AN APPARENT NEW POLARITY IN LIGHT. 
231 
Before entering- into the detailed consideration of the numerical value of this ex- 
pression, we will make a similar investigation for the supposition that the luminous 
point is too near for distinct vision. 
Let the distance of the retina from the lens be c — a!. The distance g>, of a point 
of the wave whose ordinate is y, from the point of the retina whose ordinate is b, is 
§ = V {x — a'] 2 -f y — b\ 2 } = -/{c 2 — 2 a! x — 2 b y + a' 2 + b 2 } = 
V | c — a!} 2 b 2 — 2 b y ^ y 2 ^ ; and putting e 2 = c — r/' 2 + b 2 , and expanding 
before, this becomes 
as 
s=e-—y + 
2 c e 
y- 
-f+ Yre(y-v) ’ 
cb 2 
where f=e- ^ 
The integral which expresses the disturbance of ether at the point of the retina is 
now 
sin 
2 7T . , /.x/* 7 to! ( c b \ 2 277- X\ r ’ 7ra ' ( c b \ 2 
x (® ‘ -f)J, cos \9 - s) - cos -x( vt -f)J, sm XTe \9 - s) 
to be taken from y — — h to y = g. And 
sin x (® < -/) { cos cos £r e (.y - 1?Y - s!n R X sin S O' - z) 2 } 
- cos ^ (v t -/) [ cos R .fj sin ^ ( 3 / - 7) ' " + sin R/^cos ^ ( y - $ ' ’ j 
to be taken from ?/ = + g to y = + A- 
Proceeding exactly as before, omitting the constant multiplier supposing 
’ 2 a 
/i to be large in the integral, and estimating the intensity of light on the point of the 
retina as before, we obtain this expression : 
1 + 
+ cos R X [l — 2 {c (v^-S -?)} 2 - 2 
+ sinRx [2S - ^ C Wxf e -S~ 7)] 
or 
■ +* Mv/g-s-or +* -4 
+ *Rx[l-s{c( V / ^ 
2 a' c_b 
~e ‘ a' 
+ sin R X [2 C ^ - 2 S ( ^ • 
