The elliptic form of the orbits, and the equable description of areas, constitute two of the three celebrated truths known by the name of Kepler'a laws. The third, namely, that the squares of the periodic times ?re proportional to the cubes of the mean distances from the son, was not discovered till twelve years after, Although, before the publication of his Illysterium Cosmographicum,' he had been specu lating, as we have seen, upon finding some relation between those dis tances and periodic times. The final discovery resulted, far less from philosophical deduction than from the innumerable combinations which his ever•active fancy had been calling into existence during the previous seventeen years; and indeed when ho at length detected the relation which he had so long been in search of, he was only able to offer an explanation of it upon four suppositions, three of which aro now known to bo false.
In 1620 Kepler was visited by Sir Henry Wotton, the English ambassador at Venice, who finding him, as he was always to be found, oppressed with pecuniary difficulties, urged him to go over to England, where he assured him of a welcome and honourable reception ; but Kepler could never determine on quitting the Continent, In 1624 he went to Vienna, where with difficulty he obtained 6000 florins towards completing the Iludolphine Tables, together with recommendatory letters to the states of Snabla, from whom he also collected some money due to the emperor. It was not however till 1627 that these tables she first that were calculated on the supposition that the planets move in elliptic orbits-made their appearance; and it will be sufficient to sty of them, in this place, that had Kepler done nothing in the course of his whole life but construct these, he would have well earned the title of a most useful and indefatigable calculator. In 3630 he made a final attempt to obtain a liquidation of his claims upon the imperial treasury, but the fatigue and vexation of his fruitless journey brought on a fever which terminated his life in the early part of November 1630, and in his fifty-ninth year. Ilia body was interred in St. Peter's churchyard at Ratisbon, and a simple inscription, which has long since disappeared, was placed on his tombstone. Upon the character of Kepler, upon his failures, and on his success, Delambre has pronounced the following judgment :-" Ardent, restless, burning to distinguish himself by his discoveries, he attempted everything; and having once obtained a glimpse, no labour was too hard for him in following or verifying it. All his attempts had not the tame success, and in fact that was impossible. Those which have failed seem to us only fanciful;
those which have been more fortunate appear sublime. When in search of that which really existed, he has sometimes found it ; when he devoted himself to the pursuit of a ohimera, he could nut but fail; but even there he unfolded the same qualities, and that obstinate per severance that must triumph over all difficulties but those which are insurmountable." The following is a list of Kepler's published works. His manuscripts were purchased for the library of St. Petersburg, where Euler, Lexell, and Kraft undertook to examine them, and to select the most interesting parts for publieatiou ; but the result of this examination has never appeared.
List of Kepler's published works Calender,' Gratz, 1594 ; Prodromue Dissertat. Cosmograph.,' 4to, Tiibingas, 1596; 'De Funda meals Aetrologite,' 4to, Presto, 1602; Paralipomena ad Vitellionem,' 4to, Francofurti, 1604 ; Epistola de Solis deliquio,' 1605 ; ' De Stella Nova,' 4to, Pragte,1606; Vom Kometeu,' 4to, Halle, 1603 ; Antwort an Riisliu,' 4to, Pragte, 1609 ; I Astronomia Nova,' foL, Pragte, 1609; Tortilla Interveuiene,' 4to, Frankfurt, 1610; 'Diasertatio cum Nuncio Sidereo,' 4to, Francofurti, 1610; seu be nivo sexnugula,' 4to, Frankfurt, 1611 ; Dioptrica,' 4to, Francofurti, 1611 ; 'Vora Geburts Jahro des Ileylandes; 4to, Strasburg, 1613 ; 'Ravens. ad epist. S. Calvisii,' 4to, Francofurti, 1614; ' &logos Chronicre,' 9to, Frankfurt, 1615; 'Nova Stereornetria,' 4to, Lincii, 1615; 'Ephemerides 1617 1620; 4to, Lincii, 1616; 'Epitomes Astron. Copern. Libri 8vo, Lentiis, 1618; 'De Corneas,' Aug. Vindelic., 4to, 1619; Har monica foL, Lincii, 1619; Kanones Ulmas, 1620; ' Epitomes Astron. Copern. Liber iv.,' 8vo, Lentiis, 3622; ' Epitomes Astron. Copern. Libri v. vi. 8vo, Francofurti, 1622; Discure von der grossen Conjunction,' 4to, Linz., 1623;'Chilies Logarithmorum; foL, Marpurgi, 1624; Supplementum,' 4to, Lentils, 1625; 'Hyper aspistes,' 8vo, Francofurti, 1625; 'Tabulmo Iludelphiure,' fol., UlltIre, 3627; "Reap. ad °plat. J. Bartachii,' 4to, Sagaui, 1629; "De anni 1631 Pha3nomenis,' 4to, Lipste, 1629; ' Terrentii Epistolium cum Cowmen tatiuncula; 4to, Sagaui, 1630; Ephemerides,' 4to, Sagani, 1630; 'Somnium: 4to, Fraucofurti, 1634; 'nebulas Manuales,' 12mo, Argentorati, 1700.
A splendid edition of Kepler's Correspondence' was published under the auspices of the Emperor Charles VI., in 1718, by M. G. Haunch. It is entitled Epistola3 ad J. Keplerum,' &c., and the title pago has no place of publication, but the preface is dated from Leipzig. It contains a life of Kepler.