Archive for History of Exact Sciences

, Volume 68, Issue 2, pp 137–178 | Cite as

Thomas Harriot’s optics, between experiment and imagination: the case of Mr Bulkeley’s glass

  • Robert GouldingEmail author


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.


Refraction Spherical Mirror Concave Mirror Glass Ball British Library 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



Earlier versions of parts of this article were presented at the Temper of Evidence conference at Caltech, and at the Durham Thomas Harriot Seminar, and also at the History and Philosophy of Science Seminar at Indiana University, Bloomington, and the Fellows’ Seminar at the Newberry Library, Chicago; suggestions and criticisms at all of those venues have improved this article. I am grateful to the National Endowment for the Humanities and the American Council of Learned Societies for funding the research leave during which this article was completed, and to the Newberry Library as the host of my NEH residential Fellowship. The British Library and the Oslo University Library generously allowed the images in this article to be reproduced.


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Authors and Affiliations

  1. 1.Program in History and Philosophy of Science & Program of Liberal StudiesUniversity of Notre DameNotre DameUSA

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