other areas ; Groddeck continued this work by inves-tigating the lithologic sequences, primarily in theHarz Mountains, as reflected in his booklet Abriss derGeognosie des Harzes (1871-1883). His second topic,which historically is probably much more significantand original, was the link between lithology and oregeology. Here he made a major step in a directionthat was almost entirely lost for 80 years and whichhas been rediscovered only recently . It was an obser-vational classification of ore deposits, taking intoaccount the facts of congruence between the host rockand the deposits . In his textbook on economic oredeposits,' he came very close to stating that conform-able or congruent deposits were contemporaneous,and noncongruent deposits epigenetic . This idea isreflected in his book in the following classification ofmineral deposits (p . 84) :

I . Bedrock deposits (formed in situ)A. Layered deposits

1 . massive ore strata2. coprecipitation ore strata (of dis-

seminated ore matter)3. 1enticular ore layers (or strings)

B . Massive (nonlayered) depositsC. Cavity fillings

1 . fissure fillings or dikesa. dikes in massive rocksb. dikes in layered rocks

2. fillings of cavesD. Metamorphic mineral depositsWeathering deposits (detrital deposits)

3

II .

GRODDECK

Groddeck's fifty-seven types of ore deposits wereclassified first according to geometric criteria (layered,vein type, and so on) and second according to com-position . In this morphologic trend he was closest ofall his contemporaries to the general trend of objecti-vation, that is, of an introduction of observational asagainst interpretative criteria in scientific classifica-tions. In botany, zoology, and crystallography, thisobservational pattern had been followed since the firsthalf of the eighteenth century, whereas in geology,especially in ore geology, old mythologic theories ofmagic ore sources were still fashionable, and becauseof Posepny, had again become accepted dogma in1890. Consequently, Groddeck was clearly a fore-runner of the modern approach, especially the mod-ern French morphological school of thought .

Because of his teaching and administrative duties,his early death, and probably also his less active linkswith foreign researchers, Groddeck was not veryinfluential in his field, and apparently not nearly aswell known in Anglo-Saxon countries as Posepny,who traveled in North America and whose book on

5 48

ore deposits was translated into English as early as1895. Posepny, and in part also von Cotta, were strongproponents of an almost pan-epigenetic theory of oregenesis, whereas Groddeck showed an independentnew approach, linking observations in the countryrock with his genetic interpretations . For thisindependent observation and interpretation of orefeatures he was rediscovered after 1958: an Englishtranslation of his 1879 book on ore deposits is pres-ently being prepared .

His keen scientific mind also led him to proposeother new genetic solutions to old problems, thusfar explained by complicated hypotheses based moreon ideas (projections of ideas) than on observations .For example, he showed with both observation anda sound logic of relations, that the tectonic struc-ture of the Oberharz diabase consists of a simple,compressed saddle-shaped fold . He also proved thatthe adinole schist of the Oberharz is a normal bedconcordant with the siliceous Culm schist, againdemonstrating that he was ahead of his time in re-gard to genetic understanding . He also pioneeredobservations and interpretations of wall rock altera-tions . Groddeck's work therefore deserves a more im-portant place in the history of geology than it has upto now been accorded .

BIBLIOGRAPHY

I. ORIGINAL WORKS. A bibliography of Groddeck'sworks is in Poggendorff, III, 551-552 ; IV, 537 . His majorpublications are Abriss der Geognosie des Harzes, 2 vols .(1871-1883) : and his textbook, Die Lehre von denLagerstatten der Erze (Leipzig, 1879) .

11 . SECONDARY LITERATURE . See A. K . Lossen, "Albrechtvon Groddeck," in Jahrbuch der Preussischen geologischenLandesanstalt u . Bergakademie zu Berlin, 1887 (1888), 109-132 ; and "Albrecht von Groddeck," in Neues Jahrbuch furMineralogie, Geologie and Palaontologie, 1 (1888), 24.W. Fischer, Gesteins- and Lagerstattenbildung im Wandel

der wissenschafilichen Anschauung (Stuttgart, 1961), refersoften to Groddeck's work, but does not fully appreciate therole of his work as compared to that of Cotta and Posepny .

G . C . AMSTUTZ

GROSSETESTE, ROBERT (b. Suffolk, England, ca.1168 ; d. Buckden, Buckinghamshire, England, 9 Oc-tober 1253), natural philosophy, optics, calendar re-form .

Grosseteste was the central figure in England inthe intellectual movement of the first half of thethirteenth century, yet the only evidence for his lifebefore he became bishop of Lincoln in 1235 is to be

GROSSETESTE

GROSSETESTE

found in fragmentary references by Matthew of Parisand other chroniclers, by Roger Bacon, and occa-sionally in charters, deeds and other records .' Hisbirth has been variously dated between 1168 and1175, but since he is described as "Magister RobertusGrosteste" (the first appearance of his name) in acharter of Hugh, bishop of Lincoln, of probably1186-1190, the earlier date is the more likely . Tradi-tion places his birth in Suffolk, of humble parentage .He may have been educated first at Lincoln, then atOxford, and was in the household of William de Vere,bishop of Hereford, by 1198, when a reference byGerald of Wales suggests that he may have had someknowledge of both law and medicine . After that itseems likely that he taught at Oxford in the artsschool until the dispersion of masters and scholarsduring 1209-1214. He must have taken his mastershipin theology, probably at Paris, during this period,some time before his appointment as chancellor ofthe University of Oxford, although with the titlemagister scholarum, probably about 1214-1221, whenhe must have lectured on theology .

Grosseteste was given a number of ecclesiasticalpreferments and sinecures, including the arch-deaconry of Leicester in 1229; but in 1232 he resignedthem all except for a prebend at Lincoln, writing tohis sister, a nun : "If I am poorer by my own choice,I am made richer in virtues ."' From 1229 or 1230until 1235 he was first lecturer in theology to theFranciscans, who had come to Oxford in 1224. Hisinfluence there was profound and continued after heleft Oxford in 1235 for the see of Lincoln, within thejurisdiction of which Oxford and its schools came .He contributed largely to directing the interests ofthe English Franciscans toward the study of the Bible,languages, and mathematics and natural science .Indispensable sources for this later period of his lifeare his own letters and those of his Franciscan friendAdam Marsh .

Grosseteste's career thus falls into two main parts,the first that of a university scholar and teacher andthe second that of a bishop and ecclesiastical states-man. His writings fall roughly into the same periods :to the former belong his commentaries on Aristotleand on the Bible and the bulk of a number of inde-pendent treatises, and to the latter his translationsfrom the Greek. Living at a time when the intellectualhorizons of Latin Christendom were being greatlyextended by the translations into that language ofGreek and Arabic philosophical and scientific writ-ings, he took a leading part in introducing this newlearning into university teaching . His commentary onAristotle's Posterior Analytics was one of the first andmost influential of the medieval commentaries on this

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fundamental work. Other important writings belong-ing to the first period are his commentary on Aris-totle's Physics, likewise one of the first ; independenttreatises on astronomy and cosmology, the calendar(with intelligent proposals for the reform of theinaccurate calendar then in use), sound, comets, heat,optics (including lenses and the rainbow), and otherscientific subjects ; and his scriptural commentaries,especially the Moralitates in evangelica, De cessationelegalium, Hexaemeron and commentaries on thePauline Epistles and the Psalms . Having begun tostudy Greek in 1230-1231, he used his learning fruit-fully during the period of his episcopate by makingLatin translations of Aristotle's Nicomachean Ethicsand De caelo (with Simplicius' commentary), of theDe fide orthodoxe of John of Damascus, of Pseudo-Dionysius and of other theological writings . For thiswork he brought to Lincoln assistants who knewGreek ; he also arranged for a translation of thePsalms to be made from the Hebrew and seems tohave learned something of this language .Although in content a somewhat eclectic blend of

Aristotelian and Neoplatonic ideas, Grosseteste'sphilosophical thinking shows a strong intellect curiousabout natural things and searching for a consistentlyrational scheme of things both natural and divine .His search for rational explanations was conductedwithin the framework of the Aristotelian distinctionbetween "the fact" (quia) and "the reason for the fact"(propter quid) . Essential for the latter in natural phi-losophy was mathematics, to which Grosseteste gavea role based specifically on his theory, expounded inDe luce seu de inchoatione formarum and De motucorporaai et luce, that the fundamental corporeal sub-stance was light (lux) . He held that light was the firstform to be created in prime matter, propagating itselffrom an original point into a sphere and thus givingrise to spatial dimensions and all else according toimmanent laws . Hence his conception of optics as thebasis of natural science . Lux was the instrument bywhich God produced the macrocosm of the universeand also the instrument mediating the interactionbetween soul and body and the bodily senses in themicrocosm of man . 3 Grosseteste's rational schemeincluded revelation as well as reason, and he was oneof the first medieval thinkers to attempt to deal withthe conflict between the Scriptures and the newAristotle . Especially interesting are his discussions ofthe problems of the eternity or creation of the world,of the relation of will to intellect, of angelology, ofdivine knowledge of particulars, and of the use ofallegorical interpretations of Scripture .

Grosseteste's public life as bishop of Lincoln wasinformed by both his outlook on the universe as a

GROSSETESTE

scholar and his conception of his duties as a prelatededicated to the salvation of souls . Analogous tocorporeal illumination was the divine illumination ofthe soul with truth . He extended the luminousanalogy to illustrate the relationship between thepersons of the Trinity, the operation of divine gracethrough free will like light shining through a coloredglass, 4 and the relation of pope to prelates and ofbishops to clergy : as a mirror reflects light into darkplaces, he said in asserting his episcopal rights againstthe cathedral chapter of Lincoln, so a bishop reflectspower to the clergy . 5

In practice Grosseteste was governed by threeprinciples: a belief in the supreme importance of thecure of souls ; a highly centralized and hierarchicalconception of the church, in which the papacy, underGod, was the center and source of spiritual life andenergy ; and a belief in the superiority of the churchover the state because its function, the salvation ofsouls, was more vital . Such views were widelyaccepted, but Grosseteste was unique in the ruthless-ness and thoroughness with which he applied them,for example, in opposing the widespread use ofecclesiastical benefices to endow officials in the serviceof the crown or the papacy. As a bishop he hadattended the First Council of Lyons in 1245, and ina memorandum presented to the pope there in 1250he expounded his views on the unsuitability of suchappointments while accepting the papal right todispose of all benefices . Likewise, his opposition tothe obstruction of the disciplinary work of the churchby any ecclesiastical corporation or secular authoritybrought him into conflict both with his own Lincolnchapter and with the crown over royal writs of prohi-bition when secular law clashed with church law andwhen churchmen were employed as judges or in othersecular offices . Grosseteste was a close friend of Simonde Montfort and took charge of the education of hissons, but the degree to which he shared in or influ-enced Montfort's political ideals has probably beenexaggerated . Above all he was a bishop with an ideal,an outstanding example of the new type of ecclesiastictrained in the universities .

Scientific Thought. Some of Grosseteste's scientificwritings can be dated with reasonable certainty, andmost of the others can be related to these in an orderbased on internal references and on the assumptionthat the more elaborated version of a common topicis the later. 6 From the evidence for his method ofmaking notes on his reading and thoughts to beworked up into finished essays and commentaries,'and from these writings themselves, it may beassumed that many of them arose out of his teachingin the schools. Gerald of Wales's description of

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Grosseteste at Hereford as a young clerk with a man-ifold learning "built upon the sure foundation of theliberal arts and an abundant knowledge of litera-ture" s is borne out by what is probably his earliestwork, De artibus liberalibus. In this attractive intro-duction he described how the seven liberal arts atonce acted as a purgatio erroris and gave directionto the gaze and inclination of the mind (mentisaspect us et affectus) . Of particular interest is his treat-ment of music, of which his love became proverbial,and of astronomy. As for Boethius, music for himcomprised the proportion and harmony not only ofsounds produced by the human voice and by instru-ments but also of the movements and times of thecelestial bodies and of the composition of bodiesmade of the four terrestrial elements--hence thepower of music to mold human conduct and restorehealth by restoring the harmony between soul andbody and between the bodily elements, and the re-lated power of astronomy through its indication ofthe appropriate times for such operations and for thetransmutation of metals . Related to this essay washis phonetical treatise De generatione sonorum, whichhe introduced with an account of sound as a vibratorymotion propagated from the sounding body throughthe air to the ear, from the motion of which arosea sensation in the soul .

Grosseteste developed his mature natural philoso-phy through a logic of science based on Aristotle andthrough his fundamental theory of light . In theirpresent form most of the works concerned werealmost certainly written between about 1220 and1235 . De lute and De motu corporali et luce, with hiscosmogony and cosmology of light, seem to date fromearly in this period . The structure of the universegenerated by the original point of lux was determined,first, by the supposition that there was a constantproportion between the diffusion or "multiplication"of lux, corresponding to the infinite series of naturalnumbers, and the quantity of matter given cubicdimensions, corresponding to some finite part of thatseries. Second, the intensity of this activity of luxvaried directly with distance from the primordialsource. The result was a sphere denser and moreopaque toward the center . Then from the outermostboundary of the sphere lumen emanated inward toproduce another sphere inside it, then another, andso on, until all the celestial and elementary spheresof Aristotelian cosmology were complete . Anotherseemingly early work in this series, De generationestellarum, shows Grosseteste dependent on Aristotlein many things but not in all, for he argued that thestars were composed of the four terrestrial elements .Later, in his commentary on the Physics, he con-

GROSSETESTE

trasted the imprecise and arbitrary way man mustmeasure spaces and times with God's absolute meas-ures through aggregates of infinites .

In all these writings Grosseteste made it clear thatby lux and lumen he meant not simply the visiblelight which was one of its manifestations, but a fun-damental power (virtus, species) varying in its mani-festation according to the source from which it waspropagated or multiplied and in its effect accordingto its recipient . Thus he showed in De impressionibuselementorum how solar radiation effected the trans-formation of one of the four terrestrial elements intoanother and later, in De natura locorum, how it causeddifferences in climate . An explanation of the tidesbegun in De accessione et recessione maris or De fluxuet refluxu maris (if this work is by him) 9 was com-pleted in De natura locorum, in which he argued thatthe rays of the rising moon released vapors from thedepth of the sea which pushed up the tide until themoon's strength increased so much that it drew thevapors through the water, at which time the tide fellagain. The second, smaller monthly tide was causedby the weaker lunar rays reflected back to the oppo-site side of the earth from the stellar sphere .

In De cometis et causis ipsarum Grosseteste gavea good example of his method of falsification inarguing that comets were "sublimated fire" separatedfrom their terrestrial nature by celestial powerdescending from the stars or planets and drawing upthe "fire" as a magnet drew iron . Later, in De caloresolis (ca. 1230-1235), he produced perhaps his mostelegant exercise in analysis by reduction to conclu-sions falsified either by observation or by disagree-ment with accepted theory, finally leaving a verifiedexplanation. He concluded that all hot bodiesgenerated heat by the scattering of their matter andthat the sun generated heat on the earth in directproportion to the amount of matter incorporated fromthe transparent medium (air) into its rays .Grosseteste set out and exemplified the formal

structure of his mature scientific method in hisCommentaria in libros posteriorum Aristoielis, hisCommentarius in viii libros physicorum Aristotelis, 10and four related essays giving a geometrical analysisof the natural propagation of power and light . Itseems likely that he began the commentary on thePosterior Analytics when he was still a master of arts,that is, before 1209, and completed it over a longperiod, finishing after 1220 and probably nearer theend of the decade . The commentary on the Physicswas written later, likewise certainly over a period ofyears, probably around 1230 . It has striking parallelswith some of the scientific topics of the Hexaemeronbut shows less than even the limited knowledge of

5 5 1

GROSSETESTE

Greek found in this work, suggesting that it justprecedes it .

For Grosseteste, as for Aristotle, a scientific inquirybegan with an experienced fact (quia), usually a com-posite phenomenon. The aim of the inquiry was todiscover the reason for the fact (propter quid), theproximate cause or natural agent from which thephenomenon could be demonstrated :

Every thing that is to be produced is already describedand formed in some way in the agent, whence natureas an agent has the natural things that are to be pro-duced in some way described and formed within itself,so that this description and form itself, in the very natureof things to be produced before they are produced, iscalled knowledge of nature ."

His method of discovering the causal agent was tomake first a resolutio, or analysis of the complexphenomenon into its principles, and then a composi-tio, or reconstruction and deduction of the phenom-enon from hypotheses derived from the discoveredprinciples . He verified or falsified these hypothesesby observation or by theory already verified by ob-servation.

Besides this double method, Grosseteste used in theanalysis of the causal agent as the starting-point ofdemonstration another Aristotelian procedure, that ofthe subordination of some sciences to others, forexample, of astronomy and optics to geometry andof music to arithmetic, in the sense that "the superiorscience provides the propter quid for that thing ofwhich the inferior science provides the quia ." 12 Butmathematics provided only the formal cause ; thematerial and efficient causes were provided by thephysical sciences . Thus "the cause of the equality ofthe two angles made on a mirror by the incident rayand the reflected ray is not a middle term taken fromgeometry, but is the nature of the radiation generatingitself in a straight path . . . ." 13 The echo belongedformally to the same genus as the reflection of light,but the material and efficient causes of the propagationof sound had to be sought in its fundamental sub-stance : "the substance of sound is lux incorporatedin the most subtle air . . . ." 14 This introduced afundamental addition to the very similar discussionof the propagation of sound in De artibus liberalibusand De generatione sonorum .

Grosseteste developed his geometrical analysis ofthe powers propagated from natural agents in the fourrelated essays written most probably in the period1231-1235 . He said in the first, De lineis, angulis etfiguris seu de fractionibus et reflexionibus radiorum :"All causes of natural effects have to be expressedby means of lines, angles and figures, for otherwise

GROSSETESTE

it would be impossible to have knowledge propter quidconcerning them ." 15 The same power produced aphysical effect in an inanimate body and a sensationin an animate one . He established rules for the oper-ation of powers : for example, the power was greaterthe shorter and straighter the line, the smaller theincident angle, the shorter the three-dimensional pyr-amid or cone; every agent multiplied its powerspherically. Grosseteste discussed the laws of reflec-tion and refraction (evidently taken from Ptolemy)and their causes, and went on in De natura locorumto use Ptolemy's rules and construction with planesurfaces to explain refraction by a spherical burningglass. "Hence," he resumed, "these rules and princi-ples and fundamentals having been given by thepower of geometry, the careful observer of naturalthings can give the causes of all natural effects bythis method." This was clear "first in natural actionupon matter and later upon the senses . . . . " 16

An example of the analysis of a power's producingsensation is provided by Grosseteste's De colore. Theresolutio identified the constituent principles : colorwas light incorporated by a transparent medium ;transparent mediums varied in degree of purity fromearthy matter ; light varied in brightness and in themultitude of its rays . In the compositio he assertedthat the sixteen colors ranging from white (brightlight, multitudinous rays, in a pure medium) to blackwere produced by the "intension and remission" ofthese three variable principles. "That the essence ofcolor and a multitude of the same behaves in the saidway," he concluded, "is manifest not only by reasonbut also by experiment, to those who know the prin-ciples of natural science and of optics deeply andinwardly . . . . They can show every kind of colorthey wish to visibly, by art [per artificiuml ." 17

The last of these four essays, De iride seu de irideet speculo, is the most complete example ofGrosseteste's method and his most important contri-bution to optics. The resolutio proceeds through asummary of the principle of subordination and itsrelation to demonstration propter quid into a discus-sion of the division of optics into the science of directvisual rays, of reflected rays, and of refracted rays,in order to decide to which part the study of therainbow belonged. It was subordinate to the thirdpart, "untouched and unknown among us until thepresent time" ; is and it is his treatment of refractionthat has the greatest interest .

This part of optics [perspectiva], when well under-stood, shows us how we may make things a very longdistance off appear to be placed very close, and largenear things appear very small, and how we may makesmall things placed at a distance appear as large as we

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want, so that it is possible for us to read the smallestletters at an incredible distance, or to count sand, orgrain, or seeds, or any sort of minute objects .''

The reason, as he had learned from Euclid andPtolemy, was "that the size, position and arrangementaccording to which a thing is seen depends on thesize of the angle through which it is seen and theposition and arrangement of the rays, and that a thingis made invisible not by great distance, except byaccident, but by the smallness of the angle of vision ."Hence "it is perfectly clear from geometrical reasonshow, by means of a transparent medium of knownsize and shape placed at a known distance from theeye, a thing of known distance and known size andposition will appear according to place, size and posi-tion." 26

Grosseteste followed this account of magnificationand diminution by refracting mediums with anapparently original law of refraction, according towhich the refracted ray, on entering a denser medium,bisected the angle between the projection of the inci-dent ray and the perpendicular to the interface . "Thatthe size of the angle in the refraction of a ray maybe determined in this way," he concluded, "is shownus by experiments similar to those by which we dis-covered that the reflection of a ray upon a mirrortakes place at an angle equal to the angle of inci-dence ." 21

It was also evident from the principle that naturealways acts in the best and shortest way . Grossetestewent on to use a construction of Ptolemy's to showhow to locate the refracted image, claiming again thatthis "is made clear to us by the same experiment andsimilar reasonings" 22 as those used in a similar con-struction for locating the reflected image . The firstof these references to experimental verification, sinceit would have been so inaccurate, may throw doubton all such references by Grosseteste . As was truefor the majority of medieval natural philosophers,most of these references came from books or fromeveryday experience . Clearly his interest was directedprimarily toward theory . Yet he advocated and wasguided by the principle of experiment and developedits logic.

Besides these works related to optics, Grossetestewrote important treatises on astronomical subjects . InDe sphaera, of uncertain date between perhaps 1215and 1230, and De motu supercaelestium, possibly after1230, he expounded elements of both Aristotelian andPtolemaic theoretical astronomy . In a later work, Deimpressionibus aeris seu de prognosticatione, datingapparently from 1249, he discussed astrological influ-ences and, again, his mature explanation of the tides .

GROSSETESTE

More original were Grosseteste's four separatetreatises on the calendar : Canon in kalendarium andCompotus; correcting these, Compotus correctorius,probably between 1215 and 1219 ; and Compotusminor, with further corrections, in 1244 . He showedthat with the system long in use, according to whichnineteen solar years were considered equal to 235lunar months, in every 304 years the moon wouldbe one day, six minutes, and forty seconds older thanthe calendar indicated . He pointed out in the Com-potus correctorius (cap. 10) that by his time the moonwas never full when the calendar said it should beand that this was especially obvious during an eclipse .The error in the reckoning of Easter came from theinaccuracy both of the year of 365 .25 days and ofthe nineteen-year lunar cycle .

Grosseteste's plan for reforming the calendar wasthreefold. First, he said that an accurate measuremust be made of the length of the solar year. He knewof three estimates of this: that of Hipparchus andPtolemy, accepted by the Latin computists; that ofal-Battani; and that of Thabit ibn Qurra . He dis-cussed in detail the systems of adjustments that wouldhave to be made in each case to make the solsticeand equinox occur in the calendar at the times theywere observed. Al-BattAni's estimate, he said in theCompotus correctorius (cap. 1), "agrees best with whatwe find by observation on the advance of the solsticein our time ." The next stage of the reform was tocalculate the relationship between this and the meanlunar month. For the new-moon tables of theKalendarium, Grosseteste had used a multiple nine-teen-year cycle of seventy-six years . In the Compotuscorrectorius he calculated the error this involved andproposed the novel idea of using a much more accu-rate cycle of thirty Arab lunar years, each of twelveequal months, the whole occupying 10,631 days . Thiswas the shortest time in which the cycle of wholelunations came back to the start . Grosseteste gave amethod of combining this Arab cycle with the Chris-tian solar calendar and of calculating true lunations .The third stage of the reform was to use these resultsfor an accurate reckoning of Easter . In the Compotuscorrectorius (cap. 10), he said that even without anaccurate measure of the length of the solar year, thespring equinox, on which the date of Easterdepended, could be discovered "by observation withinstruments or from verified astronomical tables ." 23

As with Grosseteste's optics, it was Roger Baconwho first took up his work on the calendar ; andAlbertus Magnus first made serious use of his com-mentary on the Posterior Analytics, as did John DunsScotus of that on the Physics. These attentions markedthe beginning of a European reputation that con-

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tinued into the early printing of his writings at Venice,the collecting of his scientific manuscripts by JohnDee, and interest in them by Thomas Hobbes . 24

NOTES

1 . See D. A . Callus, ed ., Robert Grosseteste .2 . Epistolae, H . R. Luard, ed ., p . 44 .3 . E .g ., Hexaemeron, British Museum MS Royal 6 .E .V (14 cent .),

fols . 147v-150v ; L . Baur, "Das Licht in der Naturphilosophiedes Robert Grosseteste," in Abhandlungen aus dem Gebieteder Philosophic and ihrer Geschichte. Eine Festgabe zum 70.Geburtstag Georg Freiherrn von Herding (Freiburg im Breisgau,1913), pp . 41-55 .

4 . De libero arbitrio, caps. 8 and 10, in L . Baur, Die philo-sophischen Werke des Robert Grosseteste, pp . 179, 202 .

5 . Epistolae, pp . 360, 364, 389 .6 . For the basic work on this question, see Baur, Die philo-

sophischen Werke; and S . H . Thomson, The Writings of RobertGrosseteste-with the revisions by Callus, "The Oxford Careerof Robert Grossetest," Robert Grosseteste; A. C. Crombie,Robert Grosseteste and the Origins of Experimental Science (1953,1971) ; and R . C . Dales, "Robert Grosseteste's Scientific Works,"Commentarius in viii libros .

7 . From William of Alnwick, as first noticed by A . Pelzer. SeeCallus, "The Oxford Career of Robert Grosseteste," pp . 45-47.

8 . Giraldus Cambrensis, Opera, J . S . Brewer, ed ., I (London, 1861),249 .

9 . See R. C . Dales, "The Authorship of the Questio de fluxu etrefluxu marls Attributed to Robert Grosseteste," in Speculum,37 (1962), 582-588 .

10 . See the e d . by Dales . Grosseteste wrote probably about 1230a summary of Aristotle's views in his Summa super octo librosphysicorum Aristotelis.

11 . Commentarius in viii libros physicorum Aristotelis, lib . 1, Dales,ed ., pp . 3-4.

12 . Commentaria in libros posteriorum Aristotelis, 1, 12 (1494), fols .llr-12r .

13 . Ibid., 1, 8, fol . 8r .14 . Ibid., II, 4, fol . 29v .15 . De lineis, angulis et figuris, in Baur, Die philosophischen Werke,

pp. 59-60.16 . De natura locorum, ibid., pp . 65-66 .17. De colore, ibid., pp . 78-79 .18 . De iride, ibid., p . 73. See L. Baur, Die Philosophic des Robert

Grosseteste, pp. 117-118 ; Crombie, Robert Grosseteste (1971),pp. 117-124 .

19. De iride, in Baur, Die philosophischen Werke, p . 74 .20. Ibid., p . 75 .21 . Ibid., pp . 74-75 .22 . Ibid., p . 75 .23 . Compotus, R. Steele, ed ., pp . 215, 259 .24 . See Crombie, Robert Grosseteste (1971) ; A . Pacchi, "Ruggero

Bacone e Roberto Grossetesta in un inedito hobbesiano del1634," in Rivista critica di storiadellafilosofia, 20 (1965), 499-502 ;and Convenzione e ipotesi nellaformazione dellafilosofia naturaledi Thomas Hobbes (Florence, 1965) .

BIBLIOGRAPHY

I. ORIGINAL WORKS . The earliest-dated printed ed . ofa work by Grosseteste is Commentaria in libros posteriorumAristotelis (Venice, 1494 ; 8th ed ., 1552) . It was followedby his Summa super octo libros physicorum Aristotelis(Venice, 1498 ; 9th ed ., 1637) ; Libellus de phisicis lineisangulis et figuris per quas omnes actiones naturales com-

GROSSMANN

plentur (Nuremburg, 1503) ; De sphaera, pub. a s Sphaeraecompendium (Venice, 1508 ; 5th ed ., 153 1) ; and Compotuscorrectorius (Venice, 1518) . His Opuscula (Venice, 1514 ;London, 1690) includes De artibus liberalibus, De genera-tione sonorum, De calore solis, De generatione stellarum,De colore, De impressionibus elementorum, De motucorporali, De finitate motus et temporis (appearing first asthe concluding section of his commentary on the Physics),De lineis, angulis et figuris, De natura locorum, De luce,De motu supercaelestium, and De differentiis localibus . Allthese essays, with De sphaera and the hitherto imprintedDe cometis, De impressionibus aeris and De iride, werepublished by L . Baur in Die philosophischen Werke desRobert Grosseteste (see below). For further modern textssee Canon in Kalendarium, ed. by A. Lindhagen as "DieNeumondtafel des Robertus Lincolniensis," in Archiv formatematik, astronomi och fysik (Uppsala), 11, no. 2 (1916) ;Compotus, factus ad correctionem communis kalendariinostri, R. Steele, ed ., in Roger Bacon, Opera hactenus inedita,VI (Oxford, 1926), 212 If. ; S . H. Thomson, "The Text ofGrosseteste's De cometis," in Isis, 19 (1933), 19-25 ; and"Grosseteste's Questio de calore, de cometis and De opera-cionibussolis," in Medievaliaethumanistica, 11 (1957),34-43 ;Commentarius in viii libros physicorum Aristotelis . . ., R. C.Dales, ed. (Boulder, Colo ., 1963) ; and R. C . Dales, "The Textof Robert Grosseteste's Questio defluxu et refluxu marls withan English Translation," in Isis, 57 (1966), 455-474. See alsoRoberti Grosseteste episcopi quondam Lincolniensis epistolae,H. R. Luard, ed . (London, 1861) .

11 . SECONDARY LITERATURE . For the fundamental workof identifying and listing Grosseteste's writings see L . Baur,Die philosophischen Werke des Robert Grosseteste, Bishopvon Lincoln, vol . IX of Beitrage zur Geschichte der Philo-sophie des Mittelalters (Munster, 1912) ; and S. H .Thomson, The Writings of Robert Grosseteste Bishop ofLincoln 1235-1253 (Cambridge, 1940) . For further discus-sions of his scientific writings with references to additionalitems, see D. A. Callus, "The Oxford Career of RobertGrosseteste," in Oxoniensia, 10 (1945), 42-72 ; D . A . Callus,ed ., Robert Grosseteste, Scholar and Bishop (Oxford, 1955) ;A. C. Crombie, Robert Grosseteste and the Origins of Ex-perimental Science, 1100-1700 (Oxford, 1953 ; 3rd ed ., 1971)and the comprehensive bibliography therein; and R. C .Dales, "Robert Grosseteste's Scientific Works," in Isis, 52(1961), 381-402. The basic modern biography is still F . S .Stevenson, Robert Grosseteste, Bishop of Lincoln (London,1899), while Callus, Robert Grosseteste, judiciously sumsup more recent scholarship. The pioneering account of hisscientific thought is L. Baur, Die Philosophie des RobertGrosseteste, Bischofs von Lincoln, XVIII, nos. 4-6 of Beitragezur Geschichte der Philosophie des Mittelalters (Munster,1917) .

A. C. CROMBIE

GROSSMANN, ERNST A. F. W. (b. Rothenburg,near, Bremen, Germany, 16 February 1863 ; d.Munich, Germany, 17 March 1933), astronomy.

Grossmann began to study astronomy in 1884 at

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Gottingen, where he took his doctorate underA. C. W. Schur and Leopold Ambronn in 1891 . Hewas assistant at the Gottingen observatory from 1891to 1896, at Moritz Kuffner's observatory in Viennafrom 1896 to 1898, at the Leipzig observatory from1898 to 1902, and at the Kiel observatory from 1902to 1905 . In 1905 he became observer at Munich,where he lived for the rest of his life . He retired in1928 .Grossmann was an enthusiastic and important

worker with meridian instruments . All of his workwas devoted to questions concerning fundamentalastrometric measurements . After examining system-atic errors in measurements of double stars in hisdissertation, he made careful observations with themeridian circles of all the observatories where heworked . One main area of his research was the theoryof atmospheric refraction ; his very important exami-nation of existing observations resulted in a value forthe constant of refraction of 60.15", which is still used .Grossmann's observations of fundamental right

ascensions near the celestial pole indicated clearlythat the values adopted at that time were affectedby systematic errors . Although his attempts to mea-sure stellar parallaxes by a meridian circle were un-successful, they convinced astronomers that the pho-tographic method is better . In 1921 he showed thatexisting observations of the planet Mercury were notsufficiently accurate to permit determination of areliable value of the relativistic motion of its peri-helion. It was more than twenty years later that anew comprehensive discussion of all observations ofMercury made between 1765 and 1937, which wasundertaken by the U .S. Naval Observatory atWashington, showed convincingly that the observedvalue of the motion of perihelion was in agreementwith the theory of relativity .

BIBLIOGRAPHY

Grossmann's major works are "Untersuchungen uber dieastronomische Refraktion," in Abhandlungen der K.Bayerischen Akademie der Wissenschaften, Math.-phys . Kl .,28, no. 9 (1917), 1-72 ; "Die Bewegung des Merkurperihelsnach den Arbeiten Newcombs," in AstronomischeNachrichten, 214 (1921), 41-54 ; and "Parallaxenbestim-mungen am Meridiankreise," in Neue Annalen der K.Sternwarte in Miinchen, 5, no. 1 (1926), 1-173 .

There is no secondary literature .

F. SCHMEIDLER

GROSSMANN, MARCEL (b. Budapest, Hungary, 9April 1878; d. Zurich, Switzerland, 7 September1936), mathematics.