PHILOSOPHICAL TRANSACTIONS. 



I. Supplement to a Paper " On the Theoretical Explanation of an apparent new Po- 

 larity in Light'' By G. B. Airy, Esq. M.A. F.R.S., Astronomer Royal, 



Received October 24, — Read November 19, 1840. 



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 corre- 

 sponded 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 = (page 

 229) ; and I have arrived at a result which appears completely to reconcile the seem- 

 ingly conflicting statements. 



In the following investigation I shall use the symbols and the formulae of the former 

 memoir (as far as they apply) without further reference. 



The value off in page 228 becomes, on making a = 0, 



b 

 f = ^ - T^' 



and the disturbance of ether, on the point of the retina whose distance from the 

 geometrical image is ft, produced by a small portion ly o{ the front of the wave, is 



^y X sin-^(v# — f) 



or 



^3^ X sin ^ (v ^ - e -I- -y), 



MDCCCXLI. 



