89 
of an angle of finite curvature the infinite value does not 
enter. It is worthy of notice, that the term which gives 
rise to these infinite coefficients also appears in Professor 
Stokes’ solution, where the case is treated as the limit of 
that in which 
is not zero. 
dr] 
dx dy dz 
VII. 
Eeturning now to the expressions for etc., it is plain 
that if the integral rotations and elements of the strain are 
to be identical with those in the plane polarised wave : the 
integrals of all the differential coefficients must be identical 
with the differential coefficients of the displacements in 
that wave. 
In the Paper “ On the solution of the equations of the 
vibration of light,” previously quoted, I have shown that 
the first term in ^ will be given by 
.1 , etc. 
And from this and similar relations, it is evident that in 
consequence of the previously proved theorems, the required 
conditions are satisfied. 
It appears then as if the problem were left indefinite; and 
this is so, if we deal with the plane area with boundaries at 
an infinite distance. When we deal with the question of 
the diffraction at a finite aperture, the constants in the 
complementary function become necessary to the solution ; 
but the determination of their values is probably practically 
impossible, unless it may be in the case of a sharp angle. 
Note, Jan. 8, 1886. — If diffraction is absolutely indepen- 
dent of the nature of the boundary, and dependent only on 
the intensity and wave length of the light, the complementary 
function will vanish. ~RF.G. 
