NICHOLAS COPERNICUS
GALILEO GALILEI
JOHANN KEPLER
SIR ISAAC NEWTON
Newton goes on in thePrincipiato explain the extension of gravitation to the other bodies of the solar system beyond the earth and moon. Clearly the same gravitation that holds the moon in its orbit round the earth, must extend outward from the sun also, and hold all the planets in their orbits centered about him. Newton demonstrates by calculation based on Kepler's third law that (1) the forces drawing the planets toward the sun are inversely as the squares of their mean distances from him; and (2) if the force be constantly directed toward the sun, the radius vector in an elliptic orbit must pass over equal areas in equal times.
So all of Kepler's laws could be embodied in a single law of gravitation toward a central body, whose force of attraction decreases outward in exact proportion as the square of the distance increases.
Only one farther step had to be taken, and this the most complicated of all: he must make all the bodies of the sky conform to his third law of motion. This is: Action and reaction are equal, or the mutual actions of any two bodies are always equal and oppositely directed. There must be mutual attractions everywhere: earth for sun as well as sun for earth, moon for sun and sun for moon, earth for Venus and Venus for earth, Jupiter for Saturn and Saturn for Jupiter, and so on.
The motions of the planets in the undisturbed ellipses of Kepler must be impossible. As observations of the planets became more accurate, it was found that they really did fail to move in exact accord with Kepler's laws unmodified. Newton was unable, with the imperfect processes of the mathematics of his day to ascertain whether the deviations then known could be accounted for by his law of gravitation; but he nevertheless formulated the law with entire precision, as follows:
Every particle of matter in the universe attracts every other particle with a force exactly proportionedto the product of their masses, and inversely as the square of the distance between their centers.
The centuries of astronomical research since Newton's day, however, have verified the great law with the utmost exactness. Practically every irregularity of lunar and planetary motion is accounted for; indeed, the intricacies of the problems involved, and the nicety of their solution, have led to the invention of new mathematical processes adequate to the difficulties encountered.
And about the middle of the last century, when Uranus departed from the path laid out for it by the mathematical astronomers, its orbital deviations were made the basis of an investigation which soon led to the assignment of the position where a great planet could be found that would account for the unexplained irregularities of the motion of Uranus. And the immediate discovery of this planet, Neptune, became the most striking verification of the Newtonian law that the solar system could possibly afford.
The astronomers of still later days investigating the statelier motions of stellar systems find the Newtonian law regnant everywhere among the stars where our most powerful telescopes have as yet reached. So that Newton's law is known as the law of Universal Gravitation, and its author is everywhere held as the greatest scientist of the ages.
Newton'sPrincipiamay be regarded as the culminating research of the inductive method, and further outline of its contents is desirable. It is divided into three books following certain introductory sections. The first book treats of the problems of moving bodies, the solutions being workedout generally and not with special reference to astronomy. The second book deals with the motion of bodies through resistant media, as fluids, and has very little significance in astronomy. The third book is the all important one, and applies his general principles to the case of the actual solar system, providing a full explanation of the motions of all the bodies of the system known in his day. Anyone who critically reads thePrincipiaof Newton will be forced to conclude that its author was a genius in the highest sense of the word. The elegance and thoroughness of the demonstrations, and the completeness of application of the law of gravitation are especially impressive.
The universality of his new law was the feature to which he gave particular attention. It was clear to him that the gravitation of a planet, although it acted as if wholly concentrated at the center, was nevertheless resident in every one of the particles of which the planet is composed. Indeed, his universal law was so formulated as to make every particle attract every other particle; and an investigation known as the Cavendish experiment—a research of great delicacy of manipulation—not only proves this, but leads also to a measurement of the earth's mean density, from which we can calculate approximately how much the earth actually weighs.
Another way to attack the same problem is by measuring the attraction of mountains, as Maskelyne, Astronomer Royal of Scotland did on Mount Schehallien in Scotland, which was selected because of its sheer isolation. The attraction of the mountain deflected the plumb-lines by measurable amounts, the volume of the mountain was carefullyascertained by surveys, and geologists found out what rocks composed it. So the weight of the entire mountain became pretty well known, and combining this with the observed deflection, an independent value of the earth's weight was found.
Still other methods have been applied to this question, and as an average it is found that the materials composing the earth are about five and a half times as heavy as water, and the total weight of the earth is something like six sextillions of tons.
What is the true shape of the earth? And does the earth's turning round on its axis affect this shape? Newton saw the answer to these questions in his law of gravitation. A spherical figure followed as a matter of course from the mutual attraction of all materials composing the earth, providing it was at rest, or did not turn round on its axis. But rotation bulges it at the equator and draws it in at the poles, by an amount which calculation shows to be in exact agreement with the amount ascertained by actual measurement of the earth itself.
Another curious effect, not at first apparent, was that all bodies carried from high latitudes toward the equator would get lighter and lighter, in consequence of the centrifugal force of rotation. This was unexpectedly demonstrated by Richer when the French Academy sent him south to observe Mars in 1672. His clock had been regulated exactly in Paris, and he soon found that it lost time when set up at Cayenne. The amount of loss was found by observation, and it was exactly equal to the calculated effect that the reduction of gravity by centrifugal action should produce.
Also Newton saw that his law of gravitation would afford an explanation of the rise and fall of the tides. The water on the side of the earth toward the moon, being nearer to the moon, would be more strongly attracted toward it, and therefore raised in a tide. And the water on the farther side of the earth away from the moon, being at a greater distance than the earth itself, the moon would attract the earth more strongly than this mass of water, tending therefore to draw the earth away from the water, and so raising at the same time a high tide on the side of the earth away from the moon. As the earth turns round on its axis, therefore, two tidal waves continually follow each other at intervals of about twelve hours.
The sun, too, joins its gravitating force with that of the moon, raising tides nearly half as high as those which the moon produces, because the sun's vaster mass makes up in large part for its much greater distance. At first and third quarters of the moon, the sun acts against the moon, and the difference of their tide-producing forces gives us "neap tides"; while at new moon and full, sun and moon act together, and produce the maximum effect known as "spring tides."
Newton passed on to explain, by the action of gravitation also, the precession of the equinoxes, a phenomenon of the sky discovered by Hipparchus, who pretty well ascertained its amount, although no reason for it had ever been assigned. The plane of the earth's equator extended to the celestial sphere marks out the celestial equator, and the two opposite points where it intersects the plane of the ecliptic, or the earth's path round the sun, are called the equinoctial points, or simply the equinoxes.And precession of the equinoxes is the motion of these points westward or backward, about 50 seconds each year, so that a complete revolution round the ecliptic would take place in about 26,000 years.
Newton saw clearly how to explain this: it is simply due to the attraction of the sun's gravitation upon the protuberant bulge around the earth's equator, acting in conjunction with the earth's rotation on its axis, the effect being very similar to that often seen in a spinning top, or in a gyroscope. The moon moving near the ecliptic produces a precessional effect, as also do the planets to a very slight degree; and the observed value of precession is the same as that calculated from gravitation, to a high degree of precision.
Newton died in 1727, too early to have witnessed that complete and triumphant verification of his law which ultimately has accounted for practically every inequality in the planetary motions caused by their mutual attractions. The problems involved are far beyond the complexity of those which the mathematical astronomer has to deal with, and the mathematicians of France deserve the highest credit for improving the processes of their science so that obstacles which appeared insuperable were one after another overcome.
Newton's method of dealing with these problems was mainly geometric, and the insufficiency of this method was apparent. Only when the French mathematicians began to apply the higher methods of algebra was progress toward the ultimate goal assured. D'Alembert and Clairaut for a time were foremost in these researches, but their places were soon taken by Lagrange, who wrote the "MécaniqueAnalytique," and Laplace, whose "Mécanique Céleste" is the most celebrated work of all. In large part these works are the basis of the researches of subsequent mathematical astronomers who, strictly speaking, cannot as yet be said to have arrived at a complete and rigorous solution of all the problems which the mutual attractions of all the bodies of the solar system have originated.
It may well be that even the mathematics of the present day are incompetent to this purpose. When the brilliant genius of Sir William Hamilton invented quaternion analysis and showed the marvelous facility with which it solved the intricate problems of physics, there was the expectation that its application to the higher problems of mathematical astronomy might effect still greater advances; but nothing in that direction has so far eventuated. Some astronomers look for the invention of new functions with numerical tables bearing perhaps somewhat the relation to present tables of logarithms, sines, tangents, and so on, that these tables do to the simple multiplication table of Pythagoras.
We have said that practically all the motions in the solar system have been accounted for by the Newtonian law of gravitation. It will be of interest to inquire into the instances that lead to qualification of this absolute statement.
One relates to the planet Mercury, whose orbit or path round the sun is the most elliptical of all the planetary orbits. This will be explained a little later.
The moon has given the mathematical astronomers more trouble than any other of the celestial bodies, for one reason because it is nearest to us and very minute deviations in its motion are therefore detectible. Halley it was who ascertained two centuries ago that the moon's motion round the earth was not uniform, but subject to a slight acceleration which greatly puzzled Lagrange and Laplace, because they had proved exactly this sort of thing to be impossible, unless indeed the body in question should be acted on by some other force than gravitation. But Laplace finally traced the cause to the secular or very slow reduction in the eccentricity of the earth's own orbit. The sun's action on the moon was indeed progressively changing from century to century in such manner as to accelerate the moon's own motion in its orbit round the earth.
Adams, the eminent English astronomer, revised the calculations of Laplace, and found the effect in question only half as great as Laplace had done; and for years a great mathematical battle was on between the greatest of astronomical experts in this field of research. Adams, in conjunction with Delaunay, the greatest of the French mathematicians a half century ago, won the battle in so far as the mathematical calculations were concerned; but the moon continues to the present day her slight and perplexing deviation, as if perhaps our standard time-keeper, the earth, by its rotation round its axis, were itself subject to variation. Although many investigations have been made of the uniformity of the earth's rotation, no such irregularity has been detected, and this unexplained variation of the moon's motion is one of the unsolved problems of the gravitational astronomer of to-day.
But we are passing over the most impressive of all the earlier researches of Lagrange and Laplace, which concerned the exceedingly slow changes, technically called the secular variations of the elements of the planetary orbits. These elements are geometrical relations which indicate the form of the orbit, the size of the orbit, and its position in space; and it was found that none of these relations or quantities are constant in amount or direction, but that all, with but one exception, are subject to very slow, or secular, change, or oscillation.
This question assumed an alarming significance at an early day, particularly as it affected the eccentricity of the earth's orbit round the sun. Should it be possible for this element to go on increasing for indefinite ages, clearly the earth's orbit wouldbecome more and more elliptical, and the sun would come nearer and nearer at perihelion, and the earth would drift farther and farther from the sun at aphelion, until the extremes of temperature would bring all forms of life on the earth to an end. The refined and powerful analysis of Lagrange, however, soon allayed the fears of humanity by accounting for these slow progressive changes as merely part of the regular system of mere oscillations, in entire accord with the operation of the law of gravitation; and extending throughout the entire planetary system. Indeed, the periods of these oscillations were so vast that none of them were shorter than 50,000 years, while they ranged up to two million years in length—"great clocks of eternity which beat ages as ours beat seconds."
About a century ago, an eminent lecturer on astronomy told his audience that the problem of weighing the planets might readily be one that would seem wholly impossible to solve. To measure their sizes and distances might well be done, but actually to ascertain how many tons they weigh—never!
Yet if a planet is fortunate enough to have one satellite or more, the astronomer's method of weighing the planet is exceedingly simple; and all the major planets have satellites except the two interior ones, Mercury and Venus. As the satellite travels round its primary, just as the moon does round the earth, two elements of its orbit need to be ascertained, and only two. First, the mean distance of the satellite from its primary, and second the time of revolution round it.
Now it is simply a case of applying Kepler's third law. First take the cube of the satellite's distanceand divide it by the square of the time of revolution. Similarly take the cube of the planet's distance from the sun and divide by the square of the planet's time of revolution round him. The proportion, then, of the first quotient to the second shows the relation of the mass (that is the weight) of the planet to that of the sun. In the case of Jupiter, we should find it to be 1,050, in that of Saturn 3,500, and so on.
The range of planetary masses, in fact, is very curious, and is doubtless of much significance in the cosmogony, with which we deal later. If we consider the sun and his eight planets, the mass or weight of each of the nine bodies far exceeds the combined mass of all the others which are lighter than itself.
To illustrate: suppose we take as our unit of weight the one-billionth part of the sun's weight; then the planets in the order of their masses will be Mercury, Mars, Venus, Earth, Uranus, Neptune, Saturn, and Jupiter. According to their relative masses, then, Mercury being a five-millionth part the weight of the sun will be represented by 200; similarly Venus, a four hundred and twenty-five thousandth part by 2,350, and so on. Then we have
Curious and interesting it is that Saturn is nearly three times as heavy as the six lighter planets taken together, Jupiter between two and three times heavier than all the other planets combined, while the sun's mass is 750 times that of all the great planets of his system rolled into one.
All the foregoing masses, except those of Mercury and Venus, are pretty accurately known because they were found by the satellite method just indicated. Mercury's mass is found by its disturbing effects on Encke's comet whenever it approaches very near. The mass of Venus is ascertained by the perturbations in the orbital motion of the earth. In such cases the Newtonian law of gravitation forms the basis of the intricate and tedious calculations necessary to find out the mass by this indirect method.
Its inferiority to the satellite method was strikingly shown at the Observatory in Washington soon after the satellites of Mars were discovered in 1877. The inaccurate mass of that planet, as previously known by months of computation based upon years and years of observation, was immediately discardedin favor of the new mass derived from the distance and period of the outer satellite by only a few minutes' calculation.
In weighing the planets, astronomers always use the sun as the unit. What then is the sun's own weight? Obviously the law of gravitation answers this question, if we compare the sun's attraction with the earth's at equal distances. First we conceive of the sun's mass as if all compressed into a globe the size of the earth, and calculate how far a body at the surface of this globe would fall in one second. The relation of this number to 16.1 feet, the distance a body falls in one second on the actual earth, is about 330,000, which is therefore the number of times the sun's weight exceeds that of the earth.
A word may be added regarding the force of gravitation and what it really is. As a matter of fact Newton did not concern himself in the least with this inquiry, and says so very definitely. What he did was to discover the law according to which gravitation acts everywhere throughout the solar system. And although many physicists have endeavored to find out what gravitation really is, its cause is not yet known. In some manner as yet mysterious it acts instantaneously over distances great and small alike, and no substance has been found which, if we interpose it between two bodies, has in any degree the effect of interrupting their gravitational tendency toward each other.
While the Newtonian law of gravitation has been accepted as true because it explained and accounted for all the motions of the heavenly bodies, even including such motions of the stars as have been subjected to observation, astronomers have for a longtime recognized that quite possibly the law might not be absolutely exact in a mathematical sense, and that deviations from it would surely make their appearance in time.
A crude instance of this was suggested about a century ago, when the planet Uranus was found to be deviating from the path marked out for it by Bouvard's tables based on the Newtonian law; and the theory was advocated by many astronomers that this law, while operant at the medium distances from the sun where the planets within Jupiter and Saturn travel, could not be expected to hold absolutely true at the vast distance of Uranus and beyond. The discovery of Neptune in 1846, however, put an end to all such speculation, and has universally been regarded as an extraordinary verification of the law, as indeed it is.
When, however, Le Verrier investigated the orbit of Mercury he found an excess of motion in the perihelion point of the planet's orbit which neither he nor subsequent investigators have been able to account for by Newtonian gravitation, pure and simple. If Newton's theory is absolutely true, the excess motion of Mercury's perihelion remains a mystery.
Only one theory has been advanced to account for this discrepancy, and that is the Einstein theory of gravitation. This ingenious speculation was first propounded in comprehensive form nearly fifteen years ago, and its author has developed from it mathematical formulæ which appear to yield results even more precise than those based on the Newtonian theory.
In expressing the difference between the law of gravitation and his own conception, Einstein says:"Imagine the earth removed, and in its place suspended a box as big as a moon or a whole house and inside a man naturally floating in the center, there being no force whatever pulling him. Imagine, further, this box being, by a rope or other contrivance, suddenly jerked to one side, which is scientifically termed 'difform motion,' as opposed to 'uniform motion.' The person would then naturally reach bottom on the opposite side. The result would consequently be the same as if he obeyed Newton's law of gravitation, while, in fact, there is no gravitation exerted whatever, which proves that difform motion will in every case produce the same effects as gravitation…. The term relativity refers to time and space. According to Galileo and Newton, time and space were absolute entities, and the moving systems of the universe were dependent on this absolute time and space. On this conception was built the science of mechanics. The resulting formulas sufficed for all motions of a slow nature; it was found, however, that they would not conform to the rapid motions apparent in electrodynamics…. Briefly the theory of special relativity discards absolute time and space, and makes them in every instance relative to moving systems. By this theory all phenomena in electrodynamics, as well as mechanics, hitherto irreducible by the old formulæ, were satisfactorily explained."
Natural phenomena, then, involving gravitation and inertia, as in the planetary motions, and electro-magnetic phenomena, including the motion of light, are to be regarded as interrelated, and not independent of one another. And the Einstein theory would appear to have received a striking verification in both these fields. On this theory theNewtonian dynamics fails when the velocities concerned are a near approach to that of light. The Newtonian theory, then, is not to be considered as wrong, but in the light of a first approximation. Applying the new theory to the case of the motion of Mercury's perihelion, it is found to account for the excess quite exactly.
On the electro-magnetic side, including also the motion of light, a total eclipse of the sun affords an especially favorable occasion for applying the critical test, whether a huge mass like the sun would or would not deflect toward itself the rays of light from stars passing close to the edge of its disk, or limb. A total eclipse of exceptional duration occurred on May 29, 1919, and the two eclipse parties sent out by the Royal Society of London and the Royal Astronomical Society were equipped especially with apparatus for making this test. Their stations were one on the east coast of Brazil and the other on the west coast of Africa.
Accurate calculation beforehand showed just where the sun would be among the stars at the time of the eclipse; so that star plates of this region were taken in England before the expeditions went out. Then, during the total eclipse, the same regions were photographed with the eclipsed sun and the corona projected against them. To make doubly sure, the stars were a third time photographed some weeks after the eclipse, when the sun had moved away from that particular region.
Measuring up the three sets of plates, it was found that an appreciable deflection of the light of the stars nearest alongside the sun actually exists; and the amount of it is such as to afford a fair though not absolutely exact verification of thetheory. The observed deflection may of course be due to other causes, but the English astronomers generally regard the near verification as a triumph for the Einstein theory. Astronomers are already beginning preparations for a repetition of the eclipse programme with all possible refinement of observation, when the next total eclipse of the sun occurs, September 20, 1922, visible in Australia and the islands of the Indian Ocean.
A third test of the theory is perhaps more critical than either of the others, and this necessitates a displacement of spectral lines in a gravitational field toward the red end of the spectrum; but the experts who have so far made measures for detecting such displacement disagree as to its actual existence. The work of St. John at Mt. Wilson is unfavorable to the theory, as is that of Evershed of Kodiakanal, who has made repeated tests on the spectrum of Venus, as well as in the cyanogen bands of the sun.
The enthusiastic advocates of the Einstein theory hold that, as Newton proved the three laws of Kepler to be special cases of his general law, so the "universal relativity theory" will enable eventually the Newtonian law to be deduced from the Einstein theory. "This is the way we go on in science, as in everything else," wrote Sir George Airy, Astronomer Royal; "we have to make out that something is true; then we find out under certain circumstances that it is not quite true; and then we have to consider and find out how the departure can be explained." Meanwhile, the prudent person keeps the open mind.
Halley is one of the most picturesque characters in all astronomical history. Next to Newton himself he was most intimately concerned in giving the Newtonian law to the world.
Edmund Halley was born (1656) in stirring times. Charles I. had just been executed, and it was the era of Cromwell's Lord Protectorate and the wars with Spain and Holland. Then followed (1660) the promising but profligate Charles II. (who nevertheless founded at Greenwich the greatest of all observatories when Halley was nineteen), the frightful ravages of the Black Plague, the tyrannies of James II., and the Revolution of 1688—all in the early manhood of Halley, whose scientific life and works marched with much of the vigor of the contending personalities of state.
The telescope had been invented a half century earlier, and Galileo's discoveries of Jupiter's moons and the phases of Venus had firmly established the sun-centered theory of Copernicus.
The sun's distance, though, was known but crudely; and why the stars seemed to have no yearly orbits of their own corresponding to that of the earth was a puzzle. Newton was well advanced toward his supreme discovery of the law of universal gravitation; and the authority of Kepler taught that comets travel helter-skelter throughspace in straight lines past the earth, a perpetual menace to humanity.
"Ugly monsters," that comets always were to the ancient world, the medieval church perpetuated this misconception so vigorously that even now these harmless, gauzy visitors from interstellar space possess a certain "wizard hold upon our imagination." This entertaining phase of the subject is excellently treated in President Andrew D. White's "History of the Doctrine of Comets," in the Papers of the American Historical Association. Halley's brilliant comet at its earlier apparitions had been no exception.
Halley's father was a wealthy London soap maker, who took great pride in the growing intellectuality of his son. Graduating at Queen's College, Oxford, the latter began his astronomical labors at twenty by publishing a work on planetary orbits; and the next year he voyaged to St. Helena to catalogue the stars of the southern firmament, to measure the force of terrestrial gravity, and observe a transit of Mercury over the disk of the sun.
While clouds seriously interfered with his observations on that lonely isle, what he saw of the transit led to his invention of "Halley's method," which, as applied to the transit of Venus, though not till long after his death, helped greatly in the accurate determination of the sun's distance from the earth. Halley's researches on the proper motions of the stars of both hemispheres soon made him famous, and it was said of him, "If any star gets displaced on the globe, Halley will presently find it out."
His return to London and election to the Royal Society (of which he was many years secretary) added much to his fame, and he was commissionedby the society to visit Danzig and arbitrate an astronomical controversy between Hooke and Hevelius, both his seniors by a generation.
On the continent he associated with other great astronomers, especially Cassini, who had already found three Saturnian moons; and it was then he observed the great comet of 1680, which led up to the most famous event of Halley's life.
The seerlike Seneca may almost be said to have predicted the advent of Halley, when he wrote ("Quaestiones Naturales," vii): "Some day there will arise a man who will demonstrate in what region of the heavens comets pursue their way; why they travel apart from the planets; and what their sizes and constitution are. Then posterity will be amazed that simple things of this sort were not explained before."
To Newton it appeared probable that cometary voyagers through space might have orbits of their own; and he proved that the comet of 1680 never swerved from such a path. As it could nowhere approach within the moon's orbit, clearly threats of its wrecking the earth and punishing its inhabitants ought to frighten no more.
Halley then became intensely interested in comets, and gathered whatever data concerning the paths of all these bodies he could find. His first great discovery was that the comets seen in 1531 by Apian, and in 1607 by Kepler, traveled round the sun in identical paths with one he had himself observed in 1682. A still earlier appearance of Halley's comet (1456) seems to have given rise to a popular and long-reiterated myth of a papal bull excommunicating "the Devil, the Turk, and the Comet."
No longer room for doubt: so certain was Halley that all three were one and the same comet, completing the round of its orbit in about seventy-six years, that he fearlessly predicted that it would be seen again in 1758 or 1759. And with equal confidence he might have foretold its return in 1835 and 1910; for all three predictions have come true to the letter.
Halley's span of existence did not permit his living to see even the first of these now historic verifications. But we in our day may emphatically term the epoch of the third verified returnAnnus Halleianus.
Says Turner, Halley's successor in the Savilian chair at Oxford to-day: "There can be no more complete or more sensational proof of a scientific law, than to predict events by means of it. Halley was deservedly the first to perform this great service for Newton's Law of Gravitation, and he would have rejoiced to think how conspicuous a part England was to play in the subsequent prediction of the existence of Neptune."
Halley rose rapidly among the chief astronomical figures of his day. But he had little veneration for mere authority, and the significant veering of his religious views toward heterodoxy was for years an obstacle to his advance.
Still Halley the astronomer was great enough to question any contemporary dicta that seemed to rest on authority alone. Everyone called the stars "fixed" stars; but Halley doubting this, made the first discovery of a star's individual motion—proper motion, as astronomers say. To-day, two hundred years after, every star is considered to be in motion, and astronomers are ascertaining their real motionsin the celestial spaces to a nicety undreamed of by even the exacting Halley.
The moon, of priceless service to the early navigator, was regarded by all astronomers as endowed with an average rate of motion round the earth that did not vary from age to age. But Halley questioned this too; and on comparing with the ancient value from Chaldean eclipses, he made another discovery—the secular acceleration of the moon's mean motion, as it is technically termed. This was a colossal discovery in celestial dynamics; and the reason underlying it lay hidden in Newton's law for yet another century, till the keener mathematics of Laplace detected its true origin.
With Newton, Halley laid down the firm foundations of celestial mechanics, and they pushed the science as far as the mathematics of their day would permit. Halley, however, was not content with elucidating the motion of bodies nearest the earth, and pressed to the utmost confines of the solar system known to him. Here, too, he made a signal discovery of that mutual disturbance of the planets in their motion round the sun, called the great inequality of Jupiter and Saturn.
Halley's versatile genius attacked all the great problems of the day. His observation of the sun's total eclipse in 1715 is the earliest reliable account of such a phenomenon by a trained astronomer. He described the corona minutely and was the first to see that other interesting phenomenon which only an alert observer can detect, which a great astronomer of a later day compared to the "ignition of a fine train of gunpowder," and which has ever since borne the name of "Baily's beads."
Besides being a great astronomer, Halley was a man of affairs as well, which Newton, although the greater mathematician, was not. Without Halley, Newton's superb discovery might easily have been lost to the age and nation, for the latter was bent merely on making discoveries, and on speculative contemplation of them, with never a thought of publishing to the world.
Halley, more practical and businesslike, insisted on careful writing out and publication. Newton was then only forty-two, and Halley fully fourteen years his junior. But the philosophers of that day were keenly alive to the mystery of Kepler's laws, and Halley was fully conscious of the grandeur and far-reaching significance of Newton's great generalization which embodied all three of Kepler's laws in one.
Newton at last yielded, though reluctantly, and the "Principia" was given to the world, though wholly at Halley's private charges.
But Halley was far from being completely engrossed with the absorbing problems of the sky; things terrestrial held for years his undivided attention. Imagine present-day Lords Commissioners of the Admiralty intrusting a ship of the British navy to civilian command. Yet such was their confidence in Halley that he was commissioned as captain of H. M.'s pinkParamourin 1698, with instructions to proceed to southern seas for geographical discoveries, and for improving knowledge of the longitude problem, and of the variations of the compass. Trade winds and monsoons, charts of magnetic variation, tides and surveys of the Channel coast, and experiments with diving bells were practical activities that occupied his attention.
Halley in 1720 became Astronomer Royal. He was the second incumbent of this great office, but the first to supply the Royal Observatory with instruments of its own, some of which adorn its walls even to-day. His long series of lunar observations and his magnetic researches were of immense practical value in navigation.
Halley lived to a ripe old age and left the world vastly better than he found it. His rise from humblest obscurity was most remarkable, and he lived to gratify all the ambitions of his early manhood. "Of attractive appearance, pleasing manners, and ready wit," says one of his biographers, "loyal, generous, and free from self-seeking, he was one of the most personally engaging men who ever held the office of Astronomer Royal."
He died in office at Greenwich in 1742.
"Halley was buried," says Chambers, "in the churchyard of St. Margaret's, Lee, not far from Greenwich, and it has lately been announced that the Admiralty have decided to repair his tomb at the public expense, no descendants of his being known." There is no suitable monument in England to the memory of one of her greatest scientific men. In any event the collection and republication of his epoch-making papers would be welcomed by astronomers of every nation.
Living at Kew in London early in the 18th century was an enthusiastic young astronomer, James Bradley. He is famous chiefly for his accurate observations of star places which have been invaluable to astronomers of later epochs in ascertaining the proper motions of stars.
The latitude of Bradley's house in Kew was very nearly the same as the declination of the bright star Gamma Draconis, so that it passed through his zenith once every day. Bradley had a zenith sector, and with this he observed with the greatest care the zenith distance of Gamma Draconis at every possible opportunity. This he did by pointing the telescope on the star and then recording the small angle of its inclination to a fine plumb line. So accurate were his measures that he was probably certain of the star's position to the nearest second of arc.
What he hoped to find was the star's motion round a very slight orbit once each year, and due to the earth's motion in its orbit round the sun. In other words, he sought to find the star's parallax if it turned out to be a measurable quantity.
It is just as well now that his method of observation proved insufficiently delicate to reveal the parallax of Gamma Draconis; but his assiduity in observation led him to an unexpected discovery of greater moment at that time. What he really found wasthat the star had a regular annual orbit; but wholly different from what he expected, and very much larger in amount. This result was most puzzling to Bradley. The law of relative motion would require that the star's motion in its expected orbit should be opposite to that of the earth in its annual orbit; instead of which the star was all the time at right angles to the earth's motion.
Bradley was a frequent traveler by boat on the Thames, and the apparent change in the direction of the wind when the boat was in motion is said to have suggested to him what caused the displacement of Gamma Draconis. The progressive motion of light had been roughly ascertained by Roemer: let that be the velocity of the wind. And the earth's motion in its orbit round the sun, let that be the speed of the boat. Then as the wind (to an observer on the moving boat) always seems to come from a point in advance of the point it actually proceeds from (to an observer at rest), so the star should be constantly thrown forward by an angle given by the relation of the velocity of light to the speed of the earth in orbital revolution round the sun.
The apparent places of all stars are affected in this manner, and this displacement is called the aberration of light. Astronomers since Bradley's discovery of aberration in 1726 have devoted a great deal of attention to this astronomical constant, as it is called, and the arc value of it is very nearly 20".5. This means that light travels more than ten thousand times as fast as the earth in its orbit (186,330 miles per second as against the earth's 18.5). And we can ascertain the sun's distance by aberration also because the exact values of the velocity of light and of the constant of aberration when properly combinedgive the exact orbital speed of the earth; and this furnishes directly by geometry the radius of the earth's orbit, that is the distance of the sun.
In fact, this is one of the more accurate modern methods of ascertaining the distance of the sun. As early as 1880 it enabled the writer to calculate the sun's parallax equal to 8".80, a value absolutely identical with that adopted by the Paris Conference of 1896, and now universally accepted as the standard.
In whatever part of the sky we observe, every star is affected by aberration. At the poles of the ecliptic, 23½ degrees from the earth's poles, the annual aberration orbits of the stars are very small circles, 41" in diameter. Toward the ecliptic the aberration orbits become more and more oval, ellipses in fact of greater and greater eccentricity, but with their major axes all of the same length, until we reach the ecliptic itself; and then the ellipse is flattened into a straight line 41" in length, in which the star travels forth and back once a year. Exact correspondence of the aberration ellipses of the stars with the annual motion of the earth round the sun affords indisputable proof of this motion, and as every star partakes of the movement, this proof of our motion round the sun becomes many million-fold.
Indeed, if we were to push a little farther the refinement of our analysis of the effect of aberration on stellar positions, we could prove also the rotation of the earth on its axis, because that motion is swift enough to bear an appreciable ratio to the velocity of light. Diurnal aberration is the term applied to this slight effect, and as every star partakes of it, demonstration of the earth's turning round on its axis becomes many million-fold also.
Had anyone told Ptolemy that his earth-centered system of sun, moon, and stars would ultimately be overthrown, not by philosophy but by the overwhelming evidence furnished by a little optical instrument which so aided the human eye that it could actually see systems of bodies in revolution round each other in the sky, he would no doubt have vehemently denied that any such thing was possible. To be sure, it took fourteen centuries to bring this about, and the discovery even then was without much doubt due to accident.
Through all this long period when astronomy may be said to have merely existed, practically without any forward step or development, its devotees were unequipped with the sort of instruments which were requisite to make the advance possible. There were astrolabes and armillary spheres, with crudely divided circles, and the excellent work done with them only shows the genius of many of the early astronomers who had nothing better to work with. Regarding star-places made with instruments fixed in the meridian, Bessel, often called the father of practical astronomy, used to say that, even if you provided a bad observer with the best of instruments, a genius could surpass him with a gun barrel and a cart wheel.
Before the days of telescopes, that is, prior to the seventeenth century, it was not known whether anyof the planets except the earth had a moon or not; consequently the masses of these planets were but very imperfectly ascertained; the phases of Mercury and Venus were merely conjectured; what were the actual dimensions of the planets could only be guessed at; the approximate distances of sun, moon, and planets were little better than guesses; the distances of the stars were wildly inaccurate; and the positions of the stars on the celestial sphere, and of sun, moon, and planets among them were far removed from modern standards of precision—all because the telescope had not yet become available as an optical adjunct to increase the power of the human eye and enable it to see as if distances were in considerable measure annihilated.
Galileo almost universally is said to have been the inventor of the telescope, but intimate research into the question would appear to give the honor of that original invention to another, in another country. What Galileo deserves the highest praise for, however, is the reinvention independently of an "optick tube" by which he could bring distant objects apparently much nearer to him; and being an astronomer, he was by universal acknowledgment first of all men to turn a telescope on the heavenly bodies. This was in the year 1609, and his first discovery was the phase of Venus, his second the four Medicean moons or satellites of Jupiter, discoveries which at that epoch were of the highest significance in establishing the truth of the Copernican system beyond the shadow of doubt.
But the first telescopes of which we have record were made, so far as can now be ascertained, in Holland very early in the 17th century. Metius, a professor of mathematics, and Jansen and Lipperhey,who were opticians in Middelburg—all three are entitled to consideration as claimants of the original invention of the telescope. But that such an instrument was pretty well known would appear to be shown by his government's refusal of a patent to Lipperhey in 1608; while the officials recognizing the value of such an instrument for purposes of war, got him to construct several telescopes and ordered him to keep the invention a secret.
Within a year Galileo heard that an instrument was in use in Holland by which it was possible to see distant objects as if near at hand. Skilled in optics as he was, the reinvention was a task neither long nor difficult for him. One of his first instruments magnified but three times; still it made a great sensation in Venice where he exhibited the little tube to the authorities of that city, in which he first invented it.
Galileo's telescope was of the simplest type, with but two lenses; the one a double convex lens with which an image of the distant object is formed, the other a double concave lens, much smaller which was the eye-lens for examining the image. It is this simple form of Galilean telescope that is still used in opera glasses and field glasses, because of the shorter tube necessary.
Galileo carried on the construction of telescopes, all the time improving their quality and enlarging their power until he built one that magnified thirty times. What the diameter of the object glass was we do not know, perhaps two inches or possibly a little more. Glass of a quality good enough to make a telescope of cannot have been abundant or even obtainable except with great difficulty in those early days.
Other discoveries by this first of celestial observers were the spots on the sun, the larger mountains of the moon, the separate stars of which the Milky Way is composed, and, greatest wonder of all, the anomalous "handles" (ansæ, he called them) of Saturn, which we now know as the planet's ring, the most wonderful of all the bodies in the sky.
Since Galileo's time, only three centuries past, the progress in size and improvement in quality of the telescope have been marvelous. And this advance would not have been possible except for, first, the discoveries still kept in large part secret by the makers of optical glass which have enabled them to make disks of the largest size; second, the consummate skill of modern opticians in fashioning these disks into perfect lenses; and third, the progress in the mechanical arts and engineering, by which telescope tubes of many tons' weight are mounted or poised so delicately that the thrust of a finger readily swerves them from one point of the heavens to another.
As the telescope is the most important of all astronomical instruments, it is necessary to understand its construction and adjustment and how the astronomer uses it. Telescopes are optical instruments, and nothing but optical parts would be requisite in making them, if only the optical conditions of their perfect working could be obtained without other mechanical accessories.
In original principle, all telescopes are as simple as Galileo's; first, an object glass to form the image of the distant object; second the eyepiece usually made of two lenses, but really a microscope, to magnify that image, and working in the same way that any microscope magnifies an object close at hand; and third, a tube to hold all the necessary lenses in the true relative positions.