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Leaving behind us the results of the researches of Ptolemy, who succeeded Hipparchus and whose methods have been described, and passing over the astronomy of the Arabs and Persians as being little in advance of Hipparchus and Ptolemy, we come down to the sixteenth century of our era.

Here we find ourselves in presence of the improvements in instruments effected by a man whose name is conspicuous—Tycho Brahe—a Danish nobleman who, in the year 1576, established a magnificent observatory at Huen, which may be looked upon as the next building of importance after that great edifice at Alexandria which has already been referred to.

What Hipparchus was to the astronomy of the Ancients such was Tycho to the astronomy of the Middle Ages. As such his life merits a brief notice before we proceed to his work. He was born at Knudsthorp, near Helsingborg, in Sweden, in 1546, and went to the University of Copenhagen to prepare to study law; while there he was so struck with the prediction of an eclipse of the sun by the astrological almanacks that he gave all his spare time to the study of astronomy. In 1565 his uncle died and Tycho Brahe fell into possession of one of his uncle’s estates; and as astronomy, or astrology as it was then called, was thought degrading to a man in his position by his friends, who took offence at his pursuits and made themselves very objectionable, he left for a short stay at Wittenberg, then he went to Rostock and afterwards to Augsburg, where he constructed his large quadrant. He returned to his old country in 1571; while there, Frederick II., King of Denmark, requested him to deliver a course of lectures on astronomy and astrology and became his most liberal patron. The King granted to Tycho Brahe for life the island of Huen, lying between Denmark and Sweden, and built there a magnificent observatory and apartments for Tycho, his assistants and servants. The main building was sixty feet square, with observing towers on the north and south, and a library and museum. Tycho called this Uraniberg—the city of the heavens; and he afterwards built a smaller observatory near called by him Sternberg—city of the stars, the former being insufficiently large to contain all his instruments.

The following is a list of these instruments as given in Sir David Brewster’s excellent memoir of Brahe, in Martyrs of Science:—

In the South and greater Observatory.

1. A semicircle of solid iron, covered with brass, four cubits radius.

2. A sextant of the same materials and size.

3. A quadrant of one and a half cubits radius, and an azimuth circle of three cubits.

4. Ptolemy’s parallactic rules, covered with brass, four cubits in the side.

5. Another sextant.

6. Another quadrant, like No. 3.

Fig. 15.—Portrait of Tycho Brahe (from original painting in the possession of Dr. Crompton, of Manchester).

7. Zodiacal armillaries of melted brass, and turned out of the solid, of three cubits in diameter.

Near this observatory there was a large clock with one wheel two cubits in diameter, and two smaller ones which, like it, indicated hours, minutes, and seconds.

In the South and lesser Observatory.

8. An armillary sphere of brass, with a steel meridian, whose diameter was about four cubits.

In the North Observatory.

9. Brass parallactic rules, which revolved in azimuth above a brass horizon, twelve feet in diameter.

10. A half sextant, of four cubits radius.

11. A steel sextant.

12. Another half sextant with steel limb, four cubits radius.

13. The parallactic rules of Copernicus.

14. Equatorial armillaries.

15. A quadrant of a solid plate of brass, five cubits in radius, showing every ten seconds.

16. In the museum was the large globe made at Augsburg.

In the Sternberg Observatory.

17. In the central part, a large semicircle, with a brass limb, and three clocks, showing hours, minutes, and seconds.

18. Equatorial armillaries of seven cubits, with semi-armillaries of nine cubits.

19. A sextant of four cubits radius.

20. A geometrical square of iron, with an intercepted quadrant of five cubits, and divided into fifteen seconds.

21. A quadrant of four cubits radius, showing ten seconds, with an azimuth circle.

22. Zodiacal armillaries of brass, with steel meridians, three cubits in diameter.

23. A sextant of brass, kept together by screws, and capable of being taken to pieces for travelling with. Its radius was four cubits.

24. A movable armillary sphere, three cubits in diameter.

25. A quadrant of solid brass, one cubit radius, and divided into minutes by Nonian circles.

26. An astronomical radius of solid brass, three cubits long.

27. An astronomical ring of brass, a cubit in diameter.

28. A small brass astrolabe.

Tycho Brahe carried on his work at Uraniberg for twenty-one years, and appears to have been visited by many of the princes of the period and by students anxious to learn from so great a man. In Frederick’s treatment of Tycho Brahe we have an early and munificent and, in its results, most successful instance of the endowment of research. On the death of Frederick II., in 1588, Christian IV. came to the throne. The successor cared little for astronomy, and his courtiers, who were jealous of Tycho’s position, so acted upon him that the pension, estate and canonry with which Tycho had been endowed were taken away. Unable to put up with these insults and loss of his money, he left for Wandesburg in 1597, where he was entertained by Count Henry Rantzau. It was now that he wrote and published the Astronomiæ instauratæ Mechanica, a copy of which, together with his catalogue of 1000 stars, was sent to the Emperor Rudolph II., who invited him to go to Prague. This he accepted, and he and his family went to the castle of Benach in 1599, and a pension of 3000 crowns was given to him. Ten years afterwards he removed with his instruments into Prague to a house purchased and presented to him by the Emperor; here he died in the same year.

The wonderful assistance which Tycho Brahe was able to bring to astronomy shows that then, as now, any considerable advance in physical investigation was more or less a matter of money, and whether that money be found by individuals or corporations, now or then, we cannot expect any considerable advance without such a necessary adjunct.

Fig. 16.—Tycho Brahe’s Observatory on the Island of Huen.

The principal instruments used at first by Tycho Brahe resembled the Greek ones, except that they were much larger. Hipparchus was enabled to establish the position of a heavenly body within something less than one degree of space—some say within ten minutes; but there was an immense improvement made in this direction in the instruments used by Tycho.

One of the instruments which he used was in every way similar to the equatorial astrolabe designed, by Hipparchus, and was called by Tycho, the ‘armillæ equatoriæ’ (Fig. 8). With that instrument in connection with others Tycho was enabled to make an immense advance upon the work done by Hipparchus.

Tycho, like Hipparchus, having no clock, in the modern sense, was not able to determine the difference of time between the transit of the sun or a particular star over the meridian, so that he was compelled to refer everything to the sun at the instant of observation, and he did that by means of the moon. Hipparchus, as we have seen, determined the difference of longitude, or right ascension, between the sun and the moon and between the moon and the stars, in the manner already described, and so used the moon as a means of determining differences between the longitude or right ascension of the sun and the stars.

Now Tycho, using an instrument similar to that of Hipparchus, saw that he would make an improvement if instead of using the Moon he used Venus; for the measure of the surface of the moon was considerable, and could not be easily reckoned, and its apparent position in the heavens was dependent on the position of a person on the earth—because it is so near the earth that it has a sensible parallax, that is, a person at the equator of the earth might see the moon in the direction of a certain star; but, on going to the pole, the moon would appear below the line of the star. If one were looking at a kite in the air to the south and then walked towards the south, the kite would gradually get over head, and on proceeding further it would get north. To persons at different stations the kite would appear in different positions, and the nearer the kite was to the observer the less distance he would have to go to make it change its place. So also with the moon; it is so near to us that a change of place on the earth makes a considerable difference in the direction in which it is seen. Instead, therefore, of using the Moon, Tycho used Venus, and so mapped 1,500 stars after determining their absolute right ascensions, in this manner without the use of clocks.

Fig. 8 shows the instrument called the “armillæ equatoriæ,” which he constructed, and which was based upon the principle of that which Hipparchus had used. Here the axis of motion, C, D, of these circles is so arranged that it is absolutely parallel to the axis of the earth; but instead of the circle R, Q, N, representing the equator, being fixed, it revolved in its own plane while held by the circle G, H, I, making its use probably more easy, but leaving the principles unaltered.

Tycho Brahe also used another similar instrument of much larger size for the same purposes as the one we have just considered. It consisted of a large circle, which was seven cubits in diameter, corresponding to the circle K, L, M, Fig. 8; and carrying the sights in the same manner, it was placed in a circular pit in the ground, with its diameter pointing towards the pole. This was used for measuring declinations. The circle R, Q, N, Fig. 9, was represented by a fixed circle carried on pillars surrounding the pit, and along which the right ascension of the star was measured. This instrument, therefore, was more simple than the smaller one, and probably much more accurate.

Tycho was not one of those who was aware of the true system of the universe; he thought the earth fixed, as Ptolemy and others did; but whether we suppose the earth to be movable in the middle of the vault of stars or stationary, in either case that position is absolutely immaterial in ascertaining the right ascension of stars. If one takes the terrestrial globe, and looks upon the meridians, it is at once clear that the distance from meridian to meridian remains unaltered, whether the globe is still or turning round: so the stars maintain their relative positions to each other, whether we consider the earth in motion or the sphere in which the stars are placed to revolve round it.

Fig. 17.—Tycho Brahe’s System.

The introduction of clocks gave Tycho the invention of the next instrument, which was the transit circle. At this time the pendulum had not been invented; but it struck him and others that there was no necessity for having two or more circles rotating about an axis parallel to the earth’s axis, as in the astrolabes or armillæ, but only to have one circle in the plane of the meridian of the place. So that, by the diurnal movement of the earth round its own axis, all the stars in the heavens would gradually and seriatim be brought to be visible along the arc of the circle, so he arranged matters in the following way.

The stars were observed through a hole in a wall and through an eyehole, sliding on a fixed arc. The number of degrees marked at the eyehole on the arc at once gave the altitude of the heavenly bodies as seen through that hole. If a star was very high, it would be necessary for an observer to place his eye low down to be able to see it. If it were near the horizon, he would have to travel up to the top of this circle to determine its altitude, and having done that, and knowing the latitude of the place of observation, the observer will be able to determine the position of the star with reference to the celestial equator. The actual moment at which the star was seen was noted by the clock, and the time that the sun had passed the hole being also previously noted, the length of time between the transits was known; and as the stars appear to transit or pass the meridian every twenty-four hours, it was at once known what part of the heavens was intercepted between the sun and the star in degrees, or, as is usually the case, the right ascension of the star was left expressed in hours and minutes instead of degrees; thus he had a means of determining the two co-ordinates of any celestial body.

The places of the comet of 1677, which Tycho discovered, and of many stars, were determined with absolute certainty; but astronomers began to be ambitious. It was necessary in using this instrument to wait till a celestial body got to the meridian. If it was missed, then they had to wait till the next day; and further, they had no opportunity whatever of observing bodies which set in the evening.

Fig. 18.—The Quadrans Maximus reproduced from Tycho’s plate.

Seeing, therefore, that clocks were improving, it was suggested by one of Tycho’s compeers, the Landgrave of Hesse-Cassel, that by an instrument arranged something like Fig. 18, it would be possible to determine the exact position of any body in the heavens when examined out of the meridian, and so they got again to extra-meridional observations.

The instrument used by Tycho Brahe for the purpose, called the Quadrans Maximus, is represented in Fig. 18. In this there is the quadrant B, D, one pointer being placed, as shown at the bottom, near H, and the other at the top, C. These pointers or sights were directed at the star by moving the arm C, H, on the pivot A, and turning the whole arm and divided arc round on the axis N, R. The altitude of the star is then read off on the quadrant B, D, and the azimuth, or number of degrees east or west of the north and south line, is then read off on the circle Q, R, S. The screws Y, Y, served to elevate the horizontal circle, and level it exactly with the horizon, and the plummets W and V, hanging from G, were to show when the circle was level or not; for the part A, G, being at right angles to the circle should be upright when the circle is level, so that if A, G, is upright in all positions when moved round the circle in azimuth, the circle is horizontal.

Here, then, is an instrument very different in principle from what we had before. In this case the heavens are viewed from the most general standpoint we can obtain—the horizon; but observations such as these refer to the position of the place of observation absolutely, without any reference to the position of the body with respect to the equator or the ecliptic; but knowing the latitude of the place of observation and the time, it was possible for a mathematical astronomer to reduce the co-ordinates to right ascension and declination, and so actually to look at the position of these bodies with reference to the celestial sphere.

Tycho also had various other instruments of the same kind, differing only in the position of the quadrant D, B, and of the circle on which the azimuth was measured. These instruments are the same in principle as our modern alt-azimuth, which will be described hereafter, one form having a telescope and the other being without it.

Fig. 19.—Tycho’s Sextant.

Fig. 19 is yet another very important instrument invented by Tycho Brahe; it is the prototype of our modern much used sextant. It was used by Tycho Brahe for determining the distance from one body to another in a direct line; a star or the moon, say, was observed by the pointers C, A, while another was observed by the pointers N, A, by another observer. The number of degrees then between N and C gave the angular distance of the two bodies observed. This instrument was mounted at E, so that it could be turned into any position. Not only then had this instrument its representative in our present sextant, but it was used in the same way, not requiring to be fixed in any one position. We also find represented in Tycho Brahe’s book another form of the same instrument, the sight A being next the observer, instead of away from him, so that he could observe the two stars through the sights N and C without moving the eye. In this form only one observer was required instead of two as in the last.

There was also another instrument, Fig. 6, used by this great astronomer, very similar to Ptolemy’s parallactic rules, used for measuring zenith distances, or the distances of stars from the part exactly overhead. The star or moon was observed by the sights H, I, and the angle from the upright standard D, K, given by divisions on the rod E, F, D, E being placed exactly upright by a plummet, and being also able to turn on hinges at B and C, any part of the sky could be reached. There is one more of his instruments that needs notice—he had so many of all kinds that space will not allow reference to more than a very few. This one was for measuring the altitudes of the stars as they passed the meridian; it is a more convenient form of the mural quadrant, and instead of a hole in the wall, there are sights on a movable arm, working over a divided quadrant fixed in the plane of the meridian, just like the quadrant outside the horizontal circle, so the observer had no reason to move up or down according as the star was high or low.

Here then ends the pre-telescopic age. Tycho was one of the very last of the distinguished astronomers who used instruments without the telescope. We began with the horizon, and we have now ended with the meridian. We also end with a power of determining the position of a heavenly body to ten seconds of space, the instrument of the Greeks reading to 10´ and those of Tycho to 10˝.

We began with the immovable earth fixed in the midst of the vault of the sky, and on this assumption Tycho Brahe made all his observations, which ended in enabling Kepler to give us the true system of the world, which was the requisite basis for the crowning triumph of Newton.