XIX.—On the Total Intensity of Interfering Light. By Professor Sroxrs. 
[Eatracted from a Letter addressed to Professor Kelland. | 
Premproke CoLLecr, CAMBRIDGE. 
My DEAR Sir, 
* * * * 
In reading your paper in the Transactions of the Royal Society of Edinburgh, 
vol. xv., p. 315, some years ago, it occurred to me to try whether it would not be 
possible to give a general demonstration of the theorem, applying to apertures of 
all forms. I arrived at a proof, which I wrote out, but have never published. As 
I think it will interest you I will communicate it. You may make any use you 
please of it. 
Case I. Aperture in front of a lens; light thrown on a screen at the focus, 
or received through an eye-piece, through which the luminous point is seen in 
focus. 
The expression for the intensity is given in Arry’s Tract, Prop. 20. If the in- 
tensity of the incident light at the distance of the aperture be taken for unity, 
and D be the quantity by which any element of the area of the aperture must be 
divided in forming the expression for the vibration, that expression becomes 
1 20 a+ 
D [ frin =< (ve—B+ pert) ax dy, 
the integration being extended over the whole aperture. If it should be neces- 
sary to suppose a change of phase to take place in the act of diffraction, such 
change may be included in the constant B. If, then, I be the intensity, 
_ 27 patgy = (fe 20 pxiqy 2 
are 3 
D? I= ( [fsn= era, ve dx dy) + ([feos=< 7 dx dy) : 
and if I be the total illumination, 
t=f f© tapas, 
Now, { [[ranaxay)f[fffiense.y) az ay ax ay, 
the limits of 2’, y’ being the same as those of 2, y. Hence, 
D? T= fff feos 5 (vf=2 + ay=3) ae dy dx dy. 
VOL. XX. PART III. 4R 

