7 
EXPLANATION OF AN APPARENT NEW POLARITY IN LIGHT.” 
is considered positive ; that is, it is indifferent whether the retarding plate is applied 
on the same side as the red end or the violet end of the spectrum. These appear to 
be the bars seen by Mr. Talbot and myself when the spectrum was viewed in focus. 
2\e 
They require that — be not large, that is, that the aperture of the pupil (2 h ), or 
the aperture of the telescope used be not very small ; and that the changes of R be 
not very rapid ; that is, that the plate of mica, &c. be thin. These circumstances 
held in my own experiment. I may add that the dark bands were not black, but 
merely dusky ; as indicated by the numbers above. 
Secondly. Suppose the value of to be comparable with the distance between 
those points of the image of the spectrum in which R has changed by 360° ; for in- 
stance, suppose to be equal to that distance. 
1 . Let the red end of the external spectrum be on the same side as the retarding 
plate, that is, on the side on which b is considered positive. Then on the retina the 
violet end is on that side ; or R increases towards the positive side. Let k be the 
ordinate measured from a fixed point on the retina to the centre of the diffused image 
of any colour ( k being therefore a function of X), and l the ordinate measured from 
the same fixed point to the point at which the intensity is to be ascertained ; then 
k -j- b = /, or b = l — k, and the intensity produced by any one kind of light is re- 
presented by 
• a mh n 
sin- — ( l — k) 
X 6 n 
r 7 'j 9 COS 
{!->-*>} 
mhi 
. A, e 
milk 
The sum of the intensities on one point of the retina produced by all the different 
kinds of light from the adjacent portions of the spectrum will be found by varying 
k in this expression, and adding together all the values so produced. Now if R 
increases when k increases (as occurs when the red end of the external spectrum is 
on the same side as the retarding plate), the last factor cos 2 
/ mhl 
\Xe 
mhk R\ 
TT — 2/ 
will 
undergo very great changes from the combined changes of and 77 , whatever be 
the value of /, and the succession of values which it receives will not differ materially 
sin 2 — (l — k) 
for different values of l; the first factor —? — ^ will also undergo great 
{&'-*>} 
changes, but nearly the same for different values of l ; and in consequence the aggre- 
gate of all the values for different values of k, exhibiting the total intensity of light 
upon the point /, will be nearly the same. 
This aggregation will be represented graphically by supposing the second curve in 
