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.

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= 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).

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. 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 (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, 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.

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 (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.