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 = 0 (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 of § in page 228 becomes, on making a = 0, 
b 
S = e- T y, 
and the disturbance of ether, on the point of the retina whose distance from the 
geometrical image is b, produced by a small portion § y of the front of the wave, is 
v. .2 n . . 
oy X sin — (vt — f) 
or 
ly X sin ^ (v t - e + ~y) y 
MDCCCXLI. 
B 
