CHAPTER IV

ASTRONOMICAL MEASUREMENTS

The old proverb has it that "Science is measurement," and of none of the sciences is this so true as of the science of astronomy. Indeed the measurement of time by observation of the movements of the heavenly bodies was the beginning of astronomy. The movement of the Sun gave the day, which was reckoned to begin either at sunrise or at sunset. The changes of the Moon gave the month, and in many languages the root meaning of the word for _Moon_ is "measurer." The apparent movement of the Sun amongst the stars gave a yet longer division of time, the year, which could be determined in a number of different ways, either from the Sun alone, or from the Sun together with the stars. A very simple and ancient form of instrument for measuring this movement of the Sun was the obelisk, a pillar with a pointed top set up on a level pavement. Such obelisks were common in Egypt, and one of the most celebrated, known as Cleopatra's Needle, now stands on the Thames Embankment. As the Sun moved in the sky, the shadow of the pillar moved on the pavement, and midday, or noon, was marked when the shadow was shortest. The length of the shadow at noon varied from day to day; it was shortest at mid-summer, and longest at midwinter, _i.e._ at the summer and winter solstices. Twice in the year the shadow of the pillar pointed due west at sunrise, and due east at {43} sunset--that is to say, the shadow at the beginning of the day was in the same straight line as at its end. These two days marked the two equinoxes of spring and autumn.

The obelisk was a simple means of measuring the height and position of the Sun, but it had its drawbacks. The length of the shadow and its direction did not vary by equal amounts in equal times, and if the pavement upon which the shadow fell was divided by marks corresponding to equal intervals of time for one day of the year, the marks did not serve for all other days.

But if for the pillar a triangular wall was substituted--a wall rising from the pavement at the south and sloping up towards the north at such an angle that it seemed to point to the invisible pivot of the heavens, round which all the stars appeared to revolve--then the shadow of the wall moved on the pavement in the same manner every day, and the pavement if marked to show the hours for one day would show them for any day. The sundials still often found in the gardens of country houses or in churchyards are miniatures of such an instrument.

But the Greek astronomers devised other and better methods for determining the positions of the heavenly bodies. Obelisks or dials were of use only with the Sun and Moon which cast shadows. To determine the position of a star, "sights" like those of a rifle were employed, and these were fixed to circles which were carefully divided, generally into 360 "degrees." As there are 365 days in a year, and as the Sun makes a complete circuit of the Zodiac in this time, it moves very nearly a degree in a day. The twelve Signs of the Zodiac are therefore each 30° in length, and each {44} takes on the average a double-hour to rise or set. While the Sun and Moon are each about half a degree in diameter, _i.e._ about one-sixtieth of the length of a Sign, and therefore take a double-minute to rise or set. Each degree of a circle is therefore divided into 60 minutes, and each minute may be divided into 60 seconds.

As the Sun or Moon are each about half a degree, or, more exactly, 32 minutes in diameter, it is clear that, so long as astronomical observations were made by the unaided sight, a minute of arc (written 1') was the smallest division of the circle that could be used. A cord or wire can indeed be detected when seen projected against a moderately bright background if its thickness is a second of arc (written 1")--a sixtieth of a minute--but the wire is merely perceived, not properly defined.

Tycho Brahe had achieved the utmost that could be done by the naked eye, and it was the certainty that he could not have made a mistake in an observation in the place of the planet Mars amounting to as much as 8 minutes of arc--that is to say, of a quarter the apparent diameter of the Moon--that made Kepler finally give up all attempts to explain the planetary movements on the doctrine of circular orbits and to try movements in an ellipse. But a contemporary of Kepler, as gifted as he was himself, but in a different direction, was the means of increasing the observing power of the astronomer. GALILEO GALILEI (1564-1642), of a noble Florentine family, was appointed Lecturer in Mathematics at the University of Pisa. Here he soon distinguished himself by his originality of thought, and the ingenuity and decisiveness of his experiments. Up to that time it had been taught that of {45} two bodies the heavier would fall to the ground more quickly than the lighter. Galileo let fall a 100-lb. weight and a 1-lb. weight from the top of the Leaning Tower, and both weights reached the pavement together. By this and other ingenious experiments he laid a firm foundation for the science of mechanics, and he discovered the laws of motion which Newton afterwards formulated. He heard that an instrument had been invented in Holland which seemed to bring distant objects nearer, and, having himself a considerable knowledge of optics, it was not long before he made himself a little telescope. He fixed two spectacle glasses, one for long and one for short sight, in a little old organ-pipe, and thus made for himself a telescope which magnified three times. Before long he had made another which magnified thirty times, and, turning it towards the heavenly bodies, he discovered dark moving spots upon the Sun, mountains and valleys on the Moon, and four small satellites revolving round Jupiter. He also perceived that Venus showed "+phases+"--that is to say, she changed her apparent shape just as the Moon does--and he found the Milky Way to be composed of an immense number of small stars. These discoveries were made in the years 1609-11.

A telescope consists in principle of two parts--an +object-glass+, to form an image of the distant object, and an +eye-piece+, to magnify it. The rays of light from the heavenly body fall on the object-glass, and are so bent out of their course by it as to be brought together in a point called the focus. The "light-gathering power" of the telescope, therefore, depends upon the size of the object-glass, and is proportional to its area. But the size of the image depends upon the focal length of the telescope, _i.e._ upon the distance that the focus {46} is from the object-glass. Thus a small disc, an inch in diameter--such as a halfpenny--will exactly cover the full Moon if held up nine feet away from the eye; and necessarily the image of the full Moon made by an object-glass of nine-feet focus will be an inch in diameter. The eye-piece is a magnifying-glass or small microscope applied to this image, and by it the image can be magnified to any desired amount which the quality of the object-glass and the steadiness of the atmosphere may permit.

This little image of the Moon, planet, or group of stars lent itself to measurement. A young English gentleman, GASCOIGNE, who afterwards fell at the Battle of Marston Moor, devised the "micrometer" for this purpose. The micrometer usually has two frames, each carrying one or more very thin threads--usually spider's threads--and the frames can be moved by very fine screws, the number of turns or parts of a turn of each screw being read off on suitable scales. By placing one thread on the image of one star, and the other on the image of another, the apparent separation of the two can be readily and precisely measured.

Within the last thirty years photography has immensely increased the ease with which astronomical measurements can be made. The sensitive photographic plate is placed in the focus of the telescope, and the light of Sun, Moon, or stars, according to the object to which the telescope is directed, makes a permanent impression on the plate. Thus a picture is obtained, which can be examined and measured in detail at any convenient time afterwards; a portion of the heavens is, as it were, brought actually down to the astronomer's study.

It was long before this great advance was effected. {47} The first telescopes were very imperfect, for the rays of different colour proceeding from any planet or star came to different foci, so that the image was coloured, diffused, and ill-defined. The first method by which this difficulty was dealt with was by making telescopes of enormously long focal length; 80, 100, or 150 feet were not uncommon, but these were at once cumbersome and unsteady. Sir Isaac Newton therefore discarded the use of object-glasses, and used curved mirrors in order to form the image in the focus, and succeeded in making two telescopes on this principle of reflection. Others followed in the same direction, and a century later Sir WILLIAM HERSCHEL was most skilful and successful in making "+reflectors+," his largest being 40 feet in focal length, and thus giving an image of the Moon in its focus of nearly 4-½ inches diameter.

But in 1729 CHESTER MOOR HALL found that by combining two suitable lenses together in the object-glass he could get over most of the colour difficulty, and in 1758 the optician DOLLOND began to make object-glasses that were almost free from the colour defect. From that time onward the manufacture of "+refractors+," as object-glass telescopes are called, has improved; the glass has been made more transparent and more perfect in quality, and larger in size, and the figure of the lens improved. The largest refractor now in use is that of the Yerkes Observatory, Wisconsin, U.S.A., and is 40 inches in aperture, with a focal length of 65 feet, so that the image of the Moon in its focus has a diameter of more than 7 inches. At present this seems to mark the limit of size for refractors, and the difficulty of getting good enough glass for so large a lens is very great indeed. Reflectors have therefore come again into favour, as mirrors can be made larger {48} than any object-glass. Thus Lord Rosse's great telescope was 6 feet in diameter; and the most powerful telescope now in action is the great 5-foot mirror of the Mt. Wilson Observatory, California, with a focal length, as sometimes used, of 150 feet. Thus its light-gathering power is about 60,000 times that of the unaided eye, and the full Moon in its focus is 17 inches in diameter; such is the enormous increase to man's power of sight, and consequently to his power of learning about the heavenly bodies, which the development of the telescope has afforded to him.

The measurement of time was the first purpose for which men watched the heavenly bodies; a second purpose was the measurement of the size of the Earth. If at one place a star was observed to pass exactly overhead, and if at another, due south of it, the same star was observed to pass the meridian one degree north of the zenith, then by measuring the distance between the two places the circumference of the whole Earth would be known, for it would be 360 times that amount. In this way the size of the Earth was roughly ascertained 2000 years before the invention of the telescope. But with the telescope measures of much greater precision could be made, and hence far more difficult problems could be attacked.

One great practical problem was that of finding out the position of a ship when out of sight of land. The ancient Phoenician and Greek navigators had mostly confined themselves to coasting voyages along the shores of the Mediterranean Sea, and therefore the quick recognition of landmarks was the first requisite for a good sailor. But when, in 1492, Columbus had brought a new continent to light, and long voyages were freely taken across the great oceans, it became an urgent {49} necessity for the navigator to find out his position when he had been out of sight of any landmark for weeks.

This necessity was especially felt by the nations of Western Europe, the countries facing the Atlantic with the New World on its far-distant other shore. Spain, France, England, and Holland, all were eager competitors for a grasp on the new lands, and therefore were earnest in seeking a solution of the problem of navigation.

The latitude of the ship could be found out by observing the height of the Sun at noon, or of the Pole Star at night, or in several other ways. But the longitude was more difficult. As the Earth turns on its axis, different portions of its surface are brought in succession under the Sun, and if we take the moment when the Sun is on the meridian of any place as its noon, as twelve o'clock for that place, then the difference of longitude between any two places is essentially the difference in their local times.

It was possible for the sailor to find out when it was local noon for him, but how could he possibly find out what time it was at that moment at the port from which he had sailed, perhaps several weeks before?

The Moon and stars supplied eventually the means for giving this information. For the Moon moves amongst the stars, as the hand of a clock moves amongst the figures of a dial, and it became possible at length to predict for long in advance exactly where amongst the stars the Moon would be, for any given time, of any selected place.

When this method was first suggested, however, neither the motion of the Moon nor the places of the principal stars were known with sufficient accuracy, and it was to remedy this defect, and put navigation upon {50} a sound basis, that CHARLES II. founded Greenwich Observatory in the year 1675, and appointed FLAMSTEED the first Astronomer Royal. In the year 1767 MASKELYNE, the fifth Astronomer Royal, brought out the first volume of the _Nautical Almanac_, in which the positions of the Moon relative to certain stars were given for regular intervals of Greenwich time. Much about the same period the problem was solved in another way by the invention of the chronometer, by JOHN HARRISON, a Yorkshire carpenter. The +chronometer+ was a large watch, so constructed that its rate was not greatly altered by heat or cold, so that the navigator had Greenwich time with him wherever he went.

The new method in the hands of CAPTAIN COOK and other great navigators led to a rapid development of navigation and the discovery of Australia and New Zealand, and a number of islands in the Pacific. The building up of the vast oceanic commerce of Great Britain and of her great colonial empire, both in North America and in the Southern Oceans, has arisen out of the work of the Royal Observatory, Greenwich, and has had a real and intimate connection with it.

To observe the motions of the Moon, Sun, and planets, and to determine with the greatest possible precision the places of the stars have been the programme of Greenwich Observatory from its foundation to the present time. Other great national observatories have been Copenhagen, founded in 1637; Paris, in 1667; Berlin, in 1700; St. Petersburg, in 1725, superseded by that of Pulkowa, in 1839; and Washington, in 1842; while not a few of the great universities have also efficient observatories connected with them.

Of the directly practical results of astronomy, the {51} promotion of navigation stands in the first rank. But the science has never been limited to merely utilitarian inquiries, and the problem of measuring celestial distances has followed on inevitably from the measurement of the Earth.

The first distance to be attacked was that of the nearest companion to the Earth, _i.e._ the Moon. It often happens on our own planet that it is required to find the distance of an object beyond our reach. Thus a general on the march may come to a river and need to know exactly how broad it is, that he may prepare the means for bridging it. Such problems are usually solved on the following principle. Let A be the distant object. Then if the direction of A be observed from each of two stations, B and C, and the distance of B from C be measured, it is possible to calculate the distances of A from B and from C. The application of this principle to the measurement of the Moon's distance was made by the establishment of an observatory at the Cape of Good Hope, to co-operate with that of Greenwich. It is, of course, not possible to see Greenwich Observatory from the Cape, or vice versa, but the stars, being at an almost infinite distance, lie in the same direction from both observatories. What is required then is to measure the apparent distance of the Moon from the same stars as seen from Greenwich and as seen from the Cape, and, the distance apart of the two observatories being known, the distance of the Moon can be calculated.

This was a comparatively easy problem. The next step in celestial measurement was far harder; it was to find the distance of the Sun. The Sun is 400 times as far off as the Moon, and therefore it seems to be practically in the same direction as seen from each of {52} the two observatories, and, being so bright, stars cannot be seen near it in the telescope. But by carefully watching the apparent movements of the planets their _relative_ distances from the Sun can be ascertained, and were known long before it was thought possible that we should ever know their real distances. Thus Venus never appears to travel more than 47° 15' from the Sun. This means that her distance from the Sun is a little more than seven-tenths of that of the Earth. If, therefore, the distance of one planet from the Sun can be measured, or the distance of one planet from the Earth, the actual distances of all the planets will follow. We know the proportions of the parts of the solar system, and, if we can fix the scale of one of the parts, we fix the scale of all.

It has been found possible to determine the distance of Mars, of several of the "minor planets," and especially of Eros, a very small minor planet that sometimes comes within 13,000,000 miles of the Earth, or seven times nearer to us than is the Sun.

From the measures of Eros, we have learned that the Sun is separated from us by very nearly 93,000,000 miles--an unimaginable distance. Perhaps the nearest way of getting some conception of this vast interval is by remembering that there are only 31,556,926 seconds of time in a year. If, therefore, an express train, travelling 60 miles an hour--a mile a minute--set out for the Sun, and travelled day and night without cease, it would take more than 180 years to accomplish the journey.

But this astronomical measure has led on to one more daring still. The earth is on one side of the Sun in January, on the other in July. At these two dates, therefore, we are occupying stations 186,000,000 miles {53} apart, and can ascertain the apparent difference in direction of the stars as viewed from the two points But the astonishing result is that this enormous change in the position of the Earth makes not the slightest observable difference in the position of most of the stars. A few, a very few, do show a very slight difference. The nearest star to us is about 280,000 times as far from us as the Sun; this is Alpha Centauri, the brightest star in the constellation of the Centaur and the third brightest star in the sky. Sirius, the brightest star, is twice this distance. Some forty or fifty stars have had their distances roughly determined; but the stars in general far transcend all our attempts to plumb their distances. But, from certain indirect hints, it is generally supposed that the mass of stars in the Milky Way are something like 300,000,000 times as far from us as we are from our Sun.

Thus far, then, astronomy has led us in the direction or measurement. It has enabled us to measure the size of the Earth upon which we live, and to find out the position of a ship in the midst of the trackless ocean. It has also enabled us to cast a sounding-line into space, to show how remote and solitary the earth moves through the void, and to what unimaginable lengths the great stellar universe, of which it forms a secluded atom, stretches out towards infinity.

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