publicly solved this long outstanding problem of the progression of the absces g and h two other inequalities he calculated out and predicted these variation in the motions of the absces and the nodes neither of these had then been observed and they were afterwards detected and verified a good many other minor irregularities are now known some 30 i believe and altogether the lunar theory or problem of the moon's exact motion is one of the most complicated and difficult in astronomy the perturbations being so numerous and large because of the enormous mass of the perturbing body the disturbances experienced by the planets are much smaller because they are controlled by the sun and perturbed by each other the moon is controlled only by the earth and perturbed by the sun planetary perturbations can be treated as a series of disturbances with some satisfaction not so those of the moon and yet it is the only way at present known of dealing with the lunar theory to deal with it satisfactorily would demand the solution of such a problem as this given three rigid spherical masses thrown into empty space with any initial motions whatever and abandoned to gravity to determine their subsequent motions with two masses the problem is simple enough being pretty well summed up in kepler's laws but with three masses strange to say it is so complicated as to be beyond the reach of even modern mathematics it is a famous problem known as that of the three bodies it has not yet been solved even when it is solved it will be only a close approximation to the case of the earth moon and sun for these bodies are not spherical and are not rigid one may imagine how absurdly and hopelessly complicated a complete treatment of the motions of the entire solar system would be number eight each planet is attracted not only by the sun but by the other planets hence their orbits are slightly affected by each other the subject of planetary perturbation was only just begun by newton gradually by laplace and others the theory became highly developed and as everybody knows in 1846 neptune was discovered by means of it number nine he recognized the comets as members of the solar system obedient to the same law of gravity and moving in very elongated ellipses so their return could be predicted it was a long time before newton recognized the comets as real members of the solar system and subject to gravity like the rest he at first thought they moved in straight lines it was only in the second edition of the principia that the theory of comets was introduced hailey observed a fine comet in 1682 and calculated its orbit in newtonian principles he also calculated when it ought to have been seen in past times and he found the year 1607 when one was seen by kepler also the year 1531 when one was seen by apion again he reckoned 1456 1380 1305 all these appearances were the same comet in all probability returning every 75 or 76 years the period was easily allowed to be not exact because of perturbing planets he then predicted its return for 1758 or perhaps 1759 a date he could not himself hope to see he lived to a great age but he died 16 years before this date as the time drew nigh three quarters of a century afterwards astronomers were greatly interested in this first cometary prediction and kept an eager lookout for hailey's comet claireau a most eminent mathematician and student of newton proceeded to calculate out more exactly the perturbing influence of jupiter near which it had passed after immense labor for the difficulty of the calculation was extreme and the mass of mere figures something pretentious he predicted its return of the 13th of april 759 but he considered that he might have made a possible air of a month it returned on the 13th of march 1759 and established beyond all doubt the rule of the newtonian theory over comets number 10 applying the idea of centrifugal force to the earth considered as a rotating body he perceived that it could not be a true sphere and calculated its oblateness obtaining 28 miles greater equatorial than polar diameter here we return to one of the more simple deductions a spinning body of any kind tends to swell at its circumference or equator and shrink along its axes or poles if the body is of yielding material its shape must alter under the influence of centrifugal force and if a globe of yielding substance subject to known forces rotates at a different pace its shape can be calculated thus a plastic sphere the size of the earth held together by its own gravity and rotating once a day can be shown to have its equatorial diameter 28 miles greater than its polar diameter the two diameters being 8000 and 8028 respectively now we have to guarantee that the earth is of yielding material for all newton could tell it might be extremely rigid as a matter of fact it is now very nearly rigid but he argued thus the water on it is certainly yielding and although the solid earth might decline to bulge at the equator in deference to the diurnal rotation that would not prevent the ocean from flowing from the poles to the equator and piling itself up as an equatorial ocean 14 miles deep leaving dry land everywhere near either pole nothing of this sort is observed the distribution of land and water is not thus regulated hence whatever the earth may be now it must once have been plastic enough to accommodate itself perfectly to the centrifugal forces and to make the shape appropriate to a perfectly plastic body in all probability it was once molten and for long afterwards pasty thus then the shape of the earth can be calculated from the length of its day and the intensity of its gravity the calculation is not difficult it consists in imagining a couple of holes bored to the center of the earth one from a pole and one from the equator filling these both with water and calculating how much higher the water will stand in one leg of the gigantic v-tube so formed then in the other the answer comes out about 14 miles the shape of the earth can now be observed geodetically and in accordance with calculation but the observations are extremely delicate in Newton's time the size was only barely known the shape was not observed too long after but on the principles of mechanics combined with a little common sense reasoning it could be calculated with certainty and accuracy number 11 from the observed shape of jupiter or any planet the length of its day could be estimated jupiter is much more oblate than the earth its two diameters are to one another as 17 is to 16 the ellipticity of its disk is manifest to simple inspection hence we perceive that its whirling action must be more violent it must rotate quicker as a matter of fact its day is 10 hours long five hours daylight and five hours night the times of rotation of other bodies in the solar system are recorded in a table above number 12 the so calculated shape of the earth in combination with centrifugal force causes the weight of bodies to vary with latitude and newton calculated the amount of this variation 194 pounds at pole balance 195 pounds at equator but following the calculated shape of the earth followed several interesting consequences first of all the intensity of gravity will not be the same everywhere for at the equator a stone is further from the average bulk of the earth say the center then it is at the poles and owing to this fact a mass of 590 pounds at the pole would suffice to balance 591 pounds at the equator if the two could be placed in the pans of a gigantic balance who is being straddled along an earth's quadrant this is a true variation of gravity due to the shape of the earth but besides this there is a still larger apparent variation due to centrifugal force which affects all bodies at the equator but not those at the poles from this cause even if the earth were a true sphere yet if it were spinning at its actual pace 288 pounds at the pole would balance 289 pounds at the equator because at the equator the true weight of the mass would not be fully appreciated centrifugal force would virtually diminish it by one 289th of its amount in actual fact both causes coexist and accordingly the total variation of gravity observed is compounded of the real and apparent effects the result is that 194 pounds at a pole weighs as much as 195 pounds at the equator number 13 a homogenous sphere attracts as if its mass were concentrated at its center for any other figure such as an ablate spheroid this is not exactly true a hollow concentric spherical shell exerts no force on small bodies inside it a sphere composed of uniform material or of materials arranged in concentric strata can be shown to attract external bodies as if its mass were concentrated at its center a hollow sphere similarly composed does the same but on internal bodies it exerts no force at all hence at all distances above the surface of the earth gravity decreases in inverse proportion as the square of the distance from the center of the earth increases but if you descend a mine gravity decreases in this case also as you leave the surface though not at the same rate as when you went up for as you penetrate the crust you get inside a concentric shell which is thus powerless to act upon you and the earth you are now outside is a smaller one at what rate the force decreases depends on the distribution of density if the density were uniform all through the law of variation would be the direct distance otherwise it would be more complicated anyhow the intensity of gravity is a maximum at the surface of the earth and decreases as you travel from the surface either up or down number 14 the earth's equatorial protuberance being acted on by the attraction of the sun and moon must disturb its axis of rotation in a calculated manner and thus is produced the procession of the equinoxes here we come to a truly awful piece of reasoning a sphere attracts as if its mass were concentrated at its center number 12 but a spheroid does not the earth is a spheroid and hence it pulls and is pulled by the moon with a slightly uncentric attraction in other words the line a pole does not pass through its precise center now when we have a spinning body say a top overloaded on one side so the gravity acts on it unsymmetrically what happens the axis of rotation begins to rotate cone-wise at a pace which depends on the rate of spin and on the shape and mass of the top as well as on the amount of leverage of the overloading newton calculated out the rapidity of this conical motion of the axis of the earth produced by the slightly unsymmetrical pole of the moon and found that it would complete a revolution in 26 000 years precisely what was wanted to explain the procession of the equinoxes in fact he had discovered the physical cause of that procession observe that there were three stages in this discovery of procession first the observation of Hipparchus that the nodes or intersections of the earth's orbit the sun's apparent orbit with the plane of the equator were not stationary but slowly moved second the description of this motion by Copernicus by the statement that it was due to a conical motion of the earth's axis of rotation about its center as a fixed point third the explanation of this motion by newton as due to the pole of the moon on the equatorial protuberance of the earth the explanation could not have been previously suspected for the shape of the earth on which the whole theory depends was entirely unknown till newton calculated it another and smaller motion of a somewhat similar kind has been worked out since it is due to the unsymmetrical attraction of the other planets for the same equatorial protuberance it shows itself a periodic change in the obliquity of the ecliptic or so-called recession of the apsis rather than as a motion of the nodes number 15 the waters of the ocean are attracted towards the sun and moon on one side and world a little farther away than the solid earth on the other side hence newton explained all the main phenomena of the tides and now comes another tremendous generalization the tides had long been an utter mystery coupler likens the earth to an animal and the tides to his breathings and in breathings and says they follow the moon gallio chafes him for this and says that it is mere superstition to connect the moon with the tides the cart said the moon pressed down upon the waters by the centrifugal force of its vortex and so produced a low tide under it everything was fog and darkness on the subject the legend goes that an astronomer threw himself into the sea in despair of ever being able to explain the flux and reflux of its waters newton now with consummate skill applied his theory to the effect of the moon upon the ocean and all the main details of title action gradually revealed themselves to him he treated the water rotating with the earth once a day somewhat as if it were a satellite acted on by perturbing forces the moon as it revolves around the earth is perturbed by the sun the ocean as it revolves around the earth being held on by gravitation just as the moon is is perturbed by both sun and moon the perturbing effect of a body varies directly as its mass and inversely as the cube of its distance the simple law of inverse square does not apply because a perturbation is a differential effect the satellite or ocean when nearer to the perturbing body than the rest of the earth is attracted more and when further off it is attracted less than is the main body of the earth and it is these differences alone which constitute the perturbation the moon is the more powerful of the two perturbing bodies hence the main tides are due to the moon and its chief action is to cause a pair of low waves or oceanic humps of gigantic area to travel around the earth once in a lunar day i.e. in about 24 hours and 50 minutes the sun makes a similar but still lower pair of low elevations to travel around once in a solar day of 24 hours and the combination of the two pairs of humps thus periodically overtaking each other accounts for the well-known spring and neap tides spring tides when their maxima agree neap tides when their maximum of one coincides with the minimum of the other each of which events happens regularly once a fort's night these are the main effects but besides these there are the effects of varying distances obliquity to be taken into account and so we have a whole series of minor disturbances very like those discussed in number seven under the lunar theory but more complex still because there are two perturbing bodies instead of only one the subject of the tides is therefore very recondite and though one may give some elementary account of its main features it will be best to defer this to a separate lecture lecture 17 i had better however hear say that newton did not limit himself to the consideration over the primary oceanic humps he pursued the subject into geographical detail he pointed out that although the rise and fall of the tide at mid ocean islands would be but small yet on stretches of coast the wave would fling itself and by its momentum would propel the waters to a much greater height for instance 20 or 30 feet especially in some funnel shaped openings like the bristol channel and the bay of fundy where the contrated impetus of the water is enormous he also showed how the tidal waves reached different stations in successive regular order each day and how some places might be fed with tide by two distinct channels and that if the time of these channels happen to differ by six hours a high tide might be arriving by one channel and a low tide by the other so that the place would only feel the difference and so have a very small observed rise and fall insensing a port in china in the gulf of tongquan where that approximately occurs in fact although his theory was not as we now know complete or final yet it satisfactorily explained a mass of intricate detail as well as the main features of the tides number 16 the sun's mass being known he calculated the height of the solar tide number 17 from the observed heights of spring and deep tides he determined the lunar tide and then made an estimate of the mass of the moon knowing the sun's mass and distance it was not difficult for newton to calculate the height of the protuberance caused by it in a pasty ocean covering the whole earth i say pasty because if there was any tendency for impulses to accumulate as timely pushes to a pendulum accumulate the amount of disturbance might become excessive and its calculation would involve a multitude of data the newtonian tide ignored this thus practically treating the motion as either deadbeat or else the impulses as very inadequately timed with this reservation the mid ocean tide due to the action of the sun alone comes out about one foot or let us say one foot for simplicity now the actual tide observed in mid atlantic is at the springs about four feet at the neeps about two the spring tide is lunar plus solar the neat tide is lunar minus solar hence it appears that the tide caused by the moon alone must be about three feet when unaffected by momentum from this datum newton made the first attempt to approximately estimate the mass of the moon i said that the masses of satellites must be estimated if at all by the perturbation they are able to cause the lunar tide is a perturbation in the diurnal motion of the sea and its amount is therefore a legitimate mode of calculating the moon's mass the available data were not at all good however nor are they even now very perfect and so the estimate was a good way out it is now considered that the mass of the moon is about 180th that of the earth such are some of the gems extracted from their setting in the principia and presented as clearly as i'm able before you do you realize the tremendous stride in knowledge not a stride as well all says nor yet a leap but a flight which has occurred between the dim groupings of kepler the elementary truths of galer the fascinating but wild speculations of decart and this magnificent and comprehensive system of ordered knowledge to some his genius seemed almost divine does mr newton eat drink sleep like other men and the marquee de l'hôpital a french mathematician of no mean eminence i picture him to myself as a celestial genius entirely removed from the restrictions of ordinary matter to many it seemed as if there was nothing more to be discovered as if the universe were now explored and only a few fragments of truth remained for the gleaner this is the attitude of mind expressed in pope's famous epigram nature and nature's laws lay hid in night gonson let newton be and all was light this feeling of hopelessness and impotence was very natural after the advent of so overpowering a genius and it prevailed in england for fully a century it was very natural but it was very mischievous for as a consequence nothing a great moment was done by england in science and no englishmen of the first magnitude appeared till some who are either living now or who have lived within present century it appeared to his contemporaries as if he had almost exhausted the possibility of discovery but did it so appear to newton did it seem to him as if he had seen far and deep into the truths of this great and infinite universe it did not when quite an old man full of honor and renown venerated almost worshiped by his contemporaries these were his words i know not what the world will think of my labors but to myself it seems that i have been but as a child playing on the seashore now finding some pebble rather more polished and now some shell rather more agreeably very gated then another while the immense ocean of truth extended itself unexplored before me and so it must ever seem to the wisest and greatest of men when brought into contact with the great things of gone that wish they know is as nothing and less than nothing to the infinitude of which they are ignorant newton's words sound like a simple and pleasing echo of the words that the great unknown poet the writer of the book of joe lull these are parts of his ways but how little a portion is heard of him the thunder of his power who can understand end of lecture number nine recording by john thomas kutsumarski jtk ww dot valentine your life dot com lecture 10 of pioneers of science this is a leber vox recording all leber vox recordings are in the public domain for more information or to volunteer please visit leber vox dot org this recording is by mark smith of simpsonville south carolina pioneers of science by sir oliver lodge lecture 10 notes to lecture 10 science during the century after newton the precipia was published 1687 roemer 1644 to 1710 james bradley 1692 to 1762 clareau 1713 to 1765 oiler 1707 to 1783 dalemberg 1717 to 1783 lagrange 1736 to 1813 laplace 1749 to 1827 and william hershel 1738 to 1822 olaus roemer was born in yutland and studied at copenhagen assisted picard in 1671 to determine the exact position of t-shows observatory on win a company picard to paris and 1675 read before the academy his paper on successive propagation of light as revealed by a certain inequality in the motion of jupiter's first satellite in 1681 he returned to copenhagen as professor of mathematics and astronomy and died in 1710 he invented the transit instrument murals circle equatorial mounting for telescopes and most of the other principal instruments now in use in observatories he made as many observations as t-show brahe but the records of all but the work of three days were destroyed by a great fire in 1728 bradley professor of astronomy at oxford discovered the aberration of light in 1729 while examining stars for parallax and the nutation of the earth's axis in 1748 was appointed astronomer royal in 1742 lecture 10 roemer and bradley and the velocity of light at newton's death england stood preeminent among the nations of europe in the sphere of science but the preeminence did not last long two great discoveries were made very soon after his both by professor bradley of oxford and then there came a gap a moderately great man often leaves behind him a school of disciples able to work according to their master's methods and with a healthy spirit of rivalry which stimulates and encourages them newton left indeed a school of disciples but his methods of work were largely unknown to them and such as were known were too ponderous to be used by ordinary men only one fresh result and that a small one has ever been attained by other men working according to the methods of the principia the methods were studied and commented on in england to the exclusion of all others for nigh a century and as a consequence no really important work was done on the continent however no such system of slavish imitation prevailed those methods of newtons which had been simultaneously discovered by leibniz were more thoroughly grasped modified extended and improved there arose a great school of french and german mathematicians and the laurels of scientific discovery passed to france and germany more especially perhaps at this time to france england has never wholly recovered them during the present century this country has been favored with some giants who as they become distant enough for their true magnitude to be perceived may possibly stand out as great as any who have ever lived but for the mass and bulk of scientific work at the present day we have to look to germany with its enlightened government and extensive intellectual development england however is waking up and what its government does not do private enterprise is beginning to accomplish the establishment of centers of scientific and literary activity in the great towns of england though at present they are partially encumbered with the supply of education of an exceedingly rudimentary type is a movement that in the course of another century or so will be seen to be one of the most important and fruitful steps ever taken by this country on the continent such centers have long existed almost every large town is the seat of a university and they are now liberally endowed the university of balonia where you may remember capernicus learned mathematics has recently celebrated its eight hundredth anniversary the scientific history of the century after newton summarized in the above table of dates embraces the labors of the great mathematicians clareau oiler delambert and especially of lagrange and laplace but the main work of all these men was hardly pioneering work it was rather the surveying and mapping out and bringing into cultivation of lands already discovered probably her shell may be justly regarded as the next true pioneer we shall not however properly appreciate the stages through which astronomy has passed nor shall we be prepared adequately to welcome the discoveries of modern times unless we pay some attention to the intervening age moreover during this era several facts of great moment gradually came into recognition and the importance of the discovery we have now to speak of can hardly be overestimated our whole direct knowledge of the planetary and stellar universe from the early observation of the agents down to the magnificent discoveries of a her shell depends entirely upon our happening to possess a sense of sight to know other of our senses do any other worlds than our own in the slightest degree appeal we touch them or hear them never consequently if the human race had happened to be blind no other world but the one it groped its way upon could ever have been known or imagined by it the outside universe would have existed but man would have been entirely and hopelessly ignorant of it the bare idea of an outside universe beyond the world would have been inconceivable and might have been scouted as absurd we do possess the sense of sight but is it to be supposed that we possess every sense that can be possessed by finite beings there is not the least ground for such an assumption it is easy to imagine a deaf race or a blind race is it not so easy to imagine a race more highly endowed with senses than our own and yet the sense of smell in animals may give us some aid in thinking of powers of perception which transcend our own in particular directions if there were a race with higher or other senses than our own or if the human race should ever in the process of development acquire such extra sense organs a whole universe of existent fact might become for the first time perceived by us and we should look back upon our past state as upon a blind chrysalid form of existence in which we have been unconscious of all this new wealth of perception it cannot be too clearly and strongly insisted on and brought home to every mind that the mode in which the universe strikes us our view of the universe our whole idea of matter and force and other worlds and even of consciousness depends upon the particular set of sense organs with which we as men happen to be endowed the senses of force of motion of sound of light of touch of heat of taste and of smell these we have and these are the things we primarily know all else's inference founded upon these sensations so the world appears to us but given other sense organs and it might appear quite otherwise what it is actually and truly like therefore is quite and forever beyond us so long as we are finite beings without eyes astronomy would be non-existent light it is which conveys all the information we possess or as it would seem ever can possess concerning the outer and greater universe in which this small world forms a spec light is the channel the messenger of information our eyes aided by telescopes spectroscopes and many other scopes that may yet be invented are the means by which we read the information that light brings light travels from the stars to our eyes does it come instantaneously or does it loiter by the way for if it lingers it is not bringing us information properly up to date it is only telling us what the state of affairs was when it started on its long journey now it is evidently a matter of interest to us whether we see the sun as he is now or only as he was some 300 years ago if the information came by express train it would be 300 years behind date and the sun might have gone out in the reign of queen n without our being as yet any the wiser the question therefore at what rate does our messenger travel is evidently one of great interest for astronomers and many have been the attempts made to solve it very likely the ancient Greeks pondered over this question but the earliest writer known to me who seriously discussed the question is Galileo he suggests a rough experimental means of attacking it first of all it plainly comes quicker than sound this can be perceived by merely watching distant hammering or by noticing that the flash of a pistol is seen before its report is heard or by listening to the noise of a flash of lightning sound takes five seconds to travel a mile it has about the same speed as a rifle bullet but light is much quicker than that the rude experiment suggested by Galileo was to send two men with lanterns and screens to two distant watchtowers or neighboring mountaintops and to arrange that each was to watch alternate displays and obscurations of the light made by the other and to imitate them as properly as possible either man therefore on obscuring or showing his own light would see the distant glimmer do the same and would be able to judge if there was any appreciable interval between his own action and the response of the distant light the experiment was actually tried by the Florentine academicians with the result that as practice improved the interval became shorter and shorter so that there was no reason to suppose that there was any real interval at all light in fact seemed to travel instantaneously well might they have arrived at this result even if they had made far more perfect arrangements for instance by arranging a looking glass at one of the stations in which a distant observer might see the reflection of his own lantern and watch the obscurations and flashings made by himself without having to depend on the response of human mechanism even then no interval whatever could have been detected if by some impossibly perfect optical arrangement a lighthouse here was made visible to us after reflection in a mirror erected at new york so that the light would have to travel across the atlantic and back before it could be seen even then the appearance of the light on removing a shutter or the eclipse on interposing it would seem to happen quite instantaneously there would certainly be an interval the interval would be the 50th part of a second the time a stone takes to drop one 13th of an inch but that is too short to be securely detected without mechanism with mechanism the thing might be managed for a series of shutters might be arranged like the teeth of a large wheel so that when the wheel rotates eclipses follow one another very rapidly if then and i looked through the same opening as that by which the light goes on its way to the distant mirror a tooth might have moved sufficiently to cover up this space by the time the light returned in which case the hole would appear dark for the light would be stopped by a tooth either at starting or at returning continually at higher speeds of rotation some light would reappear and at lower speeds it would also reappear by noticing therefore the precise speed at which there was constant eclipse the velocity of light could be determined this experiment has now been made in a highly refined form by viso and repeated by m corneaux with prodigious care and accuracy but with these recent matters we have no concern at present it may be instructive to say however that if the light had to travel two miles altogether the wheel would have to possess 450 teeth and to spend 100 times a second at the risk of flying to pieces in order that the ray starting through any one of the gaps might be stopped on returning by the adjacent tooth well might the velocity of light be called instantaneous by the early observers an ordinary experiment seemed and was hopeless and light was supposed to travel at an infinite speed but a phenomenon was noticed in the heavens by a quick-witted and ingenious danish astronomer which was not susceptible of any ordinary explanation and which he perceived could it once be explained if light had a certain rate of travel great indeed but something short of infinite this phenomenon was connected with the satellites of jupiter and the astronomer's name was roamer i will speak first of the observation and then of the man jupiter satellites are visible precisely as our own moon is by reason of the shimmer of sunlight which they reflect but as they revolve around their great planet they plunge into his shadow at one part of their course and so become eclipse from sunshine and invisible to us the moment of disappearance can be sharply observed take the first satellite as an example the interval between successive eclipses ought to be its period of revolution round jupiter observe this period it was not uniform on the average it was 42 hours 47 minutes but it seemed to depend on the time of year when roamer observed in spring it was less and in autumn it was more than usual this was evidently a puzzling fact what on earth can our year have to do with the motion of a moon of jupiter's it was probably therefore only an apparent change caused either by our greater or lesser distance from jupiter or else by our greater or less speed of traveling to or from him considering it thus he was led to see that when the time of revolution seemed longest we were receding fastest from jupiter and when shortest approaching fastest if then light took time on its journey if it traveled progressively the whole anomaly would be explained in a second the earth goes 19 miles therefore in 42 and 3 quarters hours the time of revolution of jupiter's first satellite it goes 2.9 million say 3 million miles the eclipse happens punctually but we do not see it till the light conveying the information has traveled the extra 3 million miles and caught up the earth evidently therefore by observing how much the apparent time of revolution is lengthened in one part of the earth's orbit and shortened in another getting all the data accurately and assuming the truth of our hypothetical explanation we can calculate the velocity of light this is what roamer did now the maximum amount of retardation is just about 15 seconds hence light takes this time to travel 3 million miles therefore its velocity is 3 million divided by 15 say 200,000 or as we now know more exactly 186,000 miles every second note that the delay does not depend on our distance but on our speed one can tell this by common sense as soon as we grasp the general idea of the explanation a velocity cannot possibly depend on a distance only roamer's explanation of the anomaly was not accepted by astronomers it excited some attention and was discussed but it was found not obviously applicable to any of the satellites except the first and not very simply and satisfactorily even to that i have of course given you the theory in its most elementary and simple form in actual fact a host of disturbing and complicated considerations come in not so violently disturbing for the first satellite as for the others because it moves so quickly but still complicated enough the fact is the real motion of jupiter satellites is a most difficult problem the motion even of our own moon the lunar theory is difficult enough perturbed as its motion is by the sun you know that newton said it cost him more labor than all the rest of the principia but the motion of jupiter satellites is far worse no one in fact has yet worked their theory completely out they are perturbed by the sun of course but they also perturb each other and jupiter is far from spherical the shape of jupiter and their mutual attractions combined to make their motions most peculiar and distracting hence an error in the time of revolution of a satellite was not surgingly due to the cause roemer suggested unless one could be sure that the inequality was not a real one unless it could be shown that the theory of gravitation was insufficient to account for it this had not then been done so the half made discovery was shelved and properly shelved as a brilliant but unverified speculation it remained on the shelf for half a century and was no doubt almost forgotten now a word or two about the man he was a dain educated at copenhagen and learned in the mathematics we first hear of him as appointed to assist picard the eminent french geodetic surveyor whose admirable work in determining the length of a degree you remembering connection with newton who had come over to denmark with the object of fixing the exact sight of the old and extinct tishonic observatory in the island of huyn for of course the knowledge of the exact latitude and longitude of every place when numerous observations have been taken must be an essential to the full interpretation of those observations the measurements being finished young roemer a company picard to paris and here it was a few years after that he read his famous paper concerning an inequality in the motion of jupiter's first satellite and its explanation by means of an hypothesis of the successive propagation of light the later years of his life he spent in copenhagen as a professor in the university and an enthusiastic observer of the heavens not a descriptive observer like hershal but a measuring observer like sir george airy or tisho brahi he was in fact a worthy follower of tisho and the main work of his life is the development and devising of new and more accurate astronomical instruments many of the large and accurate instruments with which a modern observatory is furnished are the invention of this dane one of the finest observatories in the world is the russian one at polkawa and a list of the instruments there reads like an extended catalog of roemer's inventions he not only invented the instruments he had them made being allowed money for the purpose and he used them vigorously so that at his death he left great piles of manuscript stored in the national observatory unfortunately this observatory was in the heart of the city and was thus exposed to a danger from which such places ought to be as far as possible except some eighteen years after roemer's death a great conflagration broke out in copenhagen and ruined large portions of the city the successor to roemer horrible by name fled from his house with such valuables as he possessed to the observatory and there went on with his work but before long the wind shifted and to his horror he saw the flames coming his way he packed up his own and his predecessors manuscript observations in two cases and prepared to escape with them but the neighbors had resorted to the observatory as a place of safety and so choked up the staircase with their property that he was barely able to escape himself let alone the luggage and everything was lost of all the observations only three days work remains and these were carefully discussed by dr. gala of berlin in 1845 and their nutriment extracted these ancient observations are of great use for purposes of comparison with the present state of the heavens and throw light upon possible changes that are going on of course nowadays such a series of observations would be printed and distributed in many libraries and so made practically indestructible sad as the disaster was to the posthumous fame of the great observer a considerable compensation was preparing the very year that the fire occurred in denmark a quiet philosopher in england was speculating in brooding on a remarkable observation that he had made concerning the apparent motion of certain stars and he was led thereby to a discovery of the first magnitude concerning the speed of light a discovery which resuscitated the old theory of romer about jupiter's satellites and made both it and him immortal james bradley lived a quiet uneventful studious life mainly at oxford but afterwards at the national observatory at grenich of which he was third astronomer royal flam steed and hallie having preceded him in that office he had taken orders and lectured at oxford as civilian professor it is said that he pondered his great discovery while pacing the long walk at magdalen college and a beautiful place it is to meditate in bradley was engaged in making observations to determine if possible the parallax of some of the fixed stars parallax means the apparent relative shift of bodies due to a change in the observer's position it is parallax which we observe when traveling by rail and looking out of the window at distant landscape things at different distances are left behind at different apparent rates and accordingly they seem to move relatively to each other the most distant objects are least affected and anything enormously distant like the moon is not subject to this effect but would retain its position however far we traveled unless we had some extraordinarily precise means of observation so with the fixed stars they were being observed from a moving carriage that is the earth and one moving at the rate of 19 miles a second unless they were infinitely distant or unless they were all at the same distance they must show relative apparent motions among themselves seen from one point of the earth's orbit and then in six months from an opposite point nearly 184 million miles away surely they must show some difference of aspect remember that the old Copernican difficulty had never been removed if the earth revolved round the sun how came it that the fixed stars showed no parallax the fact still remained a surprise and the question a challenge picard like other astronomers suppose that it was only because the methods of observation had not been delicate enough but now that since the invention of the telescope and the founding of the national observatories accuracy hitherto undreamt of was possible why not attack the problem anew this then he did watching the stars with great care to see if in six months they showed any change in absolute position with reverence to the pole of the heavens any known secular motion of the pole such as precession being allowed for already he thought he detected a slight parallax for several stars near the pole and the subject was exciting much interest Bradley determined to attempt the same investigation he was not destined to succeed in it not till the present century was success in that most difficult observation achieved and even now it cannot be done by the absolute methods then attempted but as so often happens Bradley in attempting one thing hit upon another and as it happened one of still greater brilliance and importance let us trace the stages of his discovery atmospheric refraction made horizontal observations useless for the delicacy of his purpose so he chose stars near the zenith particularly one why draconis this he observed very carefully at different seasons of the year by means of an instrument specially adapted for zenith observations that is of the zenith sector the observations were made in conjunction with a friend of his an amateur astronomer named molly no and they were made a queue molly no was shortly made first lord of the admiralty or something important of that sort and gave up frivolous pursuits so Bradley observed alone they observed the star accurately early in the month of December and then intended to wait six months but from curiosity Bradley observed it again only about a week later to his surprise he found that it had already changed its position he recorded his observation on the back of an old envelope it was his want thus to use up odd scraps of paper he was not I regret to say a tidy or methodical person and this odd piece of paper turned up long afterwards among his manuscripts it has been photographed and preserved as an historical relic again and again he repeated the observation of the star and continually found it moving still a little further and further south an excessively small motion but still an appreciable one not to be set down to errors of observation so it went on till March it then waited and after a bit longer began to return until June by September it was displaced as much to the north as it had been to the south and by December it had got back to its original position it had described in fact a small oscillation in the course of the year the motion affected neighboring stars in a similar way and was called an aberration or wandering from their true place for a long time Bradley pondered over this observation and over others like them which he also made he found one group of stars describing small circles while others had a distance from them were oscillating in straight lines and all the others were describing ellipses until the state of things were cleared up accurate astronomy was impossible the fixed stars they were not fixed a bit to refined in accurate observation such as was now possible they were all careering about in little orbits having a reference to the earth's year besides any proper motion which they might really have of their own though no such motion was it present known not till Herschel was that discovered not till this extraordinary aberration was allowed for could it be discovered the effect observed by Bradley and Malino must manifestly be only an apparent motion it was absurd to suppose a real stellar motion regulating itself according to the position of the earth parallax could not do it for that would display stars relatively among each other it would not move similarly a set of neighboring stars at length four years after the observation the explanation struck him while in a boat upon the Thames he noticed the apparent direction of the wind changed whenever the boat started the wind veered when the boat's motion changed of course the cause of this was obvious enough the speed of the wind and the speed of the boat were compounded and gave an apparent direction of the wind other than the true direction but this immediately suggested a cause for what he had observed in the heavens he had been observing an apparent direction of the stars other than the true direction because he was observing from a moving vehicle the real direction was doubtless fixed the apparent direction veered about with the motion of the earth it must be that light did not travel instantaneously but gradually as romer had surmised fifty years ago and that the motion of the light was compounded with the motion of the earth think of a stream of light or anything else falling on a moving carriage the carriage will run a thwart the stream the occupants of the carriage will mistake its true direction a rifle fired through the windows of a railway carriage by a man at rest outside would make its perforations not in the true line of fire unless the train is stationary if the train is moving the line joining the holes will point to a place in advance of where the rifle is really located so it is with the two glasses of a telescope the object glass and eyepiece which are pierced by the light an astronomer applying his eye to the tube and looking for the origin of the disturbance sees it apparently but not in its real position its apparent direction is displaced in the direction of the telescope's motion by an amount depending on the ratio of the velocity of the earth to the velocity of light and on the angle between those two directions but how minute is the displacement the greatest effect is obtained when the two motions are at right angles to each other i.e. when the star scene is at right angles to the direction of the earth's motion but even then it is only 20 inches or 180th part of a degree 190th of the moon's apparent diameter it could not be detected without a cross wire in the telescope and would only appear as a slight displacement from the center of the field supposing the telescope accurately pointed to the true direction but if this explanation be true it at once gives a method of determining the velocity of light the maximum angle of deviation represented as a ratio of arc divided by radius amounts to 1 divided by the quantity 180 times 57 and a third end of quantity minus 0.0001 equals one ten thousandths a gradient of one foot in two miles in other words the velocity of light must be 10 000 times as great as the velocity of the earth in its orbit this amounts to a speed of 190 000 miles a second not so very different from what romer had reckoned it in order to explain the anomalies of jupiter's first satellite stars in the direction in which the earth was moving would not be thus affected there would be nothing in mere approach or recession to alter direction or to make itself in any way visible stars at right angles to the earth's line of motion would be most affected and these would be all displaced by the full amount of 20 seconds of arc stars in intermediate directions would be displaced by intermediate amounts but the line of the earth's motion is approximately a circle round the sun hence the direction of its advances constantly though slowly changing and in one year it goes through all the points of the compass the stars being displaced always in the line of advance must similarly appear to describe little closed curves always a quadrant in advance of the earth completing their orbits once a year those near the pole of the ecliptic will describe circles being always at right angles to the motion those in the plane of the ecliptic near the zodiac will be sometimes at right angles to the motion but at other times will be approached or receded from hence these will oscillate like pendulums once a year and intermediate stars will have intermediate motions that is to say we'll describe ellipses of varying eccentricity but all completed in a year and all with the major axis 20 arc seconds this agreed very closely with what was observed the main details were thus clearly and simply explained by the hypothesis of a finite velocity for light the successive propagation of light in time this time there was no room for hesitation and astronomers hailed the discovery with enthusiasm not yet however did bradley rest the finite velocity of light explained the major part of the irregularities he had observed but not the whole the more carefully he measured the amount of the deviation the less completely accurate became its explanation there clearly was a small outstanding error or discrepancy the stars were still subject to an unexplained displacement not indeed a displacement that repeated itself every year but one that went through a cycle of changes in a longer period the displacement was only about half that of aberration and having a longer period was rather more difficult to detect securely but the major difficulty was the fact that the two sorts of disturbances were coexistent and the skill of disentangling them and exhibiting the true and complete cause of each inequality was very brilliant for nineteen years did bradley observe this minor displacement and in that time he saw it go through a complete cycle its cause was now clear to him the nineteen year period suggested the explanation it is the period in which the moon goes through all her changes a period known to the ancients as the lunar cycle or metonic cycle and used by them to predict eclipses it is still used for the first rough approximation to the prediction of eclipses and to calculate easter the golden number of the prayer book is the number of the year in the cycle the cause of the second inequality or apparent periodic motion of the stars bradley made out to be a nodding motion of the earth's axis the axis of the earth describes its processional orbit or conical motion every twenty six thousand years as had long been known but superposed upon this great movement have now been detected minute knots each with a period of nineteen years the cause of the nodding is completely accounted for by the theory of gravitation just as the precession of the equinoxes was both disturbances result from the attraction of the moon on the non-spherical earth on its protuberant equator nutation is in fact a small perturbation of precession the motion may be observed in a non sleeping top the slow conical motion of the top's slanting axis represents the course of precession sometimes this path is loopy and its little nods correspond to mutation the probable existence of some such perturbation had not escaped the sagacity of newton and he mentioned something about it in the principia but thinks it too small to be detected by observation he was thinking however of a solar disturbance rather than a lunar one and this is certainly very small though it too has now been observed newton was dead before bradley made these great discoveries else he would have been greatly pleased to hear of them these discoveries of aberration and nutation says de l'ombre the great french historian of science secured to their author a distinguished place after hipparchus and kepler among the astronomers of all ages and all countries end of lecture 10