Galileo died on Christmas Day, 1642—the day of Newton's birth. The further consideration of the grand field of discovery opened out by Galileo with his telescopes must be now postponed, to avoid discontinuity in the history of the intellectual development of this period, which lay in the direction of dynamical, or physical, astronomy.

Until the time of Kepler no one seems to have conceived the idea of universal physical forces controlling terrestrial phenomena, and equally applicable to the heavenly bodies. The grand discovery by Kepler of the true relationship of the Sun to the Planets, and the telescopic discoveries of Galileo and of those who followed him, spread a spirit of inquiry and philosophic thought throughout Europe, and once more did astronomy rise in estimation; and the irresistible logic of its mathematical process of reasoning soon placed it in the position it has ever since occupied as the foremost of the exact sciences.

The practical application of this process of reasoning was enormously facilitated by the invention of logarithms by Napier. He was born at Merchistoun, near Edinburgh, in 1550, and died in 1617. By this system the tedious arithmetical operations necessary in astronomical calculations, especially those dealing with the trigonometrical functions of angles, were so much simplified that Laplace declared that by this invention the life-work of an astronomer was doubled.

Jeremiah Horrocks (born 1619, died 1641) was an ardent admirer of Tycho Brahe and Kepler, and was able to improve the Rudolphine tables so much that he foretold a transit of Venus, in 1639, which these tables failed to indicate, and was the only observer of it. His life was short, but he accomplished a great deal, and rightly ascribed the lunar inequality called evection to variations in the value of the eccentricity and in the direction of the line of apses, at the same time correctly assigning the disturbing force of the Sun as the cause. He discovered the errors in Jupiter's calculated place, due to what we now know as the long inequality of Jupiter and Saturn, and measured with considerable accuracy the acceleration at that date of Jupiter's mean motion, and indicated the retardation of Saturn's mean motion.

Horrocks' investigations, so far as they could be collected, were published posthumously in 1672, and seldom, if ever, has a man who lived only twenty-two years originated so much scientific knowledge.

At this period British science received a lasting impetus by the wise initiation of a much-abused man, Charles II., who founded the Royal Society of London, and also the Royal Observatory of Greeenwich, where he established Flamsteed as first Astronomer Royal, especially for lunar and stellar observations likely to be useful for navigation. At the same time the French Academy and the Paris Observatory were founded. All this within fourteen years, 1662-1675.

Meanwhile gravitation in general terms was being discussed by Hooke, Wren, Halley, and many others. All of these men felt a repugnance to accept the idea of a force acting across the empty void of space. Descartes (1596-1650) proposed an ethereal medium whirling round the sun with the planets, and having local whirls revolving with the satellites. As Delambre and Grant have said, this fiction only retarded the progress of pure science. It had no sort of relation to the more modern, but equally misleading, "nebular hypothesis." While many were talking and guessing, a giant mind was needed at this stage to make things clear.



7. SIR ISAAC NEWTON—LAW OF UNIVERSAL GRAVITATION.

We now reach the period which is the culminating point of interest in the history of dynamical astronomy. Isaac Newton was born in 1642. Pemberton states that Newton, having quitted Cambridge to avoid the plague, was residing at Wolsthorpe, in Lincolnshire, where he had been born; that he was sitting one day in the garden, reflecting upon the force which prevents a planet from flying off at a tangent and which draws it to the sun, and upon the force which draws the moon to the earth; and that he saw in the case of the planets that the sun's force must clearly be unequal at different distances, for the pull out of the tangential line in a minute is less for Jupiter than for Mars. He then saw that the pull of the earth on the moon would be less than for a nearer object. It is said that while thus meditating he saw an apple fall from a tree to the ground, and that this fact suggested the questions: Is the force that pulled that apple from the tree the same as the force which draws the moon to the earth? Does the attraction for both of them follow the same law as to distance as is given by the planetary motions round the sun? It has been stated that in this way the first conception of universal gravitation arose.[1]

Quite the most important event in the whole history of physical astronomy was the publication, in 1687, of Newton's Principia (Philosophiae Naturalis Principia Mathematica). In this great work Newton started from the beginning of things, the laws of motion, and carried his argument, step by step, into every branch of physical astronomy; giving the physical meaning of Kepler's three laws, and explaining, or indicating the explanation of, all the known heavenly motions and their irregularities; showing that all of these were included in his simple statement about the law of universal gravitation; and proceeding to deduce from that law new irregularities in the motions of the moon which had never been noticed, and to discover the oblate figure of the earth and the cause of the tides. These investigations occupied the best part of his life; but he wrote the whole of his great book in fifteen months.

Having developed and enunciated the true laws of motion, he was able to show that Kepler's second law (that equal areas are described by the line from the planet to the sun in equal times) was only another way of saying that the centripetal force on a planet is always directed to the sun. Also that Kepler's first law (elliptic orbits with the sun in one focus) was only another way of saying that the force urging a planet to the sun varies inversely as the square of the distance. Also (if these two be granted) it follows that Kepler's third law is only another way of saying that the sun's force on different planets (besides depending as above on distance) is proportional to their masses.

Having further proved the, for that day, wonderful proposition that, with the law of inverse squares, the attraction by the separate particles of a sphere of uniform density (or one composed of concentric spherical shells, each of uniform density) acts as if the whole mass were collected at the centre, he was able to express the meaning of Kepler's laws in propositions which have been summarised as follows:—

The law of universal gravitation.—Every particle of matter in the universe attracts every other particle with a force varying inversely as the square of the distance between them, and directly as the product of the masses of the two particles.[2]

But Newton did not commit himself to the law until he had answered that question about the apple; and the above proposition now enabled him to deal with the Moon and the apple. Gravity makes a stone fall 16.1 feet in a second. The moon is 60 times farther from the earth's centre than the stone, so it ought to be drawn out of a straight course through 16.1 feet in a minute. Newton found the distance through which she is actually drawn as a fraction of the earth's diameter. But when he first examined this matter he proceeded to use a wrong diameter for the earth, and he found a serious discrepancy. This, for a time, seemed to condemn his theory, and regretfully he laid that part of his work aside. Fortunately, before Newton wrote the Principia the French astronomer Picard made a new and correct measure of an arc of the meridian, from which he obtained an accurate value of the earth's diameter. Newton applied this value, and found, to his great joy, that when the distance of the moon is 60 times the radius of the earth she is attracted out of the straight course 16.1 feet per minute, and that the force acting on a stone or an apple follows the same law as the force acting upon the heavenly bodies.[3]

The universality claimed for the law—if not by Newton, at least by his commentators—was bold, and warranted only by the large number of cases in which Newton had found it to apply. Its universality has been under test ever since, and so far it has stood the test. There has often been a suspicion of a doubt, when some inequality of motion in the heavenly bodies has, for a time, foiled the astronomers in their attempts to explain it. But improved mathematical methods have always succeeded in the end, and so the seeming doubt has been converted into a surer conviction of the universality of the law.

Having once established the law, Newton proceeded to trace some of its consequences. He saw that the figure of the earth depends partly on the mutual gravitation of its parts, and partly on the centrifugal tendency due to the earth's rotation, and that these should cause a flattening of the poles. He invented a mathematical method which he used for computing the ratio of the polar to the equatorial diameter.

He then noticed that the consequent bulging of matter at the equator would be attracted by the moon unequally, the nearest parts being most attracted; and so the moon would tend to tilt the earth when in some parts of her orbit; and the sun would do this to a less extent, because of its great distance. Then he proved that the effect ought to be a rotation of the earth's axis over a conical surface in space, exactly as the axis of a top describes a cone, if the top has a sharp point, and is set spinning and displaced from the vertical. He actually calculated the amount; and so he explained the cause of the precession of the equinoxes discovered by Hipparchus about 150 B.C.

One of his grandest discoveries was a method of weighing the heavenly bodies by their action on each other. By means of this principle he was able to compare the mass of the sun with the masses of those planets that have moons, and also to compare the mass of our moon with the mass of the earth.

Thus Newton, after having established his great principle, devoted his splendid intellect to the calculation of its consequences. He proved that if a body be projected with any velocity in free space, subject only to a central force, varying inversely as the square of the distance, the body must revolve in a curve which may be any one of the sections of a cone—a circle, ellipse, parabola, or hyperbola; and he found that those comets of which he had observations move in parabolae round the Sun, and are thus subject to the universal law.

Newton realised that, while planets and satellites are chiefly controlled by the central body about which they revolve, the new law must involve irregularities, due to their mutual action—such, in fact, as Horrocks had indicated. He determined to put this to a test in the case of the moon, and to calculate the sun's effect, from its mass compared with that of the earth, and from its distance. He proved that the average effect upon the plane of the orbit would be to cause the line in which it cuts the plane of the ecliptic (i.e., the line of nodes) to revolve in the ecliptic once in about nineteen years. This had been a known fact from the earliest ages. He also concluded that the line of apses would revolve in the plane of the lunar orbit also in about nineteen years; but the observed period is only ten years. For a long time this was the one weak point in the Newtonian theory. It was not till 1747 that Clairaut reconciled this with the theory, and showed why Newton's calculation was not exact.

Newton proceeded to explain the other inequalities recognised by Tycho Brahe and older observers, and to calculate their maximum amounts as indicated by his theory. He further discovered from his calculations two new inequalities, one of the apogee, the other of the nodes, and assigned the maximum value. Grant has shown the values of some of these as given by observation in the tables of Meyer and more modern tables, and has compared them with the values assigned by Newton from his theory; and the comparison is very remarkable.

Newton. Modern Tables. degrees ' " degrees ' " Mean monthly motion of Apses 1.31.28 3.4.0 Mean annual motion of nodes 19.18.1,23 19.21.22,50 Mean value of "variation" 36.10 35.47 Annual equation 11.51 11.14 Inequality of mean motion of apogee 19.43 22.17 Inequality of mean motion of nodes 9.24 9.0

The only serious discrepancy is the first, which has been already mentioned. Considering that some of these perturbations had never been discovered, that the cause of none of them had ever been known, and that he exhibited his results, if he did not also make the discoveries, by the synthetic methods of geometry, it is simply marvellous that he reached to such a degree of accuracy. He invented the infinitesimal calculus which is more suited for such calculations, but had he expressed his results in that language he would have been unintelligible to many.

Newton's method of calculating the precession of the equinoxes, already referred to, is as beautiful as anything in the Principia. He had already proved the regression of the nodes of a satellite moving in an orbit inclined to the ecliptic. He now said that the nodes of a ring of satellites revolving round the earth's equator would consequently all regress. And if joined into a solid ring its node would regress; and it would do so, only more slowly, if encumbered by the spherical part of the earth's mass. Therefore the axis of the equatorial belt of the earth must revolve round the pole of the ecliptic. Then he set to work and found the amount due to the moon and that due to the sun, and so he solved the mystery of 2,000 years.

When Newton applied his law of gravitation to an explanation of the tides he started a new field for the application of mathematics to physical problems; and there can be little doubt that, if he could have been furnished with complete tidal observations from different parts of the world, his extraordinary powers of analysis would have enabled him to reach a satisfactory theory. He certainly opened up many mines full of intellectual gems; and his successors have never ceased in their explorations. This has led to improved mathematical methods, which, combined with the greater accuracy of observation, have rendered physical astronomy of to-day the most exact of the sciences.

Laplace only expressed the universal opinion of posterity when he said that to the Principia is assured "a pre-eminence above all the other productions of the human intellect."

The name of Flamsteed, First Astronomer Royal, must here be mentioned as having supplied Newton with the accurate data required for completing the theory.

The name of Edmund Halley, Second Astronomer Royal, must ever be held in repute, not only for his own discoveries, but for the part he played in urging Newton to commit to writing, and present to the Royal Society, the results of his investigations. But for his friendly insistence it is possible that the Principia would never have been written; and but for his generosity in supplying the means the Royal Society could not have published the book.



Sir Isaac Newton died in 1727, at the age of eighty-five. His body lay in state in the Jerusalem Chamber, and was buried in Westminster Abbey.

FOOTNOTES:

[1] The writer inherited from his father (Professor J. D. Forbes) a small box containing a bit of wood and a slip of paper, which had been presented to him by Sir David Brewster. On the paper Sir David had written these words: "If there be any truth in the story that Newton was led to the theory of gravitation by the fall of an apple, this bit of wood is probably a piece of the apple tree from which Newton saw the apple fall. When I was on a pilgrimage to the house in which Newton was born, I cut it off an ancient apple tree growing in his garden." When lecturing in Glasgow, about 1875, the writer showed it to his audience. The next morning, when removing his property from the lecture table, he found that his precious relic had been stolen. It would be interesting to know who has got it now!

[2] It must be noted that these words, in which the laws of gravitation are always summarised in histories and text-books, do not appear in the Principia; but, though they must have been composed by some early commentator, it does not appear that their origin has been traced. Nor does it appear that Newton ever extended the law beyond the Solar System, and probably his caution would have led him to avoid any statement of the kind until it should be proved.

With this exception the above statement of the law of universal gravitation contains nothing that is not to be found in the Principia; and the nearest approach to that statement occurs in the Seventh Proposition of Book III.:—

Prop.: That gravitation occurs in all bodies, and that it is proportional to the quantity of matter in each.

Cor. I.: The total attraction of gravitation on a planet arises, and is composed, out of the attraction on the separate parts.

Cor. II.: The attraction on separate equal particles of a body is reciprocally as the square of the distance from the particles.

[3] It is said that, when working out this final result, the probability of its confirming that part of his theory which he had reluctantly abandoned years before excited him so keenly that he was forced to hand over his calculations to a friend, to be completed by him.



8. NEWTON'S SUCCESSORS—HALLEY, EULER, LAGRANGE, LAPLACE, ETC.

Edmund Halley succeeded Flamsteed as Second Astronomer Royal in 1721. Although he did not contribute directly to the mathematical proofs of Newton's theory, yet his name is closely associated with some of its greatest successes.

He was the first to detect the acceleration of the moon's mean motion. Hipparchus, having compared his own observations with those of more ancient astronomers, supplied an accurate value of the moon's mean motion in his time. Halley similarly deduced a value for modern times, and found it sensibly greater. He announced this in 1693, but it was not until 1749 that Dunthorne used modern lunar tables to compute a lunar eclipse observed in Babylon 721 B.C., another at Alexandria 201 B.C., a solar eclipse observed by Theon 360 A.D., and two later ones up to the tenth century. He found that to explain these eclipses Halley's suggestion must be adopted, the acceleration being 10" in one century. In 1757 Lalande again fixed it at 10."

The Paris Academy, in 1770, offered their prize for an investigation to see if this could be explained by the theory of gravitation. Euler won the prize, but failed to explain the effect, and said: "It appears to be established by indisputable evidence that the secular inequality of the moon's mean motion cannot be produced by the forces of gravitation."

The same subject was again proposed for a prize which was shared by Lagrange [1] and Euler, neither finding a solution, while the latter asserted the existence of a resisting medium in space.

Again, in 1774, the Academy submitted the same subject, a third time, for the prize; and again Lagrange failed to detect a cause in gravitation.

Laplace [2] now took the matter in hand. He tried the effect of a non-instantaneous action of gravity, to no purpose. But in 1787 he gave the true explanation. The principal effect of the sun on the moon's orbit is to diminish the earth's influence, thus lengthening the period to a new value generally taken as constant. But Laplace's calculations showed the new value to depend upon the excentricity of the earth's orbit, which, according; to theory, has a periodical variation of enormous period, and has been continually diminishing for thousands of years. Thus the solar influence has been diminishing, and the moon's mean motion increased. Laplace computed the amount at 10" in one century, agreeing with observation. (Later on Adams showed that Laplace's calculation was wrong, and that the value he found was too large; so, part of the acceleration is now attributed by some astronomers to a lengthening of the day by tidal friction.)

Another contribution by Halley to the verification of Newton's law was made when he went to St. Helena to catalogue the southern stars. He measured the change in length of the second's pendulum in different latitudes due to the changes in gravity foretold by Newton.

Furthermore, he discovered the long inequality of Jupiter and Saturn, whose period is 929 years. For an investigation of this also the Academy of Sciences offered their prize. This led Euler to write a valuable essay disclosing a new method of computing perturbations, called the instantaneous ellipse with variable elements. The method was much developed by Lagrange.

But again it was Laplace who solved the problem of the inequalities of Jupiter and Saturn by the theory of gravitation, reducing the errors of the tables from 20' down to 12", thus abolishing the use of empirical corrections to the planetary tables, and providing another glorious triumph for the law of gravitation. As Laplace justly said: "These inequalities appeared formerly to be inexplicable by the law of gravitation—they now form one of its most striking proofs."

Let us take one more discovery of Halley, furnishing directly a new triumph for the theory. He noticed that Newton ascribed parabolic orbits to the comets which he studied, so that they come from infinity, sweep round the sun, and go off to infinity for ever, after having been visible a few weeks or months. He collected all the reliable observations of comets he could find, to the number of twenty-four, and computed their parabolic orbits by the rules laid down by Newton. His object was to find out if any of them really travelled in elongated ellipses, practically undistinguishable, in the visible part of their paths, from parabolae, in which case they would be seen more than once. He found two old comets whose orbits, in shape and position, resembled the orbit of a comet observed by himself in 1682. Apian observed one in 1531; Kepler the other in 1607. The intervals between these appearances is seventy-five or seventy-six years. He then examined and found old records of similar appearance in 1456, 1380, and 1305. It is true, he noticed, that the intervals varied by a year and a-half, and the inclination of the orbit to the ecliptic diminished with successive apparitions. But he knew from previous calculations that this might easily be due to planetary perturbations. Finally, he arrived at the conclusion that all of these comets were identical, travelling in an ellipse so elongated that the part where the comet was seen seemed to be part of a parabolic orbit. He then predicted its return at the end of 1758 or beginning of 1759, when he should be dead; but, as he said, "if it should return, according to our prediction, about the year 1758, impartial posterity will not refuse to acknowledge that this was first discovered by an Englishman."[3] [Synopsis Astronomiae Cometicae, 1749.]

Once again Halley's suggestion became an inspiration for the mathematical astronomer. Clairaut, assisted by Lalande, found that Saturn would retard the comet 100 days, Jupiter 518 days, and predicted its return to perihelion on April 13th, 1759. In his communication to the French Academy, he said that a comet travelling into such distant regions might be exposed to the influence of forces totally unknown, and "even of some planet too far removed from the sun to be ever perceived."

The excitement of astronomers towards the end of 1758 became intense; and the honour of first catching sight of the traveller fell to an amateur in Saxony, George Palitsch, on Christmas Day, 1758. It reached perihelion on March 13th, 1759.

This fact was a startling confirmation of the Newtonian theory, because it was a new kind of calculation of perturbations, and also it added a new member to the solar system, and gave a prospect of adding many more.

When Halley's comet reappeared in 1835, Pontecoulant's computations for the date of perihelion passage were very exact, and afterwards he showed that, with more exact values of the masses of Jupiter and Saturn, his prediction was correct within two days, after an invisible voyage of seventy-five years!

Hind afterwards searched out many old appearances of this comet, going back to 11 B.C., and most of these have been identified as being really Halley's comet by the calculations of Cowell and Cromellin[4] (of Greenwich Observatory), who have also predicted its next perihelion passage for April 8th to 16th, 1910, and have traced back its history still farther, to 240 B.C.

Already, in November, 1907, the Astronomer Royal was trying to catch it by the aid of photography.

FOOTNOTES:

[1] Born 1736; died 1813.

[2] Born 1749; died 1827.

[3] This sentence does not appear in the original memoir communicated to the Royal Society, but was first published in a posthumous reprint.

[4] R. A. S. Monthly Notices, 1907-8.



9. DISCOVERY OF NEW PLANETS—HERSCHEL, PIAZZI, ADAMS, AND LE VERRIER.

It would be very interesting, but quite impossible in these pages, to discuss all the exquisite researches of the mathematical astronomers, and to inspire a reverence for the names connected with these researches, which for two hundred years have been establishing the universality of Newton's law. The lunar and planetary theories, the beautiful theory of Jupiter's satellites, the figure of the earth, and the tides, were mathematically treated by Maclaurin, D'Alembert, Legendre, Clairaut, Euler, Lagrange, Laplace, Walmsley, Bailly, Lalande, Delambre, Mayer, Hansen, Burchardt, Binet, Damoiseau, Plana, Poisson, Gauss, Bessel, Bouvard, Airy, Ivory, Delaunay, Le Verrier, Adams, and others of later date.

By passing over these important developments it is possible to trace some of the steps in the crowning triumph of the Newtonian theory, by which the planet Neptune was added to the known members of the solar system by the independent researches of Professor J.C. Adams and of M. Le Verrier, in 1846.

It will be best to introduce this subject by relating how the eighteenth century increased the number of known planets, which was then only six, including the earth.

On March 13th, 1781, Sir William Herschel was, as usual, engaged on examining some small stars, and, noticing that one of them appeared to be larger than the fixed stars, suspected that it might be a comet. To test this he increased his magnifying power from 227 to 460 and 932, finding that, unlike the fixed stars near it, its definition was impaired and its size increased. This convinced him that the object was a comet, and he was not surprised to find on succeeding nights that the position was changed, the motion being in the ecliptic. He gave the observations of five weeks to the Royal Society without a suspicion that the object was a new planet.

For a long time people could not compute a satisfactory orbit for the supposed comet, because it seemed to be near the perihelion, and no comet had ever been observed with a perihelion distance from the sun greater than four times the earth's distance. Lexell was the first to suspect that this was a new planet eighteen times as far from the sun as the earth is. In January, 1783, Laplace published the elliptic elements. The discoverer of a planet has a right to name it, so Herschel called it Georgium Sidus, after the king. But Lalande urged the adoption of the name Herschel. Bode suggested Uranus, and this was adopted. The new planet was found to rank in size next to Jupiter and Saturn, being 4.3 times the diameter of the earth.

In 1787 Herschel discovered two satellites, both revolving in nearly the same plane, inclined 80 degrees to the ecliptic, and the motion of both was retrograde.

In 1772, before Herschel's discovery, Bode[1] had discovered a curious arbitrary law of planetary distances. Opposite each planet's name write the figure 4; and, in succession, add the numbers 0, 3, 6, 12, 24, 48, 96, etc., to the 4, always doubling the last numbers. You then get the planetary distances.

Mercury, dist.— 4 4 + 0 = 4 Venus " 7 4 + 3 = 7 Earth " 10 4 + 6 = 10 Mars " 15 4 + 12 = 16 — 4 + 24 = 28 Jupiter dist. 52 4 + 48 = 52 Saturn " 95 4 + 96 = 100 (Uranus) " 192 4 + 192 = 196 — 4 + 384 = 388

All the five planets, and the earth, fitted this rule, except that there was a blank between Mars and Jupiter. When Uranus was discovered, also fitting the rule, the conclusion was irresistible that there is probably a planet between Mars and Jupiter. An association of twenty-four astronomers was now formed in Germany to search for the planet. Almost immediately afterwards the planet was discovered, not by any member of the association, but by Piazzi, when engaged upon his great catalogue of stars. On January 1st, 1801, he observed a star which had changed its place the next night. Its motion was retrograde till January 11th, direct after the 13th. Piazzi fell ill before he had enough observations for computing the orbit with certainty, and the planet disappeared in the sun's rays. Gauss published an approximate ephemeris of probable positions when the planet should emerge from the sun's light. There was an exciting hunt, and on December 31st (the day before its birthday) De Zach captured the truant, and Piazzi christened it Ceres.

The mean distance from the sun was found to be 2.767, agreeing with the 2.8 given by Bode's law. Its orbit was found to be inclined over 10 degrees to the ecliptic, and its diameter was only 161 miles.

On March 28th, 1802, Olbers discovered a new seventh magnitude star, which turned out to be a planet resembling Ceres. It was called Pallas. Gauss found its orbit to be inclined 35 degrees to the ecliptic, and to cut the orbit of Ceres; whence Olbers considered that these might be fragments of a broken-up planet. He then commenced a search for other fragments. In 1804 Harding discovered Juno, and in 1807 Olbers found Vesta. The next one was not discovered until 1845, from which date asteroids, or minor planets (as these small planets are called), have been found almost every year. They now number about 700.

It is impossible to give any idea of the interest with which the first additions since prehistoric times to the planetary system were received. All of those who showered congratulations upon the discoverers regarded these discoveries in the light of rewards for patient and continuous labours, the very highest rewards that could be desired. And yet there remained still the most brilliant triumph of all, the addition of another planet like Uranus, before it had ever been seen, when the analysis of Adams and Le Verrier gave a final proof of the powers of Newton's great law to explain any planetary irregularity.

After Sir William Herschel discovered Uranus, in 1781, it was found that astronomers had observed it on many previous occasions, mistaking it for a fixed star of the sixth or seventh magnitude. Altogether, nineteen observations of Uranus's position, from the time of Flamsteed, in 1690, had been recorded.

In 1790 Delambre, using all these observations, prepared tables for computing its position. These worked well enough for a time, but at last the differences between the calculated and observed longitudes of the planet became serious. In 1821 Bouvard undertook a revision of the tables, but found it impossible to reconcile all the observations of 130 years (the period of revolution of Uranus is eighty-four years). So he deliberately rejected the old ones, expressing the opinion that the discrepancies might depend upon "some foreign and unperceived cause which may have been acting upon the planet." In a few years the errors even of these tables became intolerable. In 1835 the error of longitude was 30"; in 1838, 50"; in 1841, 70"; and, by comparing the errors derived from observations made before and after opposition, a serious error of the distance (radius vector) became apparent.

In 1843 John Couch Adams came out Senior Wrangler at Cambridge, and was free to undertake the research which as an undergraduate he had set himself—to see whether the disturbances of Uranus could be explained by assuming a certain orbit, and position in that orbit, of a hypothetical planet even more distant than Uranus. Such an explanation had been suggested, but until 1843 no one had the boldness to attack the problem. Bessel had intended to try, but a fatal illness overtook him.

Adams first recalculated all known causes of disturbance, using the latest determinations of the planetary masses. Still the errors were nearly as great as ever. He could now, however, use these errors as being actually due to the perturbations produced by the unknown planet.

In 1844, assuming a circular orbit, and a mean distance agreeing with Bode's law, he obtained a first approximation to the position of the supposed planet. He then asked Professor Challis, of Cambridge, to procure the latest observations of Uranus from Greenwich, which Airy immediately supplied. Then the whole work was recalculated from the beginning, with more exactness, and assuming a smaller mean distance.

In September, 1845, he handed to Challis the elements of the hypothetical planet, its mass, and its apparent position for September 30th, 1845. On September 22nd Challis wrote to Airy explaining the matter, and declaring his belief in Adams's capabilities. When Adams called on him Airy was away from home, but at the end of October, 1845, he called again, and left a paper with full particulars of his results, which had, for the most part, reduced the discrepancies to about 1". As a matter of fact, it has since been found that the heliocentric place of the new planet then given was correct within about 2 degrees.

Airy wrote expressing his interest, and asked for particulars about the radius vector. Adams did not then reply, as the answer to this question could be seen to be satisfactory by looking at the data already supplied. He was a most unassuming man, and would not push himself forward. He may have felt, after all the work he had done, that Airy's very natural inquiry showed no proportionate desire to search for the planet. Anyway, the matter lay in embryo for nine months.

Meanwhile, one of the ablest French astronomers, Le Verrier, experienced in computing perturbations, was independently at work, knowing nothing about Adams. He applied to his calculations every possible refinement, and, considering the novelty of the problem, his calculation was one of the most brilliant in the records of astronomy. In criticism it has been said that these were exhibitions of skill rather than helps to a solution of the particular problem, and that, in claiming to find the elements of the orbit within certain limits, he was claiming what was, under the circumstances, impossible, as the result proved.

In June, 1846, Le Verrier announced, in the Comptes Rendus de l'Academie des Sciences, that the longitude of the disturbing planet, for January 1st, 1847, was 325, and that the probable error did not exceed 10 degrees.

This result agreed so well with Adams's (within 1 degrees) that Airy urged Challis to apply the splendid Northumberland equatoreal, at Cambridge, to the search. Challis, however, had already prepared an exhaustive plan of attack which must in time settle the point. His first work was to observe, and make a catalogue, or chart, of all stars near Adams's position.

On August 31st, 1846, Le Verrier published the concluding part of his labours.

On September 18th, 1846, Le Verrier communicated his results to the Astronomers at Berlin, and asked them to assist in searching for the planet. By good luck Dr. Bremiker had just completed a star-chart of the very part of the heavens including Le Verrier's position; thus eliminating all of Challis's preliminary work. The letter was received in Berlin on September 23rd; and the same evening Galle found the new planet, of the eighth magnitude, the size of its disc agreeing with Le Verrier's prediction, and the heliocentric longitude agreeing within 57'. By this time Challis had recorded, without reduction, the observations of 3,150 stars, as a commencement for his search. On reducing these, he found a star, observed on August 12th, which was not in the same place on July 30th. This was the planet, and he had also observed it on August 4th.

The feeling of wonder, admiration, and enthusiasm aroused by this intellectual triumph was overwhelming. In the world of astronomy reminders are met every day of the terrible limitations of human reasoning powers; and every success that enables the mind's eye to see a little more clearly the meaning of things has always been heartily welcomed by those who have themselves been engaged in like researches. But, since the publication of the Principia, in 1687, there is probably no analytical success which has raised among astronomers such a feeling of admiration and gratitude as when Adams and Le Verrier showed the inequalities in Uranus's motion to mean that an unknown planet was in a certain place in the heavens, where it was found.

At the time there was an unpleasant display of international jealousy. The British people thought that the earlier date of Adams's work, and of the observation by Challis, entitled him to at least an equal share of credit with Le Verrier. The French, on the other hand, who, on the announcement of the discovery by Galle, glowed with pride in the new proof of the great powers of their astronomer, Le Verrier, whose life had a long record of successes in calculation, were incredulous on being told that it had all been already done by a young man whom they had never heard of.

These displays of jealousy have long since passed away, and there is now universally an entente cordiale that to each of these great men belongs equally the merit of having so thoroughly calculated this inverse problem of perturbations as to lead to the immediate discovery of the unknown planet, since called Neptune.

It was soon found that the planet had been observed, and its position recorded as a fixed star by Lalande, on May 8th and 10th, 1795.

Mr. Lassel, in the same year, 1846, with his two-feet reflector, discovered a satellite, with retrograde motion, which gave the mass of the planet about a twentieth of that of Jupiter.

FOOTNOTES:

[1] Bode's law, or something like it, had already been fore-shadowed by Kepler and others, especially Titius (see Monatliche Correspondenz, vol. vii., p. 72).



BOOK III. OBSERVATION



10. INSTRUMENTS OF PRECISION—STATE OF THE SOLAR SYSTEM.

Having now traced the progress of physical astronomy up to the time when very striking proofs of the universality of the law of gravitation convinced the most sceptical, it must still be borne in mind that, while gravitation is certainly the principal force governing the motions of the heavenly bodies, there may yet be a resisting medium in space, and there may be electric and magnetic forces to deal with. There may, further, be cases where the effects of luminous radiative repulsion become apparent, and also Crookes' vacuum-effects described as "radiant matter." Nor is it quite certain that Laplace's proofs of the instantaneous propagation of gravity are final.

And in the future, as in the past, Tycho Brahe's dictum must be maintained, that all theory shall be preceded by accurate observations. It is the pride of astronomers that their science stands above all others in the accuracy of the facts observed, as well as in the rigid logic of the mathematics used for interpreting these facts.

It is interesting to trace historically the invention of those instruments of precision which have led to this result, and, without entering on the details required in a practical handbook, to note the guiding principles of construction in different ages.

It is very probable that the Chaldeans may have made spheres, like the armillary sphere, for representing the poles of the heavens; and with rings to show the ecliptic and zodiac, as well as the equinoctial and solstitial colures; but we have no record. We only know that the tower of Belus, on an eminence, was their observatory. We have, however, distinct records of two such spheres used by the Chinese about 2500 B.C. Gnomons, or some kind of sundial, were used by the Egyptians and others; and many of the ancient nations measured the obliquity of the ecliptic by the shadows of a vertical column in summer and winter. The natural horizon was the only instrument of precision used by those who determined star positions by the directions of their risings and settings; while in those days the clepsydra, or waterclock, was the best instrument for comparing their times of rising and setting.

About 300 B.C. an observatory fitted with circular instruments for star positions was set up at Alexandria, the then centre of civilisation. We know almost nothing about the instruments used by Hipparchus in preparing his star catalogues and his lunar and solar tables; but the invention of the astrolabe is attributed to him.[1]

In more modern times Nuremberg became a centre of astronomical culture. Waltherus, of that town, made really accurate observations of star altitudes, and of the distances between stars; and in 1484 A.D. he used a kind of clock. Tycho Brahe tried these, but discarded them as being inaccurate.

Tycho Brahe (1546-1601 A.D.) made great improvements in armillary spheres, quadrants, sextants, and large celestial globes. With these he measured the positions of stars, or the distance of a comet from several known stars. He has left us full descriptions of them, illustrated by excellent engravings. Previous to his time such instruments were made of wood. Tycho always used metal. He paid the greatest attention to the stability of mounting, to the orientation of his instruments, to the graduation of the arcs by the then new method of transversals, and to the aperture sight used upon his pointer. There were no telescopes in his day, and no pendulum clocks. He recognised the fact that there must be instrumental errors. He made these as small as was possible, measured their amount, and corrected his observations. His table of refractions enabled him to abolish the error due to our atmosphere so far as it could affect naked-eye observations. The azimuth circle of Tycho's largest quadrant had a diameter of nine feet, and the quadrant a radius of six feet. He introduced the mural quadrant for meridian observations.[2]



The French Jesuits at Peking, in the seventeenth century, helped the Chinese in their astronomy. In 1875 the writer saw and photographed, on that part of the wall of Peking used by the Mandarins as an observatory, the six instruments handsomely designed by Father Verbiest, copied from the instruments of Tycho Brahe, and embellished with Chinese dragons and emblems cast on the supports. He also saw there two old instruments (which he was told were Arabic) of date 1279, by Ko Show-King, astronomer to Koblai Khan, the grandson of Chenghis Khan. One of these last is nearly identical with the armillae of Tycho; and the other with his "armillae aequatoriae maximae," with which he observed the comet of 1585, besides fixed stars and planets.[3]

The discovery by Galileo of the isochronism of the pendulum, followed by Huyghens's adaptation of that principle to clocks, has been one of the greatest aids to accurate observation. About the same time an equally beneficial step was the employment of the telescope as a pointer; not the Galilean with concave eye-piece, but with a magnifying glass to examine the focal image, at which also a fixed mark could be placed. Kepler was the first to suggest this. Gascoigne was the first to use it. Huyghens used a metal strip of variable width in the focus, as a micrometer to cover a planetary disc, and so to measure the width covered by the planet. The Marquis Malvasia, in 1662, described the network of fine silver threads at right angles, which he used in the focus, much as we do now.

In the hands of such a skilful man as Tycho Brahe, the old open sights, even without clocks, served their purpose sufficiently well to enable Kepler to discover the true theory of the solar system. But telescopic sights and clocks were required for proving some of Newton's theories of planetary perturbations. Picard's observations at Paris from 1667 onwards seem to embody the first use of the telescope as a pointer. He was also the first to introduce the use of Huyghens's clocks for observing the right ascension of stars. Olaus Romer was born at Copenhagen in 1644. In 1675, by careful study of the times of eclipses of Jupiter's satellites, he discovered that light took time to traverse space. Its velocity is 186,000 miles per second. In 1681 he took up his duties as astronomer at Copenhagen, and built the first transit circle on a window-sill of his house. The iron axis was five feet long and one and a-half inches thick, and the telescope was fixed near one end with a counterpoise. The telescope-tube was a double cone, to prevent flexure. Three horizontal and three vertical wires were used in the focus. These were illuminated by a speculum, near the object-glass, reflecting the light from a lantern placed over the axis, the upper part of the telescope-tube being partly cut away to admit the light. A divided circle, with pointer and reading microscope, was provided for reading the declination. He realised the superiority of a circle with graduations over a much larger quadrant. The collimation error was found by reversing the instrument and using a terrestrial mark, the azimuth error by star observations. The time was expressed in fractions of a second. He also constructed a telescope with equatoreal mounting, to follow a star by one axial motion. In 1728 his instruments and observation records were destroyed by fire.

Hevelius had introduced the vernier and tangent screw in his measurement of arc graduations. His observatory and records were burnt to the ground in 1679. Though an old man, he started afresh, and left behind him a catalogue of 1,500 stars.

Flamsteed began his duties at Greenwich Observatory, as first Astronomer Royal, in 1676, with very poor instruments. In 1683 he put up a mural arc of 140 degrees, and in 1689 a better one, seventy-nine inches radius. He conducted his measurements with great skill, and introduced new methods to attain accuracy, using certain stars for determining the errors of his instruments; and he always reduced his observations to a form in which they could be readily used. He introduced new methods for determining the position of the equinox and the right ascension of a fundamental star. He produced a catalogue of 2,935 stars. He supplied Sir Isaac Newton with results of observation required in his theoretical calculations. He died in 1719.

Halley succeeded Flamsteed to find that the whole place had been gutted by the latter's executors. In 1721 he got a transit instrument, and in 1726 a mural quadrant by Graham. His successor in 1742, Bradley, replaced this by a fine brass quadrant, eight feet radius, by Bird; and Bradley's zenith sector was purchased for the observatory. An instrument like this, specially designed for zenith stars, is capable of greater rigidity than a more universal instrument; and there is no trouble with refraction in the zenith. For these reasons Bradley had set up this instrument at Kew, to attempt the proof of the earth's motion by observing the annual parallax of stars. He certainly found an annual variation of zenith distance, but not at the times of year required by the parallax. This led him to the discovery of the "aberration" of light and of nutation. Bradley has been described as the founder of the modern system of accurate observation. He died in 1762, leaving behind him thirteen folio volumes of valuable but unreduced observations. Those relating to the stars were reduced by Bessel and published in 1818, at Konigsberg, in his well-known standard work, Fundamenta Astronomiae. In it are results showing the laws of refraction, with tables of its amount, the maximum value of aberration, and other constants.

Bradley was succeeded by Bliss, and he by Maskelyne (1765), who carried on excellent work, and laid the foundations of the Nautical Almanac (1767). Just before his death he induced the Government to replace Bird's quadrant by a fine new mural circle, six feet in diameter, by Troughton, the divisions being read off by microscopes fixed on piers opposite to the divided circle. In this instrument the micrometer screw, with a divided circle for turning it, was applied for bringing the micrometer wire actually in line with a division on the circle—a plan which is still always adopted.

Pond succeeded Maskelyne in 1811, and was the first to use this instrument. From now onwards the places of stars were referred to the pole, not to the zenith; the zero being obtained from measures on circumpolar stars. Standard stars were used for giving the clock error. In 1816 a new transit instrument, by Troughton, was added, and from this date the Greenwich star places have maintained the very highest accuracy.

George Biddell Airy, Seventh Astronomer Royal,[4] commenced his Greenwich labours in 1835. His first and greatest reformation in the work of the observatory was one he had already established at Cambridge, and is now universally adopted. He held that an observation is not completed until it has been reduced to a useful form; and in the case of the sun, moon, and planets these results were, in every case, compared with the tables, and the tabular error printed.

Airy was firmly impressed with the object for which Charles II. had wisely founded the observatory in connection with navigation, and for observations of the moon. Whenever a meridian transit of the moon could be observed this was done. But, even so, there are periods in the month when the moon is too near the sun for a transit to be well observed. Also weather interferes with many meridian observations. To render the lunar observations more continuous, Airy employed Troughton's successor, James Simms, in conjunction with the engineers, Ransome and May, to construct an altazimuth with three-foot circles, and a five-foot telescope, in 1847. The result was that the number of lunar observations was immediately increased threefold, many of them being in a part of the moon's orbit which had previously been bare of observations. From that date the Greenwich lunar observations have been a model and a standard for the whole world.

Airy also undertook to superintend the reduction of all Greenwich lunar observations from 1750 to 1830. The value of this laborious work, which was completed in 1848, cannot be over-estimated.

The demands of astronomy, especially in regard to small minor planets, required a transit instrument and mural circle with a more powerful telescope. Airy combined the functions of both, and employed the same constructors as before to make a transit-circle with a telescope of eleven and a-half feet focus and a circle of six-feet diameter, the object-glass being eight inches in diameter.

Airy, like Bradley, was impressed with the advantage of employing stars in the zenith for determining the fundamental constants of astronomy. He devised a reflex zenith tube, in which the zenith point was determined by reflection from a surface of mercury. The design was so simple, and seemed so perfect, that great expectations were entertained. But unaccountable variations comparable with those of the transit circle appeared, and the instrument was put out of use until 1903, when the present Astronomer Royal noticed that the irregularities could be allowed for, being due to that remarkable variation in the position of the earth's axis included in circles of about six yards diameter at the north and south poles, discovered at the end of the nineteenth century. The instrument is now being used for investigating these variations; and in the year 1907 as many as 1,545 observations of stars were made with the reflex zenith tube.

In connection with zenith telescopes it must be stated that Respighi, at the Capitol Observatory at Rome, made use of a deep well with a level mercury surface at the bottom and a telescope at the top pointing downwards, which the writer saw in 1871. The reflection of the micrometer wires and of a star very near the zenith (but not quite in the zenith) can be observed together. His mercury trough was a circular plane surface with a shallow edge to retain the mercury. The surface quickly came to rest after disturbance by street traffic.

Sir W. M. H. Christie, Eighth Astronomer Royal, took up his duties in that capacity in 1881. Besides a larger altazimuth that he erected in 1898, he has widened the field of operations at Greenwich by the extensive use of photography and the establishment of large equatoreals. From the point of view of instruments of precision, one of the most important new features is the astrographic equatoreal, set up in 1892 and used for the Greenwich section of the great astrographic chart just completed. Photography has come to be of use, not only for depicting the sun and moon, comets and nebulae, but also to obtain accurate relative positions of neighbouring stars; to pick up objects that are invisible in any telescope; and, most of all perhaps, in fixing the positions of faint satellites. Thus Saturn's distant satellite, Phoebe, and the sixth and seventh satellites of Jupiter, have been followed regularly in their courses at Greenwich ever since their discovery with the thirty-inch reflector (erected in 1897); and while doing so Mr. Melotte made, in 1908, the splendid discovery on some of the photographic plates of an eighth satellite of Jupiter, at an enormous distance from the planet. From observations in the early part of 1908, over a limited arc of its orbit, before Jupiter approached the sun, Mr. Cowell computed a retrograde orbit and calculated the future positions of this satellite, which enabled Mr. Melotte to find it again in the autumn—a great triumph both of calculation and of photographic observation. This satellite has never been seen, and has been photographed only at Greenwich, Heidelberg, and the Lick Observatory.

Greenwich Observatory has been here selected for tracing the progress of accurate measurement. But there is one instrument of great value, the heliometer, which is not used at Greenwich. This serves the purpose of a double image micrometer, and is made by dividing the object-glass of a telescope along a diameter. Each half is mounted so as to slide a distance of several inches each way on an arc whose centre is the focus. The amount of the movement can be accurately read. Thus two fields of view overlap, and the adjustment is made to bring an image of one star over that of another star, and then to do the same by a displacement in the opposite direction. The total movement of the half-object glass is double the distance between the star images in the focal plane. Such an instrument has long been established at Oxford, and German astronomers have made great use of it. But in the hands of Sir David Gill (late His Majesty's Astronomer at the Cape of Good Hope), and especially in his great researches on Solar and on Stellar parallax, it has been recognised as an instrument of the very highest accuracy, measuring the distance between stars correctly to less than a tenth of a second of arc.

The superiority of the heliometer over all other devices (except photography) for measuring small angles has been specially brought into prominence by Sir David Gill's researches on the distance of the sun—i.e., the scale of the solar system. A measurement of the distance of any planet fixes the scale, and, as Venus approaches the earth most nearly of all the planets, it used to be supposed that a Transit of Venus offered the best opportunity for such measurement, especially as it was thought that, as Venus entered on the solar disc, the sweep of light round the dark disc of Venus would enable a very precise observation to be made. The Transit of Venus in 1874, in which the present writer assisted, overthrew this delusion.

In 1877 Sir David Gill used Lord Crawford's heliometer at the Island of Ascension to measure the parallax of Mars in opposition, and found the sun's distance 93,080,000 miles. He considered that, while the superiority of the heliometer had been proved, the results would be still better with the points of light shown by minor planets rather than with the disc of Mars.

In 1888-9, at the Cape, he observed the minor planets Iris, Victoria, and Sappho, and secured the co-operation of four other heliometers. His final result was 92,870,000 miles, the parallax being 8",802 (Cape Obs., Vol. VI.).

So delicate were these measures that Gill detected a minute periodic error of theory of twenty-seven days, owing to a periodically erroneous position of the centre of gravity of the earth and moon to which the position of the observer was referred. This led him to correct the mass of the moon, and to fix its ratio to the earth's mass = 0.012240.

Another method of getting the distance from the sun is to measure the velocity of the earth's orbital motion, giving the circumference traversed in a year, and so the radius of the orbit. This has been done by comparing observation and experiment. The aberration of light is an angle 20" 48, giving the ratio of the earth's velocity to the velocity of light. The velocity of light is 186,000 miles a second; whence the distance to the sun is 92,780,000 miles. There seems, however, to be some uncertainty about the true value of the aberration, any determination of which is subject to irregularities due to the "seasonal errors." The velocity of light was experimentally found, in 1862, by Fizeau and Foucault, each using an independent method. These methods have been developed, and new values found, by Cornu, Michaelson, Newcomb, and the present writer.

Quite lately Halm, at the Cape of Good Hope, measured spectroscopically the velocity of the earth to and from a star by observations taken six months apart. Thence he obtained an accurate value of the sun's distance.[5]

But the remarkably erratic minor planet, Eros, discovered by Witte in 1898, approaches the earth within 15,000,000 miles at rare intervals, and, with the aid of photography, will certainly give us the best result. A large number of observatories combined to observe the opposition of 1900. Their results are not yet completely reduced, but the best value deduced so far for the parallax[6] is 8".807 +/- 0".0028.[7]

FOOTNOTES:

[1] In 1480 Martin Behaim, of Nuremberg, produced his astrolabe for measuring the latitude, by observation of the sun, at sea. It consisted of a graduated metal circle, suspended by a ring which was passed over the thumb, and hung vertically. A pointer was fixed to a pin at the centre. This arm, called the alhidada, worked round the graduated circle, and was pointed to the sun. The altitude of the sun was thus determined, and, by help of solar tables, the latitude could be found from observations made at apparent noon.

[2] See illustration on p. 76.

[3] See Dreyer's article on these instruments in Copernicus, Vol. I. They were stolen by the Germans after the relief of the Embassies, in 1900. The best description of these instruments is probably that contained in an interesting volume, which may be seen in the library of the R. A. S., entitled Chinese Researches, by Alexander Wyllie (Shanghai, 1897).

[4] Sir George Airy was very jealous of this honourable title. He rightly held that there is only one Astronomer Royal at a time, as there is only one Mikado, one Dalai Lama. He said that His Majesty's Astronomer at the Cape of Good Hope, His Majesty's Astronomer for Scotland, and His Majesty's Astronomer for Ireland are not called Astronomers Royal.

[5] Annals of the Cape Observatory, vol. x., part 3.

[6] The parallax of the sun is the angle subtended by the earth's radius at the sun's distance.

[7] A. R. Hinks, R.A.S.; Monthly Notices, June, 1909.



11. HISTORY OF THE TELESCOPE

Accounts of wonderful optical experiments by Roger Bacon (who died in 1292), and in the sixteenth century by Digges, Baptista Porta, and Antonio de Dominis (Grant, Hist. Ph. Ast.), have led some to suppose that they invented the telescope. The writer considers that it is more likely that these notes refer to a kind of camera obscura, in which a lens throws an inverted image of a landscape on the wall.

The first telescopes were made in Holland, the originator being either Henry Lipperhey,[1] Zacharias Jansen, or James Metius, and the date 1608 or earlier.

In 1609 Galileo, being in Venice, heard of the invention, went home and worked out the theory, and made a similar telescope. These telescopes were all made with a convex object-glass and a concave eye-lens, and this type is spoken of as the Galilean telescope. Its defects are that it has no real focus where cross-wires can be placed, and that the field of view is very small. Kepler suggested the convex eye-lens in 1611, and Scheiner claimed to have used one in 1617. But it was Huyghens who really introduced them. In the seventeenth century telescopes were made of great length, going up to 300 feet. Huyghens also invented the compound eye-piece that bears his name, made of two convex lenses to diminish spherical aberration.

But the defects of colour remained, although their cause was unknown until Newton carried out his experiments on dispersion and the solar spectrum. To overcome the spherical aberration James Gregory,[2] of Aberdeen and Edinburgh, in 1663, in his Optica Promota, proposed a reflecting speculum of parabolic form. But it was Newton, about 1666, who first made a reflecting telescope; and he did it with the object of avoiding colour dispersion.

Some time elapsed before reflectors were much used. Pound and Bradley used one presented to the Royal Society by Hadley in 1723. Hawksbee, Bradley, and Molyneaux made some. But James Short, of Edinburgh, made many excellent Gregorian reflectors from 1732 till his death in 1768.

Newton's trouble with refractors, chromatic aberration, remained insurmountable until John Dollond (born 1706, died 1761), after many experiments, found out how to make an achromatic lens out of two lenses—one of crown glass, the other of flint glass—to destroy the colour, in a way originally suggested by Euler. He soon acquired a great reputation for his telescopes of moderate size; but there was a difficulty in making flint-glass lenses of large size. The first actual inventor and constructor of an achromatic telescope was Chester Moor Hall, who was not in trade, and did not patent it. Towards the close of the eighteenth century a Swiss named Guinand at last succeeded in producing larger flint-glass discs free from striae. Frauenhofer, of Munich, took him up in 1805, and soon produced, among others, Struve's Dorpat refractor of 9.9 inches diameter and 13.5 feet focal length, and another, of 12 inches diameter and 18 feet focal length, for Lamont, of Munich.

In the nineteenth century gigantic reflectors have been made. Lassel's 2-foot reflector, made by himself, did much good work, and discovered four new satellites. But Lord Rosse's 6-foot reflector, 54 feet focal length, constructed in 1845, is still the largest ever made. The imperfections of our atmosphere are against the use of such large apertures, unless it be on high mountains. During the last half century excellent specula have been made of silvered glass, and Dr. Common's 5-foot speculum (removed, since his death, to Harvard) has done excellent work. Then there are the 5-foot Yerkes reflector at Chicago, and the 4-foot by Grubb at Melbourne.

Passing now from these large reflectors to refractors, further improvements have been made in the manufacture of glass by Chance, of Birmingham, Feil and Mantois, of Paris, and Schott, of Jena; while specialists in grinding lenses, like Alvan Clark, of the U.S.A., and others, have produced many large refractors.

Cooke, of York, made an object-glass, 25-inch diameter, for Newall, of Gateshead, which has done splendid work at Cambridge. We have the Washington 26-inch by Clark, the Vienna 27-inch by Grubb, the Nice 29-1/2-inch by Gautier, the Pulkowa 30-inch by Clark. Then there was the sensation of Clark's 36-inch for the Lick Observatory in California, and finally his tour de force, the Yerkes 40-inch refractor, for Chicago.

At Greenwich there is the 28-inch photographic refractor, and the Thompson equatoreal by Grubb, carrying both the 26-inch photographic refractor and the 30-inch reflector. At the Cape of Good Hope we find Mr. Frank McClean's 24-inch refractor, with an object-glass prism for spectroscopic work.

It would be out of place to describe here the practical adjuncts of a modern equatoreal—the adjustments for pointing it, the clock for driving it, the position-micrometer and various eye-pieces, the photographic and spectroscopic attachments, the revolving domes, observing seats, and rising floors and different forms of mounting, the siderostats and coelostats, and other convenient adjuncts, besides the registering chronograph and numerous facilities for aiding observation. On each of these a chapter might be written; but the most important part of the whole outfit is the man behind the telescope, and it is with him that a history is more especially concerned.

SPECTROSCOPE.

Since the invention of the telescope no discovery has given so great an impetus to astronomical physics as the spectroscope; and in giving us information about the systems of stars and their proper motions it rivals the telescope.

Frauenhofer, at the beginning of the nineteenth century, while applying Dollond's discovery to make large achromatic telescopes, studied the dispersion of light by a prism. Admitting the light of the sun through a narrow slit in a window-shutter, an inverted image of the slit can be thrown, by a lens of suitable focal length, on the wall opposite. If a wedge or prism of glass be interposed, the image is deflected to one side; but, as Newton had shown, the images formed by the different colours of which white light is composed are deflected to different extents—the violet most, the red least. The number of colours forming images is so numerous as to form a continuous spectrum on the wall with all the colours—red, orange, yellow, green, blue, indigo, and violet. But Frauenhofer found with a narrow slit, well focussed by the lens, that some colours were missing in the white light of the sun, and these were shown by dark lines across the spectrum. These are the Frauenhofer lines, some of which he named by the letters of the alphabet. The D line is a very marked one in the yellow. These dark lines in the solar spectrum had already been observed by Wollaston. [3]

On examining artificial lights it was found that incandescent solids and liquids (including the carbon glowing in a white gas flame) give continuous spectra; gases, except under enormous pressure, give bright lines. If sodium or common salt be thrown on the colourless flame of a spirit lamp, it gives it a yellow colour, and its spectrum is a bright yellow line agreeing in position with line D of the solar spectrum.

In 1832 Sir David Brewster found some of the solar black lines increased in strength towards sunset, and attributed them to absorption in the earth's atmosphere. He suggested that the others were due to absorption in the sun's atmosphere. Thereupon Professor J. D. Forbes pointed out that during a nearly total eclipse the lines ought to be strengthened in the same way; as that part of the sun's light, coming from its edge, passes through a great distance in the sun's atmosphere. He tried this with the annular eclipse of 1836, with a negative result which has never been accounted for, and which seemed to condemn Brewster's view.

In 1859 Kirchoff, on repeating Frauenhofer's experiment, found that, if a spirit lamp with salt in the flame were placed in the path of the light, the black D line is intensified. He also found that, if he used a limelight instead of the sunlight and passed it through the flame with salt, the spectrum showed the D line black; or the vapour of sodium absorbs the same light that it radiates. This proved to him the existence of sodium in the sun's atmosphere.[4] Iron, calcium, and other elements were soon detected in the same way.

Extensive laboratory researches (still incomplete) have been carried out to catalogue (according to their wave-length on the undulatory theory of light) all the lines of each chemical element, under all conditions of temperature and pressure. At the same time, all the lines have been catalogued in the light of the sun and the brighter of the stars.

Another method of obtaining spectra had long been known, by transmission through, or reflection from, a grating of equidistant lines ruled upon glass or metal. H. A. Rowland developed the art of constructing these gratings, which requires great technical skill, and for this astronomers owe him a debt of gratitude.

In 1842 Doppler[5] proved that the colour of a luminous body, like the pitch or note of a sounding body, must be changed by velocity of approach or recession. Everyone has noticed on a railway that, on meeting a locomotive whistling, the note is lowered after the engine has passed. The pitch of a sound or the colour of a light depends on the number of waves striking the ear or eye in a second. This number is increased by approach and lowered by recession.

Thus, by comparing the spectrum of a star alongside a spectrum of hydrogen, we may see all the lines, and be sure that there is hydrogen in the star; yet the lines in the star-spectrum may be all slightly displaced to one side of the lines of the comparison spectrum. If towards the violet end, it means mutual approach of the star and earth; if to the red end, it means recession. The displacement of lines does not tell us whether the motion is in the star, the earth, or both. The displacement of the lines being measured, we can calculate the rate of approach or recession in miles per second.

In 1868 Huggins[6] succeeded in thus measuring the velocities of stars in the direction of the line of sight.

In 1873 Vogel[7] compared the spectra of the sun's East (approaching) limb and West (receding) limb, and the displacement of lines endorsed the theory. This last observation was suggested by Zollner.

FOOTNOTES:

[1] In the Encyclopaedia Britannica, article "Telescope," and in Grant's Physical Astronomy, good reasons are given for awarding the honour to Lipperhey.

[2] Will the indulgent reader excuse an anecdote which may encourage some workers who may have found their mathematics defective through want of use? James Gregory's nephew David had a heap of MS. notes by Newton. These descended to a Miss Gregory, of Edinburgh, who handed them to the present writer, when an undergraduate at Cambridge, to examine. After perusal, he lent them to his kindest of friends, J. C. Adams (the discoverer of Neptune), for his opinion. Adams's final verdict was: "I fear they are of no value. It is pretty evident that, when he wrote these notes, Newton's mathematics were a little rusty."

[3] R. S. Phil. Trans.

[4] The experiment had been made before by one who did not understand its meaning;. But Sir George G. Stokes had already given verbally the true explanation of Frauenhofer lines.

[5] Abh. d. Kon. Bohm. d. Wiss., Bd. ii., 1841-42, p. 467. See also Fizeau in the Ann. de Chem. et de Phys., 1870, p. 211.

[6] R. S. Phil. Trans., 1868.

[7] Ast. Nach., No. 1, 864.



BOOK IV. THE PHYSICAL PERIOD

We have seen how the theory of the solar system was slowly developed by the constant efforts of the human mind to find out what are the rules of cause and effect by which our conception of the present universe and its development seems to be bound. In the primitive ages a mere record of events in the heavens and on the earth gave the only hope of detecting those uniform sequences from which to derive rules or laws of cause and effect upon which to rely. Then came the geometrical age, in which rules were sought by which to predict the movements of heavenly bodies. Later, when the relation of the sun to the courses of the planets was established, the sun came to be looked upon as a cause; and finally, early in the seventeenth century, for the first time in history, it began to be recognised that the laws of dynamics, exactly as they had been established for our own terrestrial world, hold good, with the same rigid invariability, at least as far as the limits of the solar system.

Throughout this evolution of thought and conjecture there were two types of astronomers—those who supplied the facts, and those who supplied the interpretation through the logic of mathematics. So Ptolemy was dependent upon Hipparchus, Kepler on Tycho Brahe, and Newton in much of his work upon Flamsteed.

When Galileo directed his telescope to the heavens, when Secchi and Huggins studied the chemistry of the stars by means of the spectroscope, and when Warren De la Rue set up a photoheliograph at Kew, we see that a progress in the same direction as before, in the evolution of our conception of the universe, was being made. Without definite expression at any particular date, it came to be an accepted fact that not only do earthly dynamics apply to the heavenly bodies, but that the laws we find established here, in geology, in chemistry, and in the laws of heat, may be extended with confidence to the heavenly bodies. Hence arose the branch of astronomy called astronomical physics, a science which claims a large portion of the work of the telescope, spectroscope, and photography. In this new development it is more than ever essential to follow the dictum of Tycho Brahe—not to make theories until all the necessary facts are obtained. The great astronomers of to-day still hold to Sir Isaac Newton's declaration, "Hypotheses non fingo." Each one may have his suspicions of a theory to guide him in a course of observation, and may call it a working hypothesis. But the cautious astronomer does not proclaim these to the world; and the historian is certainly not justified in including in his record those vague speculations founded on incomplete data which may be demolished to-morrow, and which, however attractive they may be, often do more harm than good to the progress of true science. Meanwhile the accumulation of facts has been prodigious, and the revelations of the telescope and spectroscope entrancing.



12. THE SUN.

One of Galileo's most striking discoveries, when he pointed his telescope to the heavenly bodies, was that of the irregularly shaped spots on the sun, with the dark central umbra and the less dark, but more extensive, penumbra surrounding it, sometimes with several umbrae in one penumbra. He has left us many drawings of these spots, and he fixed their period of rotation as a lunar month.



It is not certain whether Galileo, Fabricius, or Schemer was the first to see the spots. They all did good work. The spots were found to be ever varying in size and shape. Sometimes, when a spot disappears at the western limb of the sun, it is never seen again. In other cases, after a fortnight, it reappears at the eastern limb. The faculae, or bright areas, which are seen all over the sun's surface, but specially in the neighbourhood of spots, and most distinctly near the sun's edge, were discovered by Galileo. A high telescopic power resolves their structure into an appearance like willow-leaves, or rice-grains, fairly uniform in size, and more marked than on other parts of the sun's surface.

Speculations as to the cause of sun-spots have never ceased from Galileo's time to ours. He supposed them to be clouds. Scheiner[1] said they were the indications of tumultuous movements occasionally agitating the ocean of liquid fire of which he supposed the sun to be composed.

A. Wilson, of Glasgow, in 1769,[2] noticed a movement of the umbra relative to the penumbra in the transit of the spot over the sun's surface; exactly as if the spot were a hollow, with a black base and grey shelving sides. This was generally accepted, but later investigations have contradicted its universality. Regarding the cause of these hollows, Wilson said:—

Whether their first production and subsequent numberless changes depend upon the eructation of elastic vapours from below, or upon eddies or whirlpools commencing at the surface, or upon the dissolving of the luminous matter in the solar atmosphere, as clouds are melted and again given out by our air; or, if the reader pleases, upon the annihilation and reproduction of parts of this resplendent covering, is left for theory to guess at.[3]

Ever since that date theory has been guessing at it. The solar astronomer is still applying all the instruments of modern research to find out which of these suppositions, or what modification of any of them, is nearest the truth. The obstacle—one that is perhaps fatal to a real theory—lies in the impossibility of reproducing comparative experiments in our laboratories or in our atmosphere.

Sir William Herschel propounded an explanation of Wilson's observation which received much notice, but which, out of respect for his memory, is not now described, as it violated the elementary laws of heat.

Sir John Herschel noticed that the spots are mostly confined to two zones extending to about 35 degrees on each side of the equator, and that a zone of equatoreal calms is free from spots. But it was R. C. Carrington[4] who, by his continuous observations at Redhill, in Surrey, established the remarkable fact that, while the rotation period in the highest latitudes, 50 degrees, where spots are seen, is twenty-seven-and-a-half days, near the equator the period is only twenty-five days. His splendid volume of observations of the sun led to much new information about the average distribution of spots at different epochs.

Schwabe, of Dessau, began in 1826 to study the solar surface, and, after many years of work, arrived at a law of frequency which has been more fruitful of results than any discovery in solar physics.[5] In 1843 he announced a decennial period of maxima and minima of sun-spot displays. In 1851 it was generally accepted, and, although a period of eleven years has been found to be more exact, all later observations, besides the earlier ones which have been hunted up for the purpose, go to establish a true periodicity in the number of sun-spots. But quite lately Schuster[6] has given reasons for admitting a number of co-existent periods, of which the eleven-year period was predominant in the nineteenth century.

In 1851 Lament, a Scotchman at Munich, found a decennial period in the daily range of magnetic declination. In 1852 Sir Edward Sabine announced a similar period in the number of "magnetic storms" affecting all of the three magnetic elements—declination, dip, and intensity. Australian and Canadian observations both showed the decennial period in all three elements. Wolf, of Zurich, and Gauthier, of Geneva, each independently arrived at the same conclusion.

It took many years before this coincidence was accepted as certainly more than an accident by the old-fashioned astronomers, who want rigid proof for every new theory. But the last doubts have long vanished, and a connection has been further traced between violent outbursts of solar activity and simultaneous magnetic storms.

The frequency of the Aurora Borealis was found by Wolf to follow the same period. In fact, it is closely allied in its cause to terrestrial magnetism. Wolf also collected old observations tracing the periodicity of sun-spots back to about 1700 A.D.

Spoerer deduced a law of dependence of the average latitude of sun-spots on the phase of the sun-spot period.

All modern total solar eclipse observations seem to show that the shape of the luminous corona surrounding the moon at the moment of totality has a special distinct character during the time of a sun-spot maximum, and another, totally different, during a sun-spot minimum.

A suspicion is entertained that the total quantity of heat received by the earth from the sun is subject to the same period. This would have far-reaching effects on storms, harvests, vintages, floods, and droughts; but it is not safe to draw conclusions of this kind except from a very long period of observations.

Solar photography has deprived astronomers of the type of Carrington of the delight in devoting a life's work to collecting data. It has now become part of the routine work of an observatory.

In 1845 Foucault and Fizeau took a daguerreotype photograph of the sun. In 1850 Bond produced one of the moon of great beauty, Draper having made some attempts at an even earlier date. But astronomical photography really owes its beginning to De la Rue, who used the collodion process for the moon in 1853, and constructed the Kew photoheliograph in 1857, from which date these instruments have been multiplied, and have given us an accurate record of the sun's surface. Gelatine dry plates were first used by Huggins in 1876.

It is noteworthy that from the outset De la Rue recognised the value of stereoscopic vision, which is now known to be of supreme accuracy. In 1853 he combined pairs of photographs of the moon in the same phase, but under different conditions regarding libration, showing the moon from slightly different points of view. These in the stereoscope exhibited all the relief resulting from binocular vision, and looked like a solid globe. In 1860 he used successive photographs of the total solar eclipse stereoscopically, to prove that the red prominences belong to the sun, and not to the moon. In 1861 he similarly combined two photographs of a sun-spot, the perspective effect showing the umbra like a floor at the bottom of a hollow penumbra; and in one case the faculae were discovered to be sailing over a spot apparently at some considerable height. These appearances may be partly due to a proper motion; but, so far as it went, this was a beautiful confirmation of Wilson's discovery. Hewlett, however, in 1894, after thirty years of work, showed that the spots are not always depressions, being very subject to disturbance.

The Kew photographs [7] contributed a vast amount of information about sun-spots, and they showed that the faculae generally follow the spots in their rotation round the sun.

The constitution of the sun's photosphere, the layer which is the principal light-source on the sun, has always been a subject of great interest; and much was done by men with exceptionally keen eyesight, like Mr. Dawes. But it was a difficult subject, owing to the rapidity of the changes in appearance of the so-called rice-grains, about 1" in diameter. The rapid transformations and circulations of these rice-grains, if thoroughly studied, might lead to a much better knowledge of solar physics. This seemed almost hopeless, as it was found impossible to identify any "rice-grain" in the turmoil after a few minutes. But M. Hansky, of Pulkowa (whose recent death is deplored), introduced successfully a scheme of photography, which might almost be called a solar cinematograph. He took photographs of the sun at intervals of fifteen or thirty seconds, and then enlarged selected portions of these two hundred times, giving a picture corresponding to a solar disc of six metres diameter. In these enlarged pictures he was able to trace the movements, and changes of shape and brightness, of individual rice-grains. Some granules become larger or smaller. Some seem to rise out of a mist, as it were, and to become clearer. Others grow feebler. Some are split in two. Some are rotated through a right angle in a minute or less, although each of the grains may be the size of Great Britain. Generally they move together in groups of very various velocities, up to forty kilometres a second. These movements seem to have definite relation to any sun-spots in the neighbourhood. From the results already obtained it seems certain that, if this method of observation be continued, it cannot fail to supply facts of the greatest importance.

It is quite impossible to do justice here to the work of all those who are engaged on astronomical physics. The utmost that can be attempted is to give a fair idea of the directions of human thought and endeavour. During the last half-century America has made splendid progress, and an entirely new process of studying the photosphere has been independently perfected by Professor Hale at Chicago, and Deslandres at Paris.[8] They have succeeded in photographing the sun's surface in monochromatic light, such as the light given off as one of the bright lines of hydrogen or of calcium, by means of the "Spectroheliograph." The spectroscope is placed with its slit in the focus of an equatoreal telescope, pointed to the sun, so that the circular image of the sun falls on the slit. At the other end of the spectroscope is the photographic plate. Just in front of this plate there is another slit parallel to the first, in the position where the image of the first slit formed by the K line of calcium falls. Thus is obtained a photograph of the section of the sun, made by the first slit, only in K light. As the image of the sun passes over the first slit the photographic plate is moved at the same rate and in the same direction behind the second slit; and as successive sections of the sun's image in the equatoreal enter the apparatus, so are these sections successively thrown in their proper place on the photographic plate, always in K light. By using a high dispersion the faculae which give off K light can be correctly photographed, not only at the sun's edge, but all over his surface. The actual mechanical method of carrying out the observation is not quite so simple as what is here described.

By choosing another line of the spectrum instead of calcium K—for example, the hydrogen line H(3)—we obtain two photographs, one showing the appearance of the calcium floculi, and the other of the hydrogen floculi, on the same part of the solar surface; and nothing is more astonishing than to note the total want of resemblance in the forms shown on the two. This mode of research promises to afford many new and useful data.

The spectroscope has revealed the fact that, broadly speaking, the sun is composed of the same materials as the earth. Angstrom was the first to map out all of the lines to be found in the solar spectrum. But Rowland, of Baltimore, after having perfected the art of making true gratings with equidistant lines ruled on metal for producing spectra, then proceeded to make a map of the solar spectrum on a large scale.

In 1866 Lockyer[9] threw an image of the sun upon the slit of a spectroscope, and was thus enabled to compare the spectrum of a spot with that of the general solar surface. The observation proved the darkness of a spot to be caused by increased absorption of light, not only in the dark lines, which are widened, but over the entire spectrum. In 1883 Young resolved this continuous obscurity into an infinite number of fine lines, which have all been traced in a shadowy way on to the general solar surface. Lockyer also detected displacements of the spectrum lines in the spots, such as would be produced by a rapid motion in the line of sight. It has been found that both uprushes and downrushes occur, but there is no marked predominance of either in a sun-spot. The velocity of motion thus indicated in the line of sight sometimes appears to amount to 320 miles a second. But it must be remembered that pressure of a gas has some effect in displacing the spectral lines. So we must go on, collecting data, until a time comes when the meaning of all the facts can be made clear.

Total Solar Eclipses.—During total solar eclipses the time is so short, and the circumstances so impressive, that drawings of the appearance could not always be trusted. The red prominences of jagged form that are seen round the moon's edge, and the corona with its streamers radiating or interlacing, have much detail that can hardly be recorded in a sketch. By the aid of photography a number of records can be taken during the progress of totality. From a study of these the extent of the corona is demonstrated in one case to extend to at least six diameters of the moon, though the eye has traced it farther. This corona is still one of the wonders of astronomy, and leads to many questions. What is its consistency, if it extends many million miles from the sun's surface? How is it that it opposed no resistance to the motion of comets which have almost grazed the sun's surface? Is this the origin of the zodiacal light? The character of the corona in photographic records has been shown to depend upon the phase of the sun-spot period. During the sun-spot maximum the corona seems most developed over the spot-zones—i.e., neither at the equator nor the poles. The four great sheaves of light give it a square appearance, and are made up of rays or plumes, delicate like the petals of a flower. During a minimum the nebulous ring seems to be made of tufts of fine hairs with aigrettes or radiations from both poles, and streamers from the equator.



On September 19th, 1868, eclipse spectroscopy began with the Indian eclipse, in which all observers found that the red prominences showed a bright line spectrum, indicating the presence of hydrogen and other gases. So bright was it that Jansen exclaimed: "Je verrai ces lignes-la en dehors des eclipses." And the next day he observed the lines at the edge of the uneclipsed sun. Huggins had suggested this observation in February, 1868, his idea being to use prisms of such great dispersive power that the continuous spectrum reflected by our atmosphere should be greatly weakened, while a bright line would suffer no diminution by the high dispersion. On October 20th Lockyer,[10] having news of the eclipse, but not of Jansen's observations the day after, was able to see these lines. This was a splendid performance, for it enabled the prominences to be observed, not only during eclipses, but every day. Moreover, the next year Huggins was able, by using a wide slit, to see the whole of a prominence and note its shape. Prominences are classified, according to their form, into "flame" and "cloud" prominences, the spectrum of the latter showing calcium, hydrogen, and helium; that of the former including a number of metals.

The D line of sodium is a double line, and in the same eclipse (1868) an orange line was noticed which was afterwards found to lie close to the two components of the D line. It did not correspond with any known terrestrial element, and the unknown element was called "helium." It was not until 1895 that Sir William Ramsay found this element as a gas in the mineral cleavite.

The spectrum of the corona is partly continuous, indicating light reflected from the sun's body. But it also shows a green line corresponding with no known terrestrial element, and the name "coronium" has been given to the substance causing it.

A vast number of facts have been added to our knowledge about the sun by photography and the spectroscope. Speculations and hypotheses in plenty have been offered, but it may be long before we have a complete theory evolved to explain all the phenomena of the storm-swept metallic atmosphere of the sun.

The proceedings of scientific societies teem with such facts and "working hypotheses," and the best of them have been collected by Miss Clerke in her History of Astronomy during the Nineteenth Century. As to established facts, we learn from the spectroscopic researches (1) that the continuous spectrum is derived from the photosphere or solar gaseous material compressed almost to liquid consistency; (2) that the reversing layer surrounds it and gives rise to black lines in the spectrum; that the chromosphere surrounds this, is composed mainly of hydrogen, and is the cause of the red prominences in eclipses; and that the gaseous corona surrounds all of these, and extends to vast distances outside the sun's visible surface.

FOOTNOTES:

[1] Rosa Ursina, by C. Scheiner, fol.; Bracciani, 1630.

[2] R. S. Phil. Trans., 1774.

[3] Ibid, 1783.

[4] Observations on the Spots on the Sun, etc., 4 degrees; London and Edinburgh, 1863.

[5] Periodicitat der Sonnenflecken. Astron. Nach. XXI., 1844, P. 234.

[6] R.S. Phil. Trans. (ser. A), 1906, p. 69-100.

[7] "Researches on Solar Physics," by De la Rue, Stewart and Loewy; R. S. Phil. Trans., 1869, 1870.

[8] "The Sun as Photographed on the K line"; Knowledge, London, 1903, p. 229.

[9] R. S. Proc., xv., 1867, p. 256.

[10] Acad. des Sc., Paris; C. R., lxvii., 1868, p. 121.



13. THE MOON AND PLANETS.

The Moon.—Telescopic discoveries about the moon commence with Galileo's discovery that her surface has mountains and valleys, like the earth. He also found that, while she always turns the same face to us, there is periodically a slight twist to let us see a little round the eastern or western edge. This was called libration, and the explanation was clear when it was understood that in showing always the same face to us she makes one revolution a month on her axis uniformly, and that her revolution round the earth is not uniform.

Galileo said that the mountains on the moon showed greater differences of level than those on the earth. Shroter supported this opinion. W. Herschel opposed it. But Beer and Madler measured the heights of lunar mountains by their shadows, and found four of them over 20,000 feet above the surrounding plains.

Langrenus [1] was the first to do serious work on selenography, and named the lunar features after eminent men. Riccioli also made lunar charts. In 1692 Cassini made a chart of the full moon. Since then we have the charts of Schroter, Beer and Madler (1837), and of Schmidt, of Athens (1878); and, above all, the photographic atlas by Loewy and Puiseux.

The details of the moon's surface require for their discussion a whole book, like that of Neison or the one by Nasmyth and Carpenter. Here a few words must suffice. Mountain ranges like our Andes or Himalayas are rare. Instead of that, we see an immense number of circular cavities, with rugged edges and flat interior, often with a cone in the centre, reminding one of instantaneous photographs of the splash of a drop of water falling into a pool. Many of these are fifty or sixty miles across, some more. They are generally spoken of as resembling craters of volcanoes, active or extinct, on the earth. But some of those who have most fully studied the shapes of craters deny altogether their resemblance to the circular objects on the moon. These so-called craters, in many parts, are seen to be closely grouped, especially in the snow-white parts of the moon. But there are great smooth dark spaces, like the clear black ice on a pond, more free from craters, to which the equally inappropriate name of seas has been given. The most conspicuous crater, Tycho, is near the south pole. At full moon there are seen to radiate from Tycho numerous streaks of light, or "rays," cutting through all the mountain formations, and extending over fully half the lunar disc, like the star-shaped cracks made on a sheet of ice by a blow. Similar cracks radiate from other large craters. It must be mentioned that these white rays are well seen only in full light of the sun at full moon, just as the white snow in the crevasses of a glacier is seen bright from a distance only when the sun is high, and disappears at sunset. Then there are deep, narrow, crooked "rills" which may have been water-courses; also "clefts" about half a mile wide, and often hundreds of miles long, like deep cracks in the surface going straight through mountain and valley.

The moon shares with the sun the advantage of being a good subject for photography, though the planets are not. This is owing to her larger apparent size, and the abundance of illumination. The consequence is that the finest details of the moon, as seen in the largest telescope in the world, may be reproduced at a cost within the reach of all.

No certain changes have ever been observed; but several suspicions have been expressed, especially as to the small crater Linne, in the Mare Serenitatis. It is now generally agreed that no certainty can be expected from drawings, and that for real evidence we must await the verdict of photography.

No trace of water or of an atmosphere has been found on the moon. It is possible that the temperature is too low. In any case, no displacement of a star by atmospheric refraction at occultation has been surely recorded. The moon seems to be dead.

The distance of the moon from the earth is just now the subject of re-measurement. The base line is from Greenwich to Cape of Good Hope, and the new feature introduced is the selection of a definite point on a crater (Mosting A), instead of the moon's edge, as the point whose distance is to be measured.

The Inferior Planets.—When the telescope was invented, the phases of Venus attracted much attention; but the brightness of this planet, and her proximity to the sun, as with Mercury also, seemed to be a bar to the discovery of markings by which the axis and period of rotation could be fixed. Cassini gave the rotation as twenty-three hours, by observing a bright spot on her surface. Shroter made it 23h. 21m. 19s. This value was supported by others. In 1890 Schiaparelli[2] announced that Venus rotates, like our moon, once in one of her revolutions, and always directs the same face to the sun. This property has also been ascribed to Mercury; but in neither case has the evidence been generally accepted. Twenty-four hours is probably about the period of rotation for each of these planets.