I. Supplement to a paper “On the theoretical explanation of an apparent new polarity in light."

Abstract

In the Second Part of the Transactions of the year 1840, the Royal Society has published a memoir by me, explaining, on the undulatory theory of light, the apparent new polarity observed by Sir David Brewster; which explanation is based upon the assumption that the spectrum is viewed out of focus; an assumption which corresponded to the circumstances of my own observations, and to those of some other persons. Since the publication of that memoir, I have been assured by Sir David Brewster that the phenomenon was most certainly observed with great distinctness when the spectrum was viewed so accurately in focus that many of Fraunhofer’s finer lines could be seen. This observation appeared to be contradictory to those of Mr. Talbot, cited by me in page 226 of the memoir, as well as to my own. With the view of removing the obscurity that still appeared to embarrass this subject, I have continued the theoretical investigation for that case which was omitted in the former memoir, namely, when the spectrum is viewed in focus, or when a = 0 (page 229); and I have arrived at a result which appears completely to reconcile the seemingly conflicting statements. In the following investigation I shall use the symbols and the formulæ of the former memoir (as far as they apply) without further reference.