80 
And that if be the three components of a light 
vibration, the condition 
dr) d^ 
dx ^ dy^ dz 
= 0 is satisfied. 
provided x^_-^ + + ^r^-\ = 0 
when ^u, ^y, etc., denote terms in the expansion of etc. 
It is in the first place my object to shew that if the 
sources of light are distributed over a portion of a plane, we 
can obtain the form of the integral disturbance at any point. 
Take the origin at a point in the plane of the sources, so 
that the normal at the origin passes through the point at 
which the integral disturbance is sought. Take this line as 
the axis of x, and any two lines in the plane at right-angles 
as the axes of y and 0. Then the coordinates of a source 
of light bring (o, y, z), and those of the given point o, o), 
the change required to be made in the general equations is 
to write for x, and ~y and —zioxy and 0 respectively. 
No convenience results from writing xd' for x^ and therefore 
we will retain x. 
Write y = pcosd . 0 = psin0 
then r^ = p^ + x^ 
and rdr = pdp. 
The components of the integral disturbance at (x, o, o) 
due to the distribution of sources will be 
y * J lpdpdQ = J J IrdrdQ) &c. 
taken between the proper limits. 
Let now h be a function such that 
Write = { Uo + U_ 1 + U_2 + &c. } cos - r) 
+ { Vo + V_ 1 + V_2 + &c. } sin^9(rtt - ?■) 
