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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