AN APPARENT NEW POLARITY IN LIGHT. 
235 
tina whose ordinate is b, becomes, in the case in which the eye is too far from the 
luminous point to see it distinctly, 
2 ~ G (v/S’T + s) - C0S *(\/^rT + e) 
+ g (v / ^-V 4 + «-)- cosR - cos ^('\/^-t+s') 
+ G (V • sin R. sin® fy/ ’l±. e ^+ g ) 
+ G (v / ^ 7-^ + «)- C0S { ?, ('\/^-T+^)- r }- 
And similarly, in the case in which the eye is too near to see distinctly, the ex- 
pression for the intensity is 
2 - 
cb \ 
v -g) .cos <p 
2 a! 
Ace 
+ G (a /^7 •V-^)- cos {*(V] 
2 a' 
Ace 
It must be remarked that, in every part of the investigation, we suppose the square 
root to be taken with the positive sign. 
To present to the eye a representation of the value of G (s) cos <p (s), upon which 
the whole of our computations now depend, I have constructed the curve, Plate VIII. 
fig. 1., in which the abscissa represents the value of s, and the ordinate represents the 
value of G (s) cos <p (s). The curve corresponding to the value of G (s) cos {<p (s) — R} 
maybe sufficiently well inferred from this, by conceiving the whole curve to be pushed 
on, not through the same space in all parts, but in different parts through different 
spaces, bearing always the same proportion to the length of one of the waves which 
R bears to 360°. Thus G (.s) cos {<p (s) — 90°} is represented by the curve in fig. 2. 
From an inspection of fig. 1, the following points are easily ascertained. First, 
that the variations of intensity of light, which are represented by G (s) . cos <p (s), are 
so small when s is large, that they might on that account alone be rejected. Secondly, 
that if the intensities of a great number of non-interfering streams of light be aggre- 
gated, the origin of s for each of the streams having a different position, but the in- 
termediate distances of these origins being small : the variations of intensity near the 
origins of s may all sensibly coincide so as to produce a set of strong alternations of 
light and dark in the aggregate ; while at the places where s is large, the small di- 
stances of the origins and the corresponding displacement of the waves of the curve 
will be sufficiently great to cause the elevated parts of one curve to answer to the 
depressed parts of another, &c., or the strong light of one stream to be mingled with 
2 h 2 
