Some time in the late 1590s, the Welsh amateur mathematician John Bulkeley wrote to Thomas Harriot asking his opinion about the properties of a truly gargantuan (but totally imaginary) plano-spherical convex lens, 48 feet in diameter. While Bulkeley’s original letter is lost, Harriot devoted several pages to the optical properties of “Mr Bulkeley his Glasse” in his optical papers (now in British Library MS Add. 6789), paying particular attention to the place of its burning point. Harriot’s calculational methods in these (...) papers are almost unique in Harriot’s optical remains, in that he uses both the sine law of refraction and interpolation from Witelo’s refraction tables in order to analyze the passage of light through the glass. For this and other reasons, it is very likely that Harriot wrote his papers on Bulkeley’s glass very shortly after his discovery of the law and while still working closely with Witelo’s great Optics; the papers represent, perhaps, his very first application of the law. His and Bulkeley’s interest in this giant glass conform to a long English tradition of curiosity about the optical and burning properties of large glasses, which grew more intense in late sixteenth-century England. In particular, Thomas Digges’s bold and widely known assertions about his father’s glasses that could see things several miles distant and could burn objects a half-mile or further away may have attracted Harriot and Bulkeley’s skeptical attention; for Harriot’s analysis of the burning distance and the intensity of Bulkeley’s fantastic lens, it shows that Digges’s claims could never have been true about any real lens (and this, I propose, was what Bulkeley had asked about in his original letter to Harriot). There was also a deeper, mathematical relevance to the problem that may have caught Harriot’s attention. His most recent source on refraction—Giambattista della Porta’s De refractione of 1593—identified a mathematical flaw in Witelo’s cursory suggestion about the optics of a lens (the only place that lenses appear, however fleetingly, in the writings of the thirteenth-century Perspectivist authors). In his early notes on optics, in a copy of Witelo’s optics, Harriot highlighted Witelo’s remarks on the lens and della Porta’s criticism (which he found unsatisfactory). The most significant problem with Witelo’s theorem would disappear as the radius of curvature of the lens approached infinity. Bulkeley’s gigantic glass, then, may have provided Harriot an opportunity to test out Witelo’s claims about a plano-spherical glass, at a time when he was still intensely concerned with the problems and methods of the Perspectivist school. (shrink)

This paper aims to show that the seventeenth-century conception of mechanics as the science of particles in motion founded on universal laws of motion owes much to the employment of a new conceptual resource – the physics of motion developed within optics. The optical analysis of reflection was dynamically interpreted through the mechanical analogy of rebound. The kinematical and dynamical principles so employed became directly applicable to natural phenomena after the eventual transformation of light's ontological status from that of an (...) Aristotelian ‘quality’ to a corpuscular phenomenon, engendered by the rise of atomism during the first half of the seventeenth century. The mechanization of light led to a conceptual shift from the analogical employment of dynamical principles in the physical interpretation of reflection to the mechanical generalization of optical principles – the direct application of kinematical and dynamical principles of reflection to mechanical collisions. This first part of the paper traces out the first conceptual shift from Aristotle's original analogy of reflection as rebound to its full concretization. A second part will trace out the second conceptual shift, from the full concretization of this analogy to the axiomatization of already generalized kinematical and dynamical principles of reflection into laws of nature and of motion. (shrink)