Part 3 (1/2)

The remarkably accurate instruments devised by Tycho Brahe and employed by him in improving the observations of the positions of the heavenly bodies were no doubt built after descriptions of astrolabes such as Hipparchus used, as described by Ptolemy. In his ”Astronomiae Instauratae Mechanica” we find ill.u.s.trations and descriptions of many of them.

One is a polar astrolabe, mounted somewhat as a modern equatorial telescope is, and the meridian circle is adjustable so that it can be used in any place, no matter what its lat.i.tude might be. There is a graduated equatorial ring at right angles to the polar axis, so that the astrolabe could be used for making observations outside the meridian as well as on it. This equatorial circle slides through grooves, and is furnished with movable sights, and a plumb line from the zenith or highest point of the meridian circle makes it possible to give the necessary adjustment in the vertical. Screws for adjustment at the bottom are provided, just as in our modern instruments, and two observers were necessary, taking their sights simultaneously; unless, as in one type of the instrument, a clock, or some sort of measure of time, was employed.

Another early type of instrument is called by Tycho the ecliptic astrolabe (_Armillae Zodiacales_, or the Zodiacal Rings). It resembles the equatorial astrolabe somewhat, but has a second ring inclined to the equatorial one at an angle equal to the obliquity of the ecliptic. In observing, the equatorial ring was revolved round till the ecliptic ring came into coincidence with the plane of the ecliptic in the sky. Then the observation of a star's longitude and lat.i.tude, as referred to the ecliptic plane, could be made, quite as well as that of right ascension and declination on the equatorial plane. But it was necessary to work quickly, as the adjustment on the ecliptic would soon disappear and have to be renewed.

Tycho is often called the father of the science of astronomical observation, because of the improvements in design and construction of the instruments he used. His largest instrument was a mural quadrant, a quarter-circle of copper, turning parallel to the north-and-south face of a wall, its axis turning on a bearing fixed in the wall. The radius of this quadrant was nine feet, and it was graduated or divided so as to read the very small angle of ten seconds of arc--an extraordinary degree of precision for his day.

Tycho built also a very large alt-azimuth quadrant, of six feet radius.

Its operation was very much as if his mural quadrant could be swung round in azimuth. At several of the great observatories of the present day, as Greenwich and Was.h.i.+ngton, there are instruments of a similar type, but much more accurate, because the mechanical work in bra.s.s and steel is executed by tools that are essentially perfect, and besides this the power of the telescope is superadded to give absolute direction, or pointing on the object under observation.

Excellent clocks are necessary for precise observation with such an instrument; but neither Tycho Brahe, nor Hevelius was provided with such accessories. Hevelius did not avail himself of the telescope as an aid to precision of observation, claiming that pinhole sights gave him more accurate results. It was a dispute concerning this question that Halley was sent over from London to Danzig to arbitrate.

There could be but one way to decide; the telescope with its added power magnifies any displacement of the instrument, and thereby enables the observer to point his instrument more exactly. So he can detect smaller errors and differences of direction than he can without it. And what is of great importance in more modern astronomy, the telescope makes it possible to observe accurately the position of objects so faint that they are wholly invisible to the naked eye.

CHAPTER X

KEPLER, THE GREAT CALCULATOR

Most fortunate it was for the later development of astronomical theory that Tycho Brahe not only was a practical or observational astronomer of the highest order, but that he confined himself studiously for years to observations of the places of the planets. Of Mars he acc.u.mulated an especially long and accurate series, and among those who a.s.sisted him in his work was a young and brilliant pupil named Johann Kepler.

Strongly impressed with the truth of the Copernican System, Kepler was free to reject the erroneous compromise system devised by Tycho Brahe, and soon after Tycho's death Kepler addressed himself seriously to the great problem that no one had ever attempted to solve, viz: to find out what the laws of motion of the planets round the sun really are. Of course he took the fullest advantage of all that Ptolemy and Copernicus had done before him, and he had in addition the splendid observations of Tycho Brahe as a basis to work upon.

Copernicus, while he had effected the tremendous advance of subst.i.tuting the sun for the earth as the center of motion, nevertheless clung to the erroneous notion of Ptolemy that all the bodies of the sky must perforce move at uniform speeds, and in circular curves, the circle being the only ”perfect curve.” Kepler was not long in finding out that this could not be so, and he found it out because Tycho Brahe's observations were much more accurate than any that Copernicus had employed.

Naturally he attempted the nearest planet first, and that was Mars--the planet that Tycho had a.s.signed to him for research. How fortunate that the orbit of Mars was the one, of all the planets, to show practically the greatest divergence from the ancient conditions of uniform motion in a perfectly circular orbit! Had the orbit of Mars chanced to be as nearly circular as is that of Venus, Kepler might well have been driven to abandon his search for the true curve of planetary motion.

However, the facts of the cosmos were on his side, but the calculations essential in testing his various hypotheses were of the most tedious nature, because logarithms were not yet known in his day. His first discovery was that the orbit of Mars is certainly not a circle, but oval or elliptic in figure. And the sun, he soon found, could not be in the center of the ellipse, so he made a series of trial calculations with the sun located in one of the foci of the ellipse instead.

Then he found he could make his calculated places of Mars agree quite perfectly with Tycho Brahe's observed positions, if only he gave up the other ancient requisite of perfectly uniform motion. On doing this, it soon appeared that Mars, when in perihelion, or nearest the sun, always moved swiftest, while at its greatest distance from the sun, or aphelion, its...o...b..tal velocity was slowest.

Kepler did not busy himself to inquire why these revolutionary discoveries of his were as they were; he simply went on making enough trials on Mars, and then on the other planets in turn, to satisfy himself that all the planetary orbits are elliptical, not circular in form, and are so located in s.p.a.ce that the center of the sun is at one of the two foci of each orbit. This is known as Kepler's first law of planetary motion.

The second one did not come quite so easy; it concerned the variable speed with which the planet moves at every point of the orbit. We must remember how handicapped he was in solving this problem: only the geometry of Euclid to work with, and none of the refinements of the higher mathematics of a later day. But he finally found a very simple relation which represented the velocity of the planet everywhere in its...o...b..t. It was this: if we calculate the area swept, or pa.s.sed over, by the planet's radius vector (that is, the line joining its center to the sun's center) during a week's time near perihelion, and then calculate the similar area for a week near aphelion, or indeed for a week when Mars is in any intermediate part of its...o...b..t, we shall find that these areas are all equal to each other. So Kepler formulated his second great law of planetary motion very simply: the radius vector of any planet describes, or sweeps over, equal areas in equal times. And he found this was true for all the planets.

But the real genius of the great mathematician was shown in the discovery of his third law, which is more complex and even more significant than the other two--a law connecting the distances of the planets from the sun with their periods of revolution about the sun.

This cost Kepler many additional years of close calculation, and the resulting law, his third law of planetary motion is this: The cubes of the mean or average distances of the planets from the sun are proportional to the squares of their times of revolution around him.

So Kepler had not only disposed of the sacred theories of motion of the planets held by the ancients as inviolable, but he had demonstrated the truth of a great law which bound all the bodies of the solar system together. So accurately and completely did these three laws account for all the motions, that the science of astronomy seemed as if finished; and no matter how far in the future a time might be a.s.signed, Kepler's laws provided the means of calculating the planet's position for that epoch as accurately as it would be possible to observe it. Kepler paused here, and he died in 1630.

CHAPTER XI

GALILEO, THE GREAT EXPERIMENTER

The fifteenth and sixteenth centuries, containing the lives and work of Copernicus, Tycho, Galileo, Kepler, Huygens, Halley, and Newton, were a veritable Golden Age of astronomy. All these men were truly great and original investigators.