FROM GALILEI TO NEWTON.
“And now the lofty telescope, the scale
By which they venture heaven itself t’assail.
Was raised, and planted full against the moon.”
_Hudibras_
152. Between the publication of Galilei’s _Two New Sciences_ (1638)
and that of Newton’s _Principia_ (1687) a period of not quite half a
century elapsed; during this interval no astronomical discovery of
first-rate importance was published, but steady progress was made on
lines already laid down.
On the one hand, while the impetus given to exact observation by Tycho
Brahe had not yet spent itself, the invention of the telescope and
its gradual improvement opened out an almost indefinite field for
possible discovery of new celestial objects of interest. On the other
hand, the remarkable character of the three laws in which Kepler had
summed up the leading characteristics of the planetary motions could
hardly fail to suggest to any intelligent astronomer the question _why_
these particular laws should hold, or, in other words, to stimulate
the inquiry into the possibility of shewing them to be necessary
consequences of some simpler and more fundamental law or laws, while
Galilei’s researches into the laws of motion suggested the possibility
of establishing some connection between the causes underlying these
celestial motions and those of ordinary terrestrial objects.
153. It has been already mentioned how closely Galilei was followed
by other astronomers (if not in some cases actually anticipated) in
most of his telescopic discoveries. To his rival Christopher Scheiner
(chapter VI., §§ 124, 125) belongs the credit of the discovery of
bright cloud-like objects on the sun, chiefly visible near its edge,
and from their brilliancy named =faculae= (little torches). Scheiner
made also a very extensive series of observations of the motions and
appearances of spots.
The study of the surface of the moon was carried on with great care
by _John Hevel_ of Danzig (1611-1687), who published in 1647 his
_Selenographia_, or description of the moon, magnificently illustrated
by plates engraved as well as drawn by himself. The chief features of
the moon—mountains, craters, and the dark spaces then believed to be
seas—were systematically described and named, for the most part after
corresponding features of our own earth. Hevel’s names for the chief
mountain ranges, _e.g._ the _Apennines_ and the _Alps_, and for the
seas, _e.g._ _Mare Serenitatis_ or Pacific Ocean, have lasted till
to-day; but similar names given by him to single mountains and craters
have disappeared, and they are now called after various distinguished
men of science and philosophers, _e.g._ _Plato_ and _Coppernicus_,
in accordance with a system introduced by _John Baptist Riccioli_
(1598-1671) in his bulky treatise on astronomy called the _New
Almagest_ (1651).
Hevel, who was an indefatigable worker, published two large books
on comets, _Prodromus Cometicus_ (1654) and _Cometographia_ (1668),
containing the first systematic account of all recorded comets. He
constructed also a catalogue of about 1,500 stars, observed on the
whole with accuracy rather greater than Tycho’s, though still without
the use of the telescope; he published in addition an improved set of
tables of the sun, and a variety of other calculations and observations.
154. The planets were also watched with interest by a number of
observers, who detected at different times bright or dark markings on
Jupiter, Mars, and Venus. The two appendages of Saturn which Galilei
had discovered in 1610 and had been unable to see two years later
(chapter VI., § 123) were seen and described by a number of astronomers
under a perplexing variety of appearances, and the mystery was only
unravelled, nearly half a century after Galilei’s first observation,
by the greatest astronomer of this period, _Christiaan Huygens_
(1629-1695), a native of the Hague. Huygens possessed remarkable
ability, both practical and theoretical, in several different
directions, and his contributions to astronomy were only a small
part of his services to science. Having acquired the art of grinding
lenses with unusual accuracy, he was able to construct telescopes of
much greater power than his predecessors. By the help of one of these
instruments he discovered in 1655 a satellite of Saturn (_Titan_).
With one of those remnants of mediaeval mysticism from which even
the soberest minds of the century freed themselves with the greatest
difficulty, he asserted that, as the total number of planets and
satellites now reached the perfect number 12, no more remained to be
discovered—a prophecy which has been abundantly falsified since (§ 160;
chapter XII., §§ 253, 255; chapter XIII., §§ 289, 294, 295).
Using a still finer telescope, and aided by his acuteness in
interpreting his observations, Huygens made the much more interesting
discovery that the puzzling appearances seen round Saturn were due to
a thin ring (fig. 64) inclined at a considerable angle (estimated by
him at 31°) to the plane of the ecliptic, and therefore also to the
plane in which Saturn’s path round the sun lies. This result was first
announced—according to the curious custom of the time—by an anagram,
in the same pamphlet in which the discovery of the satellite was
published, _De Saturni Luna Observatio Nova_ (1656); and three years
afterwards (1659) the larger _Systema Saturnium_ appeared, in which the
interpretation of the anagram was given, and the varying appearances
seen both by himself and by earlier observers were explained with
admirable lucidity and thoroughness. The ring being extremely thin is
invisible either when its edge is presented to the observer or when it
is presented to the sun, because in the latter position the rest of the
ring catches no light. Twice in the course of Saturn’s revolution round
the sun (at B and D in fig. 66), _i.e._ at intervals of about 15 years,
the plane of the ring passes for a short time through or very close
both to the earth and to the sun, and at these two periods the ring is
consequently invisible (fig. 65). Near these positions (as at Q, R, S,
T) the ring appears much foreshortened, and presents the appearance
of two arms projecting from the body of Saturn; farther off still
the ring appears wider and the opening becomes visible; and about
seven years before and after the periods of invisibility (at A and C)
the ring is seen at its widest. Huygens gives for comparison with his
own results a number of drawings by earlier observers (reproduced in
fig. 67), from which it may be seen how near some of them were to the
discovery of the ring.
[Illustration: FIG. 64.—Saturn’s ring, as drawn by Huygens. From the
_Systema Saturnium_.]
[Illustration: FIG. 65.—Saturn, with the ring seen edge-wise. From the
_Systema Saturnium_.]
[Illustration: FIG. 66.—The phases of Saturn’s ring. From the _Systema
Saturnium_.]
155. To our countryman _William Gascoigne_ (1612?-1644) is due the
first recognition that the telescope could be utilised, not merely
for observing generally the appearances of celestial bodies, but also
as an instrument of precision, which would give the directions of
stars, etc., with greater accuracy than is possible with the naked
eye, and would magnify small angles in such a way as to facilitate the
measurement of angular distances between neighbouring stars, of the
diameters of the planets, and of similar quantities. He was unhappily
killed when quite a young man at the battle of Marston Moor (1644),
but his letters, published many years afterwards shew that by 1640
he was familiar with the use of telescopic “sights,” for determining
with accuracy the position of a star, and that he had constructed a
so-called =micrometer=[95] with which he was able to measure angles
of a few seconds. Nothing was known of his discoveries at the time,
and it was left for Huygens to invent independently a micrometer of an
inferior kind (1658), and for _Adrien Auzout_ (?-1691) to introduce
as an improvement (about 1666) an instrument almost identical with
Gascoigne’s.
The systematic use of telescopic sights for the regular work of an
observatory was first introduced about 1667 by Auzout’s friend and
colleague _Jean Picard_ (1620-1682).
[Illustration: FIG. 67.—Early drawings of Saturn. From the _Systema
Saturnium_.]
156. With Gascoigne should be mentioned his friend _Jeremiah Horrocks_
(1617?-1641), who was an enthusiastic admirer of Kepler and had made
a considerable improvement in the theory of the moon, by taking the
elliptic orbit as a basis and then allowing for various irregularities.
He was the first observer of a transit of Venus, _i.e._ a passage of
Venus over the disc of the sun, an event which took place in 1639,
contrary to the prediction of Kepler in the _Rudolphine Tables_, but
in accordance with the rival tables of _Philips von Lansberg_
(1561-1632) which Horrocks had verified for the purpose. It was not,
however, till long afterwards that Halley pointed out the importance
of the transit of Venus as a means of ascertaining the distance of the
sun from the earth (chapter X., § 202). It is also worth noticing that
Horrocks suggested the possibility of the irregularities of the moon’s
motion being due to the disturbing action of the sun, and that he also
had some idea of certain irregularities in the motion of Jupiter and
Saturn, now known to be due to their mutual attraction (chapter X., §
204; chapter XI., § 243).
157. Another of Huygens’s discoveries revolutionised the art of exact
astronomical observation. This was the invention of the pendulum-clock
(made 1656, patented in 1657). It has been already mentioned how the
same discovery was made by Bürgi, but virtually lost (see chapter V., §
98); and how Galilei again introduced the pendulum as a time-measurer
(chapter VI., § 114). Galilei’s pendulum, however, could only be used
for measuring very short times, as there was no mechanism to keep it in
motion, and the motion soon died away. Huygens attached a pendulum to
a clock driven by weights, so that the clock kept the pendulum going
and the pendulum regulated the clock.[96] Henceforward it was possible
to take reasonably accurate time-observations, and, by noticing the
interval between the passage of two stars across the meridian, to
deduce, from the known rate of motion of the celestial sphere, their
angular distance east and west of one another, thus helping to fix the
position of one with respect to the other. It was again Picard (§ 155)
who first recognised the astronomical importance of this discovery, and
introduced regular time-observations at the new Observatory of Paris.
158. Huygens was not content with this practical use of the pendulum,
but worked out in his treatise called _Oscillatorium Horologium_ or
_The Pendulum Clock_ (1673) a number of important results in the theory
of the pendulum, and in the allied problems connected with the motion
of a body in a circle or other curve. The greater part of these
investigations lie outside the field of astronomy, but his formula
connecting the time of oscillation of a pendulum with its length and
the intensity of gravity[97] (or, in other words, the rate of falling
of a heavy body) afforded a practical means of measuring gravity, of
far greater accuracy than any direct experiments on falling bodies;
and his study of circular motion, leading to the result that a body
moving in a circle must be acted on by some force towards the _centre_,
the magnitude of which depended in a definite way on the speed of the
body and the size of the circle,[98] is of fundamental importance in
accounting for the planetary motions by gravitation.
159. During the 17th century also the first measurements of the earth
were made which were a definite advance on those of the Greeks and
Arabs (chapter II., §§ 36, 45, and chapter III., § 57). _Willebrord
Snell_ (1591-1626), best known by his discovery of the law of
refraction of light, made a series of measurements in Holland in 1617,
from which the length of a degree of a meridian appeared to be about
67 miles, an estimate subsequently altered to about 69 miles by one
of his pupils, who corrected some errors in the calculations, the
result being then within a few hundred feet of the value now accepted.
Next, _Richard Norwood_ (1590?-1675) measured the distance from London
to York, and hence obtained (1636) the length of the degree with an
error of less than half a mile. Lastly, Picard in 1671 executed some
measurements near Paris leading to a result only a few yards wrong. The
length of a degree being known, the circumference and radius of the
earth can at once be deduced.
160. Auzout and Picard were two members of a group of observational
astronomers working at Paris, of whom the best known, though probably
not really the greatest, was _Giovanni Domenico Cassini_ (1625-1712).
Born in the north of Italy, he acquired a great reputation, partly
by some rather fantastic schemes for the construction of gigantic
instruments, partly by the discovery of the rotation of Jupiter
(1665), of Mars (1666), and possibly of Venus (1667), and also by his
tables of the motions of Jupiter’s moons (1668). The last caused Picard
to procure for him an invitation from Louis XIV. (1669) to come to
Paris and to exercise a general superintendence over the Observatory,
which was then being built and was substantially completed in 1671.
Cassini was an industrious observer and a voluminous writer, with a
remarkable talent for impressing the scientific public as well as the
Court. He possessed a strong sense of the importance both of himself
and of his work, but it is more than doubtful if he had as clear ideas
as Picard of the really important pieces of work which ought to be
done at a public observatory, and of the way to set about them. But,
notwithstanding these defects, he rendered valuable services to various
departments of astronomy. He discovered four new satellites of Saturn:
_Japetus_ in 1671, _Rhea_ in the following year, _Dione_ and _Thetis_
in 1684; and also noticed in 1675 a dark marking in Saturn’s ring,
which has subsequently been more distinctly recognised as a division
of the ring into two, an inner and an outer, and is known as Cassini’s
division (see fig. 95 facing p. 384). He also improved to some extent
the theory of the sun, calculated a fresh table of atmospheric
refraction which was an improvement on Kepler’s (chapter VII., § 138),
and issued in 1693 a fresh set of tables of Jupiter’s moons, which were
much more accurate than those which he had published in 1668, and much
the best existing.
161. It was probably at the suggestion of Picard or Cassini that one
of their fellow astronomers, _John Richer_ (?-1696), otherwise almost
unknown, undertook (1671-3) a scientific expedition to Cayenne (in
latitude 5° N.). Two important results were obtained. It was found that
a pendulum of given length beat more slowly at Cayenne than at Paris,
thus shewing that the intensity of gravity was less near the equator
than in higher latitudes. This fact suggested that the earth was not a
perfect sphere, and was afterwards used in connection with theoretical
investigations of the problem of the earth’s shape (cf. chapter IX., §
187). Again, Richer’s observations of the position of Mars in the sky,
combined with observations taken at the same time Cassini, Picard,
and others in France, led to a reasonably accurate estimate of the
distance of Mars and hence of that of the sun. Mars was at the time in
opposition (chapter II., § 43), so that it was nearer to the earth than
at other times (as shewn in fig. 68), and therefore favourably situated
for such observations. The principle of the method is extremely simple
and substantially identical with that long used in the case of the moon
(chapter II., § 49). One observer is, say, at Paris (P, in fig. 69),
and observes the direction in which Mars appears, _i.e._ the direction
of the line P M; the other at Cayenne (C) observes similarly the
direction of the line C M. The line C P, joining Paris and Cayenne, is
known geographically; the shape of the triangle C P M and the length of
one of its sides being thus known, the lengths of the other sides are
readily calculated.
[Illustration: FIG. 68.—Mars in opposition.]
[Illustration: FIG. 69.—The parallax of a planet.]
The result of an investigation of this sort is often most conveniently
expressed by means of a certain angle, from which the distance in
terms of the radius of the earth, and hence in miles, can readily be
deduced when desired.
The parallax of a heavenly body such as the moon, the sun, or a planet,
being in the first instance defined generally (chapter II., § 43) as
the angle (O M P) between the lines joining the heavenly body to the
observer and to the centre of the earth, varies in general with the
position of the observer. It is evidently greatest when the observer
is in such a position, as at Q, that the line M Q touches the earth;
in this position M is on the observer’s horizon. Moreover the angle O
Q M being a right angle, the shape of the triangle and the ratio of
its sides are completely known when the angle O M Q is known. Since
this angle is the parallax of M, when on the observer’s horizon, it
is called the =horizontal parallax= of M, but the word horizontal is
frequently omitted. It is easily seen by a figure that the more distant
a body is the smaller is its horizontal parallax; and with the small
parallaxes with which we are concerned in astronomy, the distance and
the horizontal parallax can be treated as inversely proportional to
one another; so that if, for example, one body is twice as distant as
another, its parallax is half as great, and so on.
It may be convenient to point out here that the word “parallax” is
used in a different though analogous sense when a fixed star is in
question. The apparent displacement of a fixed star due to the earth’s
motion (chapter IV., § 92), which was not actually detected till long
afterwards (chapter XIII., § 278), is called =annual= or =stellar
parallax= (the adjective being frequently omitted); and the name is
applied in particular to the greatest angle between the direction of
the star as seen from the sun and as seen from the earth in the course
of the year. If in fig. 69 we regard M as representing a star, O the
sun, and the circle as being the earth’s path round the sun, then the
angle O M Q is the annual parallax of M.
In this particular case Cassini deduced from Richer’s observations,
by some rather doubtful processes, that the sun’s parallax was about
9″·5, corresponding to a distance from the earth of about 87,000,000
miles, or about 360 times the distance of the moon, the most probable
value, according to modern estimates (chapter XIII., § 284), being
a little less than 93,000,000. Though not really an accurate result,
this was an enormous improvement on anything that had gone before, as
Ptolemy’s estimate of the sun’s distance, corresponding to a parallax
of 3′, had survived up to the earlier part of the 17th century,
and although it was generally believed to be seriously wrong, most
corrections of it had been purely conjectural (chapter VII., §§ 145).
162. Another famous discovery associated with the early days of the
Paris Observatory was that of the velocity of light. In 1671 Picard
paid a visit to Denmark to examine what was left of Tycho Brahe’s
observatory at Hveen, and brought back a young Danish astronomer,
_Olaus Roemer_ (1644-1710), to help him at Paris. Roemer, in studying
the motion of Jupiter’s moons, observed (1675) that the intervals
between successive eclipses of a moon (the eclipse being caused by the
passage of the moon into Jupiter’s shadow) were regularly less when
Jupiter and the earth were approaching one another than when they were
receding. This he saw to be readily explained by the supposition that
light travels through space at a definite though very great speed. Thus
if Jupiter is approaching the earth, the time which the light from one
of his moons takes to reach the earth is gradually decreasing, and
consequently the interval between successive eclipses as seen by us
is apparently diminished. From the difference of the intervals thus
observed and the known rates of motion of Jupiter and of the earth, it
was thus possible to form a rough estimate of the rate at which light
travels. Roemer also made a number of instrumental improvements of
importance, but they are of too technical a character to be discussed
here.
163. One great name belonging to the period dealt with in this chapter
remains to be mentioned, that of _René Descartes_[99] (1596-1650).
Although he ranks as a great philosopher, and also made some extremely
important advances in pure mathematics, his astronomical writings
were of little value and in many respects positively harmful. In his
_Principles of Philosophy_ (1644) he gave, among some wholly erroneous
propositions, a fuller and more general statement of the first law
of motion discovered by Galilei (chapter VI., §§ 130, 133), but did
not support it by any evidence of value. The same book contained an
exposition of his famous theory of vortices, which was an attempt to
explain the motions of the bodies of the solar system by means of a
certain combination of vortices or eddies. The theory was unsupported
by any experimental evidence, and it was not formulated accurately
enough to be capable of being readily tested by comparison with actual
observation; and, unlike many erroneous theories (such as the Greek
epicycles), it in no way led up to or suggested the truer theories
which followed it. But “Cartesianism,” both in philosophy and in
natural science, became extremely popular, especially in France, and
its vogue contributed notably to the overthrow of the authority of
Aristotle, already shaken by thinkers like Galilei and Bacon, and thus
rendered men’s minds a little more ready to receive new ideas: in this
indirect way, as well as by his mathematical discoveries, Descartes
probably contributed something to astronomical progress.