At length, in 1609 appeared his 'New Astronomy,' containing his great and extraordinary book Ou the Motion of Mars ; ' a work a hich bolds the intermediate place, and is the connecting liuk, between the discoveries of Copernicus and those of Newton. Tho introduction is occupied in refuting the then commonly-received theory of gravity, and in declaring what were his own opinions upon the same subject.
In the course of this dismission he states distinctly that since the attractive virtue of the moon extends as far as tho earth, as is evident from its enticing up the waters of the earth, with greater reason it follows that the attractive virtue of the earth extends as far as the moon, and much farther ; and he likewise asserts that if two bodies of like nature be placed in any part of the world near each other, but beyond the Influence of any other body, they would approach each other like two magnets, each pa.sing over a space reciprocally iu pro portion to its mass ; so that if the moon and earth were not retained in their orbits by their animal force, or some other equivalent to it, the earth would approach the moon by the 54th part of their distance, and the moon would approach the earth by the remaining 53 parts. Previous to the publication of this remarkable work it was supposed that each planet moved uniformly iu a email circle called an epicycle, the centre of which epicycle moved with an equal angular velocity iu the opposite direction round the centre of the earth, thus describing a larger circle which was called the deferent. Subsequent observations being found irreconcileable with the foregoing hypothesis, it was mall fled by supposing the uniform angular motion of the epicycle to be descrilxd about a point not coinciding with the centre of the earth, a necessary consequence of which supposition was that the linear motion of the epicycle ceased to be uniform. The work of Copernicus ' De Itevolutionibus Orblum Clelestium' bad appeared in 1543, wherein he considers the sun to le the fixed centre about which the planets move with uniform motions, but retains tho complicated machinery of the deferent and epicycle in order to account for the variations arising from the actual inequality of the planet's motion. The system of Tycho Prah4 himself was id,ntical with one which Copernicus had rejected, and consisted in supposing the aim to revolve about the earth, carrying with it all the other planate revolving about him ; and indeed Tycho not only denied the revolution of the earth about the tun, but likewise its diurnal rotation upon its axis. Such is an imper fect outline of the theory of the universe before the timo of Kepler. The theory adopted by Kepler in the early part of his discussion of Tycho's olservations, appear. to have been that the orbit of each planet, iucluding the earth, was circular ; that it was described with a uniform angular velocity about a point within, called the centre of the equant, and that the centre of the orbit lay in the liue joining the centre of the equant and the place of the sun, but not equidistant between those points, as had been previously supposed. With respect
to the earth however, in particular, he bad started with the erroneous opinion, then generally entertained by all astronomers, that the centre of the earth's equnnt coincided with that of its orbit, and that cense quently not only its angular but also its linear motion wee uniform, although its distance from the sun was known to vary. After four years of laborious calculation, tho non-accordaoce of his results with observation obliged him to fix upon the bisection of the line joining the centre of the equant and the place of the sun, for the centre of the planet's orbit ; and shortly after he was led to the conclusion that one of the two other principles upon which his theory rested must be erroneous; that either the orbit of the planet was not a perfect circle, or that there was no point within it round which it moved with a uniform velocity.
Having easily proved that at the upsides, that is, the two points of the planet's orbit which are nearest to and farthest from the sun, the times of describing equal small arcs are nearly proportional to the distances of the planet from the sun, he concluded with his accustomed precipitancy that the same relation existed at all other points of the orbit. An almost immediate consequence of this assumption was that the time of describing an are of any length whatever would be pro portional to the sum of all the lines which could be drawn from the sun to every point of that arc; but as the calculation of these distances was found to be excessively operose, he snbstituted the approximate area of the figure bounded by the are,and the two extreme distances for the sum of all the distances, and was thus led from erroneous principles to that beautiful law of the planetary motions by which the area described by the revolving radius vector is proportional to the time of its description. When however he came to apply this theory to the motion of Mars, the excentricity of whose orbit is much greater than that of the Earth's, he found that the circular hypothesis gave results differing from the observations of Tycho by at least eight minutes; and Ube considered that difference too great to be attributed to the error of so exact an observer, he concluded that the suspicions which, as was above stated, he had long previously entertained relative to the form of the planets' orbits, were well founded, at least with respect to the planet Mars. At length he deduced, from observation, of that planet near the quadratures, that its orbit was an oval elongated in the direction of its upsides, and was thus led to the law of elliptic motions.