Osiris Volume 11 issue 1954 [doi 10.2307%2F301673] Carl B. Boyer -- Robert Grosseteste on the Rainbow.pdf

Robert Grosseteste on the RainbowAuthor(s): Carl B. BoyerSource: Osiris, Vol. 11 (1954), pp. 247-258Published by: The University of Chicago Press on behalf of The History of Science SocietyStable URL: http://www.jstor.org/stable/301673 .Accessed: 15/11/2014 14:33

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Robert Grosseteste on the Rainbow Historians and scientists in i8I4 were startled by the dis-

closure (i) that the Cartesian geometrical explanation of the rainbow had been anticipated, in all but its quantitative aspect, by more than three hundred years. The achievement of THEODORIC OF FREIBERG in giving (some time between I304 and I3 I) the correct explanation of both the primary and secondary bows has been justly acclaimed as one of the greatest of medieval contribu- tions to physical science; but the very magnitude of his accomplish- ment has effectually overshadowed theories of the rainbow proposed during the preceding century, the high point of scholasticism. For this reason it is desirable to call attention to views on the rainbow which were held just before the correct theory was proposed.

Scientific explanations of the rainbow appear to go back at least as far as the time of PERICLES (490-429 B.C.). To his tutor, ANAXAGORAS (c. 500-428), is ascribed the view that the rainbow is caused by the incidence of rays of the sun upon a round and hollow cloud from which they are reflected to the eye of the observer (2). This plausible view underwent numerous changes, even in antiquity; but the reflection of solar rays remained the basis for all theories of the rainbow before the thirteenth century, as well as for most theories prior to i6oo. ARISTOTLE (384-322 B.C.) gave a complicated geometrical explanation which obviated the necessity for a hollow or spherical cloud, but he retained the basic element of reflection from a moist dark cloud (3). His

(i) By GIAMBATISTA VENTURI. See his Commentarj sopra la storia e le teorie dell' ottica, vol. I (only one published, Bologna, I8I4), PP. I49-I80.

(2) OTTO GILBERT, Die meteorologischen Theorien des griechischen Altertums (Leipzig, I907), p. 6o6 f.

(3) A. SAYILI, " The Aristotelian explanation of the rainbow," Isis, XXX (I939) 65-83; T. L. HEATH, Mathematics in Aristotle (Oxford, I949); FR. POSKE, " Die Erklarung des Regenbogens bei Aristoteles," Zeitschrift fur Mathematik und Physik, Historisch-literarische Abteilung, XXVIII (I883), I34-I38.


248 CARL B. BOYER

elaborately developed color theory, based apparently upon earlier ideas of ANAXIMENES, attributed the hues of the rainbow (which he held to be three in number) to the mixing of the brightness of the sun's rays with the darkness of the moist cloud. POSIDONIUS (c. I30-50 B.C.) and SENECA (c. 3 B.C.-65 A.D.) questioned certain elements of the Aristotelian theory, but they were in agreement that the rainbow is in some way caused by reflection from a cloud as from a speculum (i).

The early medieval period added nothing essentially new to the physical theory of the rainbow. ISIDORE OF SEVILLE (c. 560-636) characteristically thought he saw some significance in the similarity of the words " iris " and " aeris "; and, in harmony with the ancient theory of the four elements, he held, against ARISTOTLE, that the bow was quadricolor (5). His views, somewhat similar to SENECA'S, were paraphrased by the Venerable BEDE (677-785) in England (6). More sophisticated theories of the rainbow were proposed a little later by Muslim scholars. AVICENNA (980-Io37) frankly admitted to being a peripatetic, but he departed nevertheless from the Aristotelian rainbow theory. Independent observ- ation had demonstrated to him that the bow is not formed in the dark cloud but rather in the very thin mist lying between the cloud and the sun or observer. The cloud, he thought, serves simply as the background of this thin substance, much as a quick- silver lining is placed upon the rear surface of the glass in a mirror. AVICENNA would change the place not only of the bow, but also of the color formation, holding the iridescence to be merely a subjective sensation in the eye. The one element of the ancient theories which he retained is the basic phenomenon of reflection. AVICENNA modestly closes with the frank statement, " This is all I know about the rainbow. Further clarification must be sought of others" (7). Among the " others" one would have hoped to include ALHAZEN (t I038), mathematician, physicist, and author of the Treasury of optics. ALHAZEN performed experiments with

(4) JOHN CLARKE, Physical science in the times of Nero. Being a translation of the Quaestiones naturales of Seneca (London, i9io), pp. i6-33.

(5) GUSTAV HELLMANN, Neudrucke von Schriften und Karten fiber Meteorologie und Erdmagnetismus, vol. XV (Berlin, I904), P. I5 of introduction and p. 2 of text.

(6) HELLMANN, Neudrucke, XV, 7- I0. (7) M. HORTEN, " Avicennas Lehre vom Regenbogen nach seinem Werk al

Schifa," Meteorologische Zeitschrift, XXX (19I3), 533-544.


ROBERT GROSSETESTE ON THE RAINBOW 249

a spherical glass globe filled with water, and he also made studies of refraction. It is tantalizing that he failed to associate these with the rainbow and that in his Treasury he fails to mention the bow. From his other writings, however, it is known that he clung to the old Anaxagorean idea of the bow as caused by reflection from a concave cloud (8).

With the opening of the thirteenth century the theory of the rainbow was little advanced over that in the days of SENECA and ARISTOTLE. The situation, however, was to change radically during the next hundred years, in both the Latin and Arabic civilizations; and in this movement GROSSETESTE (C. II75-I253) occupies a key position. Among ROBERT'S numerous works is one with the title, De iride seu de iride et speculo (9), written probably before I225 (io). This opens with the inauspicious assertion that the rainbow belongs both to physics, which tells " what," and to perspective, which tells " because of what." Inasmuch as ARISTOTLE had given only the physical quiddity of the situation, ROBERT GROSSETESTE boasts that he himself will furnish the propter quid. Proceeding traditionally, he outlines the usual three divisions of perspective: direct vision (optics), reflection (catoptrics) and refraction (dioptrics). The last of the three he holds to be much more difficult than the others and, by nature of its profundity, more marvelous. Through it the most distant things are made to appear near and small things appear large, so that the smallest letters can be read at a great distance. [This almost fifty years before BACON'S Opus majus !] In reflection the angle of incidence is in all cases equal to the angle of reflection; but in refraction the phenomena depend upon the angle at which the object is seen, the position and order of the rays, and upon the distance. By refraction the largest parts can be made to appear smallest, and those farthest away are made easily visible. And it is to this third part of perspective that the science of the rainbow belongs (i i).

(8) JOSEPH WORSCHMIDT, " Die Theorie des Regenbogens und des Halo bei Ibn al Haitham und bei Dietrich von Freiberg," Meteorologische Zeitschrift, XXXI (I9I4), 484-487.

(g) Edited by LUDWIG BAUR in Beitrdge zur Geschichte der Philosophie des Mittelalters, IX (Miinster i.W., I9I2), Texte, pp. 72-78.

(IO) JOSIAH C. RUSSELL, " Phases of Grosseteste's intellectual life," The Harvard Theological Review, XLIII (1950), 93-Ii6.

(I I) Ibid., p. 75. Italics are mine.


250 CARL B. BOYER

In these words GROSSETESTE brings out, possibly for the first time, the association of the bow with the all-important phenomenon of refraction. Yet his contribution seems to have been overlooked by historians of physics, and it has become traditional to ascribe to WITELO-writing probably in I269, sixteen years after GROSSE- TESTE had died-the first use of refraction in explaining the rainbow (I2).

In presenting his novel theory GROSSETESTE first refutes the traditional idea that the rainbow is due to reflection of the sun's rays upon the surface of a cloud as from a concave or convex mirror. Were this the case, he held, the altitude of the bow would vary directly-rather than inversely, as is the case-with the altitude of the sun. Then he asserts that the bow is due instead to the refraction of the rays within a convex moist cloud. The details of his theory are, in the light of modern views, singular indeed. The interior of the cloud he holds to be concave, " according to the nature of light and heavy." As the moisture of the cloud descends from the concavity, it forms a convex pyramid or cone in which the portion near the earth is more condensed than is the higher part. There are, therefore, four transparent media through which the sun's rays pass-the pure air surrounding the cloud, the cloud itself, the higher (hence rarer) moisture coming from the cloud, and the lower and more dense moisture in the pyramidal cone. Inasmuch as the sun's rays are refracted upon passing from one medium to the next, there must be three refractions in all. Refraction had indeed entered with a vengeance into the theory of the rainbow. But unfortunately GROSSETESTE seems to have left little room for reflection, which also is an essential ingredient in the modern theory.

It is not clear whether ROBERT GROSSETESTE had worked out an actual geometrical picture of his theory. He says that the bow is not a complete circle but a figure similar to the curve on the surface of a circular cone, the larger half of which falls upon

(I2) See J. C. POGGENDORFF, Geschichte der Physik (Leipzig, I879), p. 92; FERDINAND ROSENBERGER, Geschichte der Physik (3 vols., Braunschweig, I882- I890), I, I03; FLORIAN CAJORI, History of Physics (New York, i906), p. 26. E. GERLAND, Geschichte der Physik (MUnchen & Berlin, I9I3), p. i98 f.; EDMUND HOPPE, Histoire de la physique (transl. by HENRI BESSON, Paris, I928), p. 3i8; See also GEORGE SARTON, Introduction to the history of science (3 vols. in 5, Baltimore, I927-1948), II, 76i.


ROBERT GROSSETESTE ON THE RAINBOW 25 1

the earth and the smaller half upon the cloud. Hence, the higher the sun, the smaller the bow; and this, as ARISTOTLE had known, explains why no bow is seen about noon. GROSSETESTE appears to be concerned primarily with the shape of the bow; he does not explicitly state that the element of refraction had been adduced by him in order to explain the formation of colors. There is a hint, however, that Robert may indeed have associated color and refraction, for he says that the variety of hues is due to the ad- mixture of light with the diaphanous media. Color depends not only upon the purity or impurity of the medium, but also upon the clarity and obscurity of the light, and upon the multitude or paucity of the rays. These six conditions, he held, generate all of the colors; but he did not here go into detail.

It must be admitted that GROSSETESTE'S theory of the rainbow is crude and fantastic, but it should also be recalled that this is the first attempt to bring refraction into the picture. His treatise on the rainbow undoubtedly was widely read during the thirteenth and fourteenth centuries, for half a dozen manuscript copies of the work are extant in libraries at Madrid, Oxford, Florence, Groningen, Prague, and the Vatican (I3).

The account of the rainbow given by ROBERT GROSSETESTE stands in marked contrast to that of ALBERTUS MAGNUS (t I28o), both in its brevity and its originality. The voluminous De meteoris libri IV of ALBERT includes twenty-nine chapters on the rainbow and halo (14). Much of this material consists of comments on opinions held by others from HESIOD to his own times. He was particularly intrigued by metaphorical allusions to the rainbow in ancient literature which, he concluded, showed that " philo- sophers, both natural and perspective, as well as poets, agree in this, that the rainbow is an image of the sun on a aqueous cloud." ALBERT suggests some modifications in previous theory, but he holds that these are in agreement with the opinion of ARISTOTLE. Instead of a spherical cloud he suggests a pyramid of vapor, with base on the earth and vertex in the cloud, and having the heavier parts near the base. He then goes on to postulate four transparent

( 3) S. HARRISON THOMSON, The Writings of Robert Grosseteste, Bishop of Lincoln, I235-I253 (Cambridge University Press, I940), P. I05.

(14) Opera (ed. by PETER JAMMY, 2I vols., Lugduni, i651), vol. II, De meteoris, III, Tractatus IV.


252 CARL B. BOYER

media: a thick black cloud; a subtle distillate of minute drops in the upper part of the pyramid just beneath the concave cloud; heavier and more coagulated moisture in the lower part of the pyramid; and, finally, air mixed in with the whole. In the reflection of the sunlight by these media, the rays are bent, the refraction being at the extremities of the watery pyramid, just as when a globe is cut somewhat above the middle. Rays at this extremity are multiplied and generate the rainbow; and those near the top, being farther from the dense portion, are red. The semicircular form is due to the fact that a cone of rays from the sun strikes the round pyramid of vapor. Only half of the circle is seen because the other rays are extinguished by the heavy material in the pyramid. One can not resist the temptation to see here the influence of ROBERT GROSSETESTE, a friend of the Franciscans, although ALBERTUS MAGNUS, a Dominican, does not refer to him. ALBERT's studies at Paris may well have included ROBERT'S De iride; but if so, the introduction of refraction seems not to have made a deep impression. His use of the word refractio is not decisive, for Aristotelian works used the term as synonymous with reflection. Moreover, neither the form of the bow nor its colors are attributed to this phenomenon. The circularity is the result of the intersection of two cones, and the colors are due to the mixture of light and dampness. Except for the cone or pyramid of vapor, ALBERT'S exposition is Aristotelian, whereas ROBERT'S indicated a marked innovation.

It is certain that GROSSETESTE'S theory of multiple refractions was familiar to ROGER BACON (C. I214-I292), who cites it only to refute it (I5). Exhorbitant claims have been made for BACON'S work on the rainbow, and one author (i6) goes so far as to assert that BACON " represented exactly the path of the luminous ray." It is difficult to see, however, in what respect BACON's lengthy explanation in the Opus majus (composed I266-I267) is better than, or even as good as, that of his teacher, GROSSETESTE. BACON does indeed mention the all-important word " refraction " in this

(I5) In view of this, it is odd that the De iride has been ascribed also to BACON, although it appears now that there can be no doubt of GROSSETESTE's authorship. See BAUR, " Die philosophischen Werke des Robert Grdsseteste Bischofs von Lincoln," Beitrige zur Geschichte des Philosophie der Mittelalters, IX, (Milnster i. W., 1912), p. 83.

(i 6) HOPPE, 10c. cit.



connection, but the reference is very casual: " The disappearance of the aqueous vapor cannot take place through the rainbow except by reason of the solar rays that cause it, for through various reflections and refractions an infinite number of rays are assembled, and the assemblage of the rays is the cause of the resolution and disappearance of the waters, and therefore, the rainbow is produced by multiple reflections. For the rays cannot assemble except through refraction and reflection" (I7). The word " refraction" must here be used very loosely, for later (i8) one reads that " the observer alone produces the bow, nor is there anything present except reflection." Certainly he did not look upon the colors of the bow as due to refraction, for he repeatedly asserted that, unlike the colors seen when light rays pass through a glass prism, those of the rainbow are purely subjective-an appearance only, and not a reality. Nor, apparently, did BACON think that refraction had anything to do with the shape of the bow, for he goes on to say that " they " are in error who hold the bow to be due to refraction. He repeats almost verbatim GROSSETESTE'S explanation in terms of three refractions; but he rejects this theory on the ground that rainbows are seen also in local water sprays, " where there cannot be three refractions." Instead, BACON explains the form of the bow as due to the fact that " all parts must have the same position with respect to the solar ray and the eye... For this occurs only in the position of a circle, as is apparent in the reflections and refractions of a concave mirror and of other mirrors; and therefore there can be four or five circles of the rainbow in the drops from which reflections to the eye are made at angles equal to the angles of incidence, color can be produced in them, and the phenomena of the rainbow appear" (i9). This passage raises the very pertinent question as to whether BACON was indeed using the word " refraction" in the modern sense or whether it was not here synonymous with " reflection," a usage common from ARISTOTLE to KEPLER.

One reads frequently that BACON was ahead of this time, yet his account of the rainbow will strike the modern reader as

( I7) The opus majus of Roger Bacon (trans. by ROBERT BELLE BURKE, 2 vols., Philadelphia, I928), I, 50-5I.

(i8) Ibid., II, 6o6. (iv) Ibid., II, 6io.


254 CARL B. BOYER

thoroughly " medieval" in the popular sense of the word. The material cause of the bow he took to be the cloud; the effective cause was the rays of the sun; and the final cause was the dissipation of moist vapors which otherwise might cause a renewal of the flood, contrary to God's promise. In spite of his vaunted mathe- matical ability, numerology is a decisive factor in BACON's assertion that there are five colors in the bow-" For the number five is better than all other numbers... Because the number five distinguishes things more definitely and better, nature for this reason rather intends that there shall be five colors. Therefore these five colors are in the rainbow, rather than other colors, in accordance with the general arrangement of nature, which carries into effect and purposes that which is better." In line with his idea that the hues of the rainbow, unlike prismatic colors, are optical illusions, BACON associated the five colors of the bow with the five bodies in the eye (three humors and two coatings).

Retrogressive though his theory was in many respects, there is an important quantitative aspect of BACON's work on the rainbow which warrants admiration. Having advised an experimenter interested in the formation of the bow to study various modes of color formation, BACON suggests that he then take " the required instrument " and find the altitudes of the sun and the rainbow. Ever since the days of ARISTOTLE it had been known that the higher the sun is, the lower is the bow; but BACON gave a remarkably accurate value-42?-for the maximum elevation of the rainbow. BACON does not say that the oft-repeated value of 420 is the apparant radius of the bow, but this is implied in his statement that all parts of the bow must have the same position with respect to the solar rays and the eye. This is possibly the earliest extant measure of the rainbow, and no more accurate value for the primary bow was given until the days of DESCARTES and NEWTON.

If there is room for doubt as to BACON'S use of refraction in the theory of the rainbow, there can be none when it comes to his contemporary, the Polish physicist and philosopher, WITELO (born c. I230). He was educated at Paris, Padua, and Viterbo, and hence may well have known of the work of GROSSETESTE, if not also of that of BACON. About i269 (2o) he wrote a treatise

(zo) SARTON, Op. Cit., II (), IO27, places the date of its composition as between 1270 and I278.



on Optics which is derived so largely from the Treasury of IBN AL-HAITHAM as to earn for WITELO the soubriquet, "ALHAZEN' S ape "; but the work closes with a tediously long section, a score of folio pages, devoted to the rainbow in which the author shows distinct independence of thought. Here one finds, unequivocally expressed possibly for the first time, a theory based upon both reflection and refraction. WITELO compared the colors of the rainbow with those seen when a round glass vase full of water is exposed to the light of the sun which undergoes various refractions as the rays pass from air to glass, then glass to water, then water to glass, and finally from glass to air again. But, he adds cautiously, " Yet these [prismatic] colors are not truly like the colors of the rainbow, for the former are seen directly while the latter are seen by reflection " (2 I). One can not help wondering if these words were not suggested by GROSSETESTE'S multiple refractions and BACON's distinction between prismatic and rainbow colors. In any case, WITELO'S words seem to have a more modern ring to them, even though one is disappointed by the vagueness of his over-all picture of the rainbow.

WITELO, like ROBERT OF LINCOLN, first refuted the older view of the rainbow as resulting only from reflection. Were this the case, he held, the bow should not move from side to side as the observer moves laterally. Instead, the bow is caused by an aggregation of reflected and refracted rays. One should not read too much into these words, for WITELO apparently did not have in mind the modern idea of rays which are refracted, then reflected, and once more refracted before reaching the eye. In his theory some rays were reflected only, others underwent refraction. Clouds are a mixture of dry and moist vapors. Light does not penetrate the dry vapors, and hence some rays are reflected from the surface of the cloud; other rays penetrate the moist vapors and are refracted within the dense portions of the cloud. It is a peculiar combination of these rays, he thought, which causes the bow.

Ever since ancient Greek and Roman days there had been conflicting and confused ideas as to the relationship between the raindrops and the cloud. ARISTOTLE had regarded the dewy cloud

(zI) Vitellonis filii Thuringorum et Polonorum opticae (Basileae, 1572), p. 474. This is the well-known Risner edition published with ALHAZEN'S Opticae thesaurus.

17


256 CARL B. BOYER

as a multitude of tiny drops which reflected the solar rays; but the droplets were too small to serve as mirrors in which images are seen, and so he had based his geometrical study upon the aggregation of drops. One of the moot questions since his day had been the way in which the individual drops fitted into the scheme as a whole. GROSSETESTE disregarded the problem of atom- icity in a raincloud, treating his diaphanous media as continua. WITELO raised the old question once more, although he gave no satisfactory answer. Between the continuous aqueous vapor and the discrete drops of rain water there is a dewy transition stage in which the rarer parts of the vapor are beginning to be round, to condense, and to take on a downward motion. These dewy particles are somewhat like little mirrors (in the sense of ARISTOTLE) in which color, but not form, is presented; and, as BACON had asserted, only those rays are reflected which make the proper angle. The colors of the bow result from the weakening of light by the mixture of dry and moist vapors. At one point WITELO came close to the true approach to a study of the rainbow, for he noted that if a round glass vase full of water is exposed to the sun, colors similar to those of the rainbow are seen. These are caused by the four refractions which light undergoes as it passes from air into glass, then into water, then into glass again, and finally out into the air once more. But then WITELO makes the disillusioning comment that these colors are not truly those of the rainbow, for the former are seen directly whereas the latter are seen by reflection. Evidently the role of refraction in the rainbow was quite a minor one, although to refraction within the moist vapor WITELO ascribed the putative constancy in the obliquity of the plane of the rainbow to the horizontal surface.

With the exception of WITELO'S work, the most popular optical treatise of the thirteenth century was the Perspectiva communis (22) of JOHN PECKHAM (t I292), Archbishop of Canterbury. This is a much smaller book than WITELO'S Optics, and hence correspondingly less space is devoted to the rainbow. PECKHAM'S theory is a combination of ideas expressed by GROSSETESTE, BACON, and WITELO. The rainbow, PECKHAM says, is generated by the

(22) A copy of the edition published by PETREIJS at Nuremberg in 1542 is available at Columbia University.



reflection of rays in spherical drops which serve as mirrors. How- ever, part of the cause lies in rays which penetrate the water in the dewy vapor, converge to a point (as in refraction), then diverge again into a pyramid the middle of which falls on a cloud. The semicircular impression thus formed is then reflected to the observer. Hence the circularity of the bow is due to the cloud rather than the rays. The diversity of colors arises partly from the cloud and partly from variations in the light rays. The rain descends to a center, forming a round cone with gradually in- creasing density; and hence the nobler colors are along the higher or exterior part of the bow. The concourse of rays reflected from the cloud with direct rays brings about an attenuation of vapors; and hence the formation of the rainbow, which accompanies the consumption of the substance of rain, precludes a cataclysm. The rainbow belongs to all three parts of perspective, for it is formed by direct, reflected, and refracted rays.

If, as is commonly believed, the medieval period was an age of excessive reliance upon authority, then the study of the rainbow in the thirteenth century must be regarded as quite exceptional. From GROSSETESTE on there was an earnest criticism of earlier writers, ARISTOTLE not excepted; and the search for new and improved explanations was carried out with remarkable enthusiasm. Even ROGER BACON, who was so prone to criticize the credulity of his contemporaries, was compelled to admit that ROBERT GROSSETESTE, in treating of scientific matters, neglected the books of ARISTOTLE for his own experiments (23); and much of his spirit seems to have persisted after ROBERT's death. One must admit that the efforts of the century failed to effect a satisfactory solution of the rainbow problem; but this failure should not obscure the fact that an important contribution was made the introduction of the essential idea that refraction is necessary for the explanation of the rainbow. What one misses most in the explanations of the time is a clear-cut geometrization of dioptrics comparable to that of optics and catoptrics. Lack of a mathematically precise law of refraction may have discouraged attempts in this direction,

(23) F. S. STEVENSON, Robert Grosseteste, Bishop of Lincoln. A contribution to the religious, political and intellectual history of the thirteenth century (London, i899); also LYNN THORNDIKE, History of magic and experimental science (6 vols,. New York, l929-1941), II, 436-453.


258 CARL B. BOYER

but, as the next century was to prove, a correct rainbow theory nevertheless lay entirely within their power. GROSSETESTE had, in fact, proposed in De iride a crude law equivalent to the statement that the angle of refraction is half the angle of incidence; and in another little treatise, De fractionibus et reflexionibus radiorum (published at Nuremberg in I 503 as Libellus de phisicis lineis angulis et figuris per quas omnes acciones naturales complentur) (24), he sought to explain the laws of reflection and refraction in terms of lengths of lines and a vague sort of principle of least action. But he did not associate such ideas with a quantitative geometrical study of the rainbow. Had he done so, he might have come close to anti- cipating the work of DESCARTES. BACON and WITELO measured the bow, but they did not study it with the precision afforded by Euclidean geometry. Thus every scholar of the century missed the key to the solution which was discovered shortly afterward by THEODORIC (and simultaneously also by the Persian mathematician QUTB AL-DIN)-passage of light rays though a large spherical globe of water as through a magnified raindrop. The synthetic view of the cloud as a whole had to give way to an analysis of the behavior of light in the smallest component; but such an analysis might have been fruitless had not the thirteenth century in general, and GROSSETESTE in particular, introduced the magical word refraction (25).

(Brooklyn College CARL B. BOYER. Brooklyn, N.Y.).

(24) Bibliotheca Mathematica (3), I (1900) 55-59, II (1901) 443-444. (25) Since this article was written there has appeared a book which reduces it

largely to a work of supererogation. A. C. Crombie's volume on Robert Grosseteste and the origins of experimental science ii00-I700 (Oxford, i953), includes a full account of theories of the rainbow in the thirteenth century, together with the influence of these upon later writers. The reader therefore is referred for further information to this scholarly treatise.


Article Contentsp. [247]p. 248p. 249p. 250p. 251p. 252p. 253p. 254p. 255p. 256p. 257p. 258

Issue Table of ContentsOsiris, Vol. 11 (1954), pp. i-iv+1-536Front Matter [pp. i-iii]Preface to Osiris XI [pp. 1-2]Lynn Thorndike [pp. 4-22]The De Occultis Naturae Attributed to Albertus Magnus [pp. 23-39]La contribution de la Grande Bretagne au dveloppement des Sciences Mathmatiques depuis un Sicle[pp. 40-49]Abraham Savasorda and His Algorism: A Study in Early European Logistic [pp. 50-64]The Scriptural Geologists: An Episode in the History of Opinion [pp. 65-86]Experiments with Truth by Faraday, Darwin and Gandhi [pp. 87-107]Reminiscences of a Pioneer [pp. 108-118]A Turning Point in Freud's Life: Zur Auffassung der Aphasien [pp. 119-126]John Floyer and Chinese Medicine [pp. 127-156]Search for the Germ of Wegener's Concept of Continental Drift [pp. 157-167]Petrarch's Views on the Individual and His Society [pp. 168-198]Louis Le Roy on Science and Progress (1575) [pp. 199-210]The Discovery of the Element Carbon [pp. 211-220]John of Gmunden and Campanus of Novara [pp. 221-246]Robert Grosseteste on the Rainbow [pp. 247-258]An Anonymous Latin Herbal in the Pierpont Morgan Library [pp. 259-266]The Counter-Earth [pp. 267-294]The De curvis superficiebus Archimenidis: A Medieval Commentary of Johannes de Tinemue on Book I of the De sphaera et cylindro of Archimedes [pp. 295-346]Some Additional Propositions of the De Curvis Superficiebus Archimenidis [pp. 347-358]A Medieval Latin Translation of a Short Arabic Tract on the Hyperbola [pp. 359-364+366-385]The Natural History of Metals and Minerals in the Universe of Milton's Paradise Lost [pp. 386-421]Forces and Substances of Life [pp. 422-437]Science and Its Function in Early Nineteenth Century England [pp. 438-454]Manuscripts of Engelbert of Admont (Chiefly in Austrian and German Libraries) [pp. 455-485]Matthaeus Zeisius, Author of a Tract on the Comet of 1577 [pp. 486-503]Sebastian Muenster (1489-1552): A Sixteenth-Century Ethnographer [pp. 504-529]Back Matter [pp. 530-536]

Osiris Volume 11 issue 1954 [doi 10.2307%2F301673] Carl B. Boyer -- Robert Grosseteste on the Rainbow.pdf

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