Physico-mathesis de lumine coloribus, et iride, aliisque adnexis libri duo: in quorum Primo afferuntur noua experimenta, et rationes ab ijs deductæ pro substantialitate luminis. In secundo autem dissoluuntur argumenta in primo adducta, & probabiliter sustineri posse docetur sententia Peripatetica de accidentalitate luminis: qua occasione de hactenus incognita luminis diffusione, de reflexionis, refractionis, ac diffractionis modo et causis, de visione, deque speciebus intentionalibus visibilium et audibilium, ac de substantiali magnetis efluuio omnia corpora peruadente, non pauca scitu digna proferuntur, & speciali etiam argumento impugnantur atomistæ.

Bologna: heirs of Vittorio Benacci for Girolamo Bernia, 1665.

First edition, rare, of Grimaldi’s only book, in which he describes his discovery of the diffraction of light, “a new mode of transmission of light [that] contradicts the notion of an exclusively rectilinear passage of light” (DSB). This is perhaps the rarest of all great optical books, especially complete with both title-pages and in such good condition, and marks the first scientific attempt to establish a comprehensive wave theory of light which influenced the researches of Hooke and Newton. “Grimaldi’s concept of light probably originated in his discovery of the new optical phenomenon that he called diffractio. In a series of delicate experiments, he studied the shadow projected on a distant screen by a narrow object when illuminated by sunlight passing through a small hole in a shutter. He observed that the penumbra was larger than implied by the size of the hole and exhibited colored fringes both within and without the geometric shadow. He carefully determined that this phenomenon depended on a new mode of propagation of light, differing from reflection (by the edges of the object), refraction (by some heterogeneous medium), or diffusion (by the air). Grimaldi explained the observed images by analogy with the undulation of the surface of a stream beyond an obstacle, judging that ‘light seem[ed] to be some very fast fluid, sometimes also undulating, and pouring through diaphanous media.’ A visible, macroscopic undulation occurred in the case of diffraction fringes. A much finer, invisible undulation occurred in the light reflected or transmitted by colored bodies, as a consequence of the disturbance of the luminous flow by the minute porous structure of the body … Although Grimaldi seems to have reached this correspondence between color and undulation through the water-stream analogy, he devoted a full section of his treatise to another analogy between the variety of sounds and the variety of colors in nature … he defended the idea of a mechanical vibration transmitted from the sonorous body to the ear through successive elements of the intermediate air. The implied undulations of the air, he went on, reflected the complexity of the vibrations of the source and were thus able to produce the whole range of musical or phonetic sounds. Thanks to the bridging concept to undulation, he compared this diversity of sounds with the diversity of colors acquired by light” (Darrigol, pp. 58-60). “Newton was aware of Grimaldi’s work, but only at second-hand, crediting Honoré Fabri [Dialogi Physici, 1669] as the source of his knowledge on diffraction … By 1686 he came to deny the existence of internal fringes on the basis of experiments. In the Opticks he described and tried to explain only the external fringes, which he never ceased to regard as a sort of refraction” (DSB). ABPC/RBH lists four copies in the last 40 years (one in modern binding, another lacking the second title page).

Provenance: Letterpress title with old inscription and stamp in lower right blank corner (placed over a previous stamp which has been erased).

“Grimaldi’s primary contribution to positive science was the discovery of optical diffraction. A comprehensive treatise on light, the complete descriptive title is A physico-mathematical thesis on light, colors, the rainbow and other related topics in two books, the first of which adduces new experiments and reasons deduced from them in favor of the substantiality of light. In the second, however, the arguments adduced in the first book are refuted and the Peripatetic teaching of the accidentality of light is upheld as probable. The title page also states that he deals with “the previously unknown diffusion of light; the manner and causes of reflection, refraction, and diffraction; vision and the intentional species of visibles and audibles; the substantial effluvium of the magnet, which pervades all bodies; and in a special argument the atomists are attacked.” A final descriptive element appears on the subtitle page preceding book II, where he notes that, in any case, “permanent colors are nothing other than light.” If we take Grimaldi at his word, he is presenting two possible basic theses about the nature of light. It may be substance, or it may be accident, i.e., a quality of some other substance. His personal choice appears in his preface to the work, where he says he would be delighted by a student who would be persuaded that the experiments supporting the substantiality of light have no force and who could confirm better than he ‘the doctrine which we personally embrace and finally sustain in the present opuscule.’ At various places in book I he prescinds from a substantial theory of light in arguing a proposition e.g., prop. 10, which deals with the nature of the propagation of light. His position in book I is thus not always in support of the substantial theory of light. As a philosopher he stands against the certainty of either hypothesis, each called an ‘opinion,’ on the nature of light. He says ultimately that the many experiments of book I, albeit persuasive, ‘do not in any way lead to the substantiality of light’ (II, 2).

“Grimaldi’s position on the substance-accident question is better understood by a look at the whole book and what it deals with. Book I (sixty propositions, 472 pages) devotes the first twenty-seven propositions (229 pages) essentially to the four modes of light, the porous nature of bodies, and the propagation of light. Thereafter book I deals with colors and the rainbow (props. 28-60, 244 pages). The substance accident question is not much debated after prop. 27, nor is it made a necessary basis for the treatment of colors and the rainbow. While books I and II present opposing views on the substantial nature of light, they agree on other major points. In both books Grimaldi opposes any corpuscular theory of light. In both books he is concerned to show color to be nothing more than a modification of light. Color is not the addition of something else to light. Both books agree on the fluid nature of light phenomena. Light may be a fluid substance or the accidents of some other fluid substance(s). Grimaldi expressly chooses the latter version of fluid theory.

“The discussion of diffraction (book I, prop. 1, pp. 1-11) is the basis for introducing a fluid, but not necessarily substantial, view of light. The experiments on diffraction are clear and well described by Grimaldi. He used bright sunlight introduced into a completely darkened room via a hole about 1/60 inch across. The cone of light thus produced was projected to a white screen at an angle so as to form an elliptical image of the sun on the screen. At a distance of ten to twenty feet from the slit he inserted a narrow opaque rod into the cone of light to cast a shadow on the screen. The border of this shadow, he noted, is not clear, and the size of the shadow is far beyond what rectilinear projection would predict. Having demonstrated this, he proceeded to his description of external diffraction bands. These bands are never more than three, and they increase in intensity and in width nearer to the shadow. The series of bands nearest the shadow has a wide central band of white with a narrow violet band nearer the shadow and a narrow red band away from the shadow. Grimaldi warned that there and violet bands must be observed closely to avoid mistaking the series for alternating bands of light and dark. After describing these parallel bands, he turned to examine the effect of varying the shape of the opaque object. In place of the rod he used a step-shaped object to cast a shadow with two rectangular corners. Still describing external bands, he carefully described the curvature of the bands around the outer corner and continuing to follow the shadow border. When the series approaches parallel to the other side of this corner. He noted that as they cross each other the colors “are either augmented intensively or are mixed.” Nothing more about the appearance of these intersecting bands is found in the description.

“In the diffraction experiments he now turned to a description of internal fringes. Here he omitted naming the colors or their order. His diagram shows two pairs of twin contiguous tracks following the border of an L-shaped shadow. These bands are said to appear only in pairs, while the number increases with the width of the obstacle and its distance from the screen. The bands bend around in a semicircle at the end of the L, remaining continuous. At the corner of the L he made a further observation. Here not only do the bands curve around to follow the shadow outline, but a shorter and brighter series of colors appears. He showed these as five feather-shaped fringes radiating from the inside corner of the L and perpendicularly crossing the previously described internal paired tracks of light. The nature of this phenomenon seems to have impressed him as being like the wash of a moving ship.

“The final diffraction experiment allowed a cone of light to pass first through two parallel orifices, the first being 1/60 inch and the second being 1/10 inch in diameter. The distances between the holes and between the screen and second hole are equal, at least twelve feet each. The screen is parallel to the orifices. The screen holds a circle of direct illumination just over 1/5 inch across. The circle is significantly wider than rectilinear propagation allows and the border is colored red in part, blue in part. Neither the width nor order of these colors is given.

“These diffraction experiments showed Grimaldi that a new mode of transmission of light had been discovered and that this mode contradicts the notion of an exclusively rectilinear passage of light. Diffraction thus gave prima facie evidence for a fluid nature of light. The name “diffraction” comes from the loss of uniformity observed in the flow of a stream of water as it “splits apart” around a slender obstacle placed in its path. He discussed other fluid phenomena analogously with light. To explain color and the varieties of color he decided that a “change in agitation” of the luminous flow is responsible. A light ray is conceived like a column of fluid in vibration, but not regular vibration. Lighter colors are said to result from a greater density of rays and darker colors from a lower density” (DSB).

Most of the lines of scientific work pursued by Newton in his mature years were prepared by his youthful interest. The two obvious exceptions were his investiga­tions and speculations about electricity and diffraction. Both caused him immense difficulties, for neither could easily be made to fit dynamical theories … Diffraction forced Newton to abandon Opticks unfinished. Its Book II had ended on a successful note, after Newton had demonstrated to his own satisfaction the homogeneity of reflection and refraction, and of prismatic, reflected and refracted colours. In the third book, no doubt, he planned to bring the phenomena of diffraction into the same picture. Nothing that he understood of it before he began his own experiments gave him reason to fear that his own simple model of ‘exterior refraction’ might prove inadequate or that diffraction colours would prove more recalcitrant than those in thin plates.

“When he at last came to the diffraction experiments described in Opticks, perhaps about the year 1692 … he must have been appalled to realize how much more perplexing the phenomena were, than he had supposed them to be. None of his former notions were appropriate … and Newton was compelled to postulate a repulsive force by which

‘the Hair [diffracting a narrow beam] acts upon the Rays of Light at a good distance in their passing by it. But the Action is strongest on the Rays which pass by at least distances, and grows weaker and weaker accordingly as the Rays pass by at distances greater and greater’ …

“Such late patching could hardly conceal the fact that experiments on diffraction had taught Newton that neither the analogy with refraction nor the dynamical model were adequate to provide a theory of its phenomena, nor able to account for his own carefully measured results. Grimaldi’s discovery of the extension of the shadow beyond the geometric limit was confirmed. So was Hooke’s observation of light penetrating far into the geometric shadow. The ‘three Parallel Fringes or Bands of Colour’d Light’ were not at all as he had formerly imagined them. Because diffraction effects proved so resistant to analysis in terms of the ideas of light and of the interaction between light and matter that Newton had hitherto formed, he cast the remainder of his ideas into the form of enigmatic Queries” (Hall, pp. 21-22).

Grimaldi (1618-63) studied theology and philosophy at Bologna, which brought him a doctorate in 1647. He came under the influence of Giovanni Battista Riccioli (1592–1671), prefect of studies at Bologna. In 1640 Grimaldi conducted experiments on free fall for Riccioli, dropping weights from the Asinelli tower and using a pendulum as timer. He found that the square of the time is proportional to the distance of free fall from rest. Riccioli credited him as being absolutely essential to the completion, in 1651, of Almagestum novum. Grimaldi’s contributions included such measurements as the heights of lunar mountains and the height of clouds. He is responsible for the practice of naming lunar regions after astronomers and physicists. From 1655 to the end of his life his scientific efforts were devoted essentially to the preparation of De lumine; his death came shortly after finishing this work.

Albert, Norton, & Hurtes, Source Book of Ophthalmology 919 (contains “Grimaldi's work on the discovery of the diffraction (Newton's inflexion) of light. Considered a classic in the history of optics, this work makes the first scientific attempt to establish the wave theory”); Macclesfield 943 (lacking the letterpress title-page); BOA Catalogue 1, p. 83; Crawford Library Catalogue 211; DSB V, 544; Jesuit Science in the Age of Galileo 11; Kemp, The Science of Art, p. 285; Krivatsy 5001; Lalande p. 260; Parkinson, Breakthroughs p. 103; Riccardi I, 631 (“celebrated and scarce work”); Sommervogel III, 1833 1. Hall, ‘Beyond the Fringe: Diffraction as Seen by Grimaldi, Fabri, Hooke and Newton,’ Notes and Records of the Royal Society of London, Vol. 44 (1990), pp. 13-23.



4to ((252 x 184 mm)), pp. [xxii] (including the second, letterpress title-page), 535, [16], with title-pages printed in red and black, the first with engraved arms, and numerous woodcut illustrations in text (letter press title and a4 with some light damp staining, a few upper margins with some mild smudging). Contemporary vellum, manuscript lettering to spine, edges sprinkled in red. A fine, unsophisticated copy.

Item #3397

Price: $25,000.00