of the Vibrations of Polarized Light by Diffraction. 3828 
rate of propagation, and¢thetime. This equation will obviously 
be satistied by the expression 
valea’ obi! § 
Y 
where r=,/x* + (y—6)?-+ (z—y)?, and therefore also by 
A Se Ls p(wi—r, B,y) ‘ 
D= on a3 ay rere 
which function ®, when the limits of integration are determined 
by the boundaries of the opening, also possesses the property 
that its differential coefficient with respect to z becomes equal to 
d (w, t, y, z) when « decreases to nothing, and the point yz is 
within the opening. If 2 increases to nothing, the value of the. 
differential coefficient is —d(wt, y, 2); and if the point yz is 
without the opening, it becomes nothing when x=0; for by 
differentiating the integral with respect to 2, w=O enters asa 
factor, thus causing every element of the integral to disappear, 
except those in which r=0, that is to say, y=, z=y. Whence, 
if 2 is positive, and the point (yz) is within the limits of the 
integral, : 
ST = feelers] Ho rmters9 
and if x is negative, 
di *=0 
| =a Hels ys 2) 
_ Introduce now other functions VY, X, ©,, V,, X,, which are 
related to the respective functions yp, x, $,, Wy; X, m the same 
way as ® is to @, and put 
| d®, d(F+F 
ee ee 
Ps dv, d(F+F)) is 
y= V+ a F <a ° ° e ° ( ) 
ee ee TE) 
titres Ge ods Sd 
where the functions F, F, are so chosen that 
du, doy , dey 
dz dy. az 
ae 2 
