TOT 



KEPLER, Jonx. 



KEY, THOMAS HEWITT 



TM 



the opposite direction round the centre of the earth, thai describing a 

 larger circle which waa called the deferent Subaequent observations 

 b**og foand irreconcilable with the foregoing hypothesis, it ww modi- 

 fled by supposing the uniform angular motion of the epicycle to be 

 dsMribcd about a point nut coinciding with the centre of the earth, a 

 Meaamry consequence of which supposition wai that the linear 

 motion of the epicycle ecaied to be uniform. The work of Copernicus 

 ' I>e Kevolutionibus Orbium Ciclestium ' hud appeared in 1S4S, wherein 

 be oooiiders the sun to be the fixed centre about which the planeU 

 move with uniform motions, but retains the complicated machinery of 

 the deferent and epicycle in order to account for the variations arieing 

 from the actual inequality of the planet's motion. The system of 

 Tycho I'nbi himself was idtntical with one which Copernicus had 

 rejected, and consisted in supposing the inn to revolre about the 

 earth, carrying with it all the other planets revoking about him ; and 

 indetd Tycho not only denied the revolution of the earth about the 

 tun, but likewise its diurnal rotation upon its axia. Such is an imper- 

 fect outline of the theory of the universe before the time of Kepler. 

 Tbo theory adopted by Kepler in the early part of his discussion of 

 Tycho's ot-st nations, appears to have been that the orbit of each 

 planet, including the earth, was circular ; that it was described with a 

 uniform angular velocity about a point within, called the centre of the 

 quant, and that the centre of the orbit lay in the line joining the 

 centre of the eqnant and the place of the mm, 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 cqunnt coincided with that of its orbit, and that conse- 

 quently not only its angular but also its linear motion was uniform, 

 although its distance from the sun was known to vary. After four 

 years of laborious calculation, the non-accordance of bis 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 be 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 waa 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 apsides, that i?, 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 arc 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 substituted the approximate 

 area of the figure bounded by the arc.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 be came to apply this theory 

 to the motion of Mars, the excentricity of whose orbit ia 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 as he 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 Mar*. At length he deduced, from observations 

 of that planet near the quadratures, that its orbit was an oval elongated 

 in the direction of its apsides, and was thus led to the law of elliptic 

 motions. 



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's laws. The third, namely, that the squares of the periodic 

 times are proportional to the cubes of the mean distances from the 

 sun, was not discovered till twelve years after, although, before the 

 publication of his ' Mysteriutn Cosmogrsphicum,' he had been specu- 

 lating, as we have seen, upon finding some relation between those dis- 

 tance* and periodic times. The final discovery resulted, far less from 

 philosophical deduction than from the innumerable combinations 

 which his ever-active fancy bad been calling into existence during the 

 previous seventeen yean; and indeed when he 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 are 

 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 welcome and honourable reception ; bul 

 Kepler could never determine on quitting the Continent In 1624 he 

 went to V ienna, where with difficulty he obtained 6000 florins towards 

 completing the Kudolphine Tables, together with recommendatory 

 letters to the states of Snabia, from whom he also collected some inonej 

 doe to the emperor. It was not however till 1027 that thete tables 

 the first that were calculated on the supposition that the planets move 



n elliptic orbits made their appearance ; and it will be sufficient to 

 say of them, in this place, that had Kepler done nothing in the course 

 of his whole life but construct these, lie would have well earned tha 

 Jtle of a most useful and indefatigable calculator. In 1630 he mado 

 a final attempt to obtain a liquidation of his claims upon the imperial 

 treasury, but the fatiguo and vexation of his fruitless journey brought 

 on a fever which terminated his life in the early part of November 

 1630, and in hU fifty-ninth year. His 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, Delsmbre has pronounced 

 :1) following judgment : " Ardent, restless, burning to tii'tinguish 

 liinself 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 same success, and in fact 

 that waa impossible. Those which have failed seem to us only fanciful ; 

 those which have bi-eu more fortunate appear sublime. When in 

 search of that which really existed, he has sometimes found it ; when 

 lie devoted himself to the pursuit of a chimera, 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, Leiell, 

 and Kraft undertook to examine them, and to select the most 

 interesting parts for publication ; but the result of this examination 

 bas never appeared. 



List of Kepler's published works: 'Kin Calender,' Gratz, 1594 ; 

 ' Prodromus Dissertat. Cosmograph.,' 4to, Tiibingn, 1596 ; De Funda- 

 mentis Astrologite,' 4to, ProgK, 1602 ; ' 1'anilipomeiia ad Yitrllionem,' 

 4 to, Francofurti, 1604 ; ' Epistola de Solis deliquio,' 1605 ; ' Do StellA 

 Nova,' 4to, Pragtc, 1606 ; ' Vom Kometen,' 4 to, Halle, 1603 ; ' Antwort 

 an Kosliu,' 4to, Pragic, 1C09; ' Aatronomia Nova,' fol., Pragro, 1609; 

 ' Tertius Interveniens,' 4to, Frankfurt, 1610; ' Dissertatio cum Nuncio 

 Sidereo,' 4to, Francofurti, 1610; ' Strena, seu De nive sexangula,' 4t<>, 

 Frankfurt, 1011 ; ' Dioptrics,' 4to, Francofurti, 1611 ; 'Vom Oeburts 

 Jahre des Heylandes,' 4 to, Strasburg, 1613; 'Respong. ail epist S. 

 Calvisii,' 4to, Francofurti, 1014; ' Eclogse Chronicte,' 4to, Frankfurt, 

 1616; 'Nova Stereometria,' 4to, Lincii, 1615; 'Ephemerides K.17- 

 1620,' 4to, Lincii, 1616; 'Epitomes Astron. Copern. Libri i. ii. iii.,' 

 8vo, Lentiis, 1618; 'De Cometis,' Aug. Vindelic., 4 to, 1619; ' Hr- 

 monice Mundi,' foL, Lincii, 1619 ; ' Kanones Pueriles, 1 Ulmee, 1620 ; 

 ' Epitomes Astron. Copern. Liber iv.,' 8vo, Lentiis, 1622; 'Epitomes 

 Astron. Copern. Libri v. vi. vii.,' iivo, Francofurti, 1622; 'Discurs von 

 der grossen Conjunction,' 4to, Linz., 1623; 'Chilias Logarithmorum,' 

 foL, Marpurgi, 1624; ' Supplementum,' 4to, Lentiis, 1625; 'Hyper- 

 aspiates,' 8vo, Francofurti, 1625; 'Tabula Rudolphinac,' fol., Ultnjc, 

 1627; 'Heap, ad epist J. Bartschii,' 4to, Sagani, 1629; 'De anni 1631 

 Phtenomenis," 4to, Lipate, 1629; ' Terrentii Epistolium cum Commen- 

 tatiuncula,' 4 to, Sagani, 1630; 'Ephemerides,' 4 to, Sagani, 1630; 

 Somnium,' 4 to, Francofurti, 1634; 'Tabula Monuales,' 12mo, 

 Argentorati, 1700. 



A spleudid edition of Kepler's 'Correspondence' was published 

 under the auspices of the Emperor Charles VI., in 1718, by M. O. 

 Hanscli. It is entitled ' Epistolic ad J. Keplermn,' Ac., and the title- 

 page has no place of publication, but the preface is dated from Leipzig. 

 It contains a life of Kepler. 



*KEY, THOMAS HKWITT, was born in Southwark, March 20, 

 1799, the son of Dr. Key, a medical practitioner in London, lii- 

 father was married twice bis only aon by his first wife (a relative of 

 Sir Charles Barry) being the late eminent surgeon C. Aston Key ; and 

 his youngest son by his second (a sister of the former wife) beiug the 

 subject of this notice. After receiving his school-education at Bunting- 

 ford Grammar-school in Hertfordshire a school founded by Seth 

 Ward Mr. Key passed to St John's College, Cambridge, in October 

 1817, and was elected a scholar of this college in the following month. 

 In the spring of 1819 he exchanged St. John's for Trinity College in 

 the same university ; of which he was also elected a scholar. In 1821 

 he took his degree of B.A., obtaining a place in the list of Wranglers 

 there being then no classical tripos. Residing in Cambridge two 

 yean as B.A. he studied medicine ; and in 1S23-4 he continued his 

 medical studies at Uuy's Hospital, London. In 1824 however after 

 taking his M.A. degree, he made the acquaintance of Mr. Gilmore, an 

 American gentleman, at that time on a visit to Europe with a com- 

 mission to till up certain professorships in the university of Virginia, 

 then just founded under the rectorship of the ex-president Jefferson, 

 with the ex-prosidents Madison and Monroe, and others, as his 

 coadjutors. The consequence was that Mr. Key accepted the pro- 

 fessorship of Pure Mathematics in that University. The duties of 

 this office he discharged for three sessions; but the climate of 

 Virginia not agreeing with his health, ho returned to England in 1827. 

 During his residence in America he had applied his leisure to the 

 study of the Latin language in its deeper philological relations; and 

 some of his new conclusions ou this subject having becomo known 

 to Mr. George Long, his colleague iu the Virginian University as 

 Professor of Greek and Latin, ho was, chiefly at the instance of Mr. 

 Long, elected in the autumn of 1828, to fill the Latin chair in tho 

 University of London, then on the point of opening. This chair he 



