4G8 
PROF. J. W. NICHOLSON AND DR. T. R. MERTON ON THE 
through the combined action of the exponentials of arguments —Jc 2 x 2 and — 
respectively. At X and Y, for example, >7 = 0, since no wedge has been traversed, 
and therefore, if XY = 2D, 
I c = I u e- A " 2D t 
In fact, X and Y are the traces of the extreme ends (photographically extreme) 
of the original line, and 2D would be its photographic breadth in the absence of 
the wedge. 
At the apex Z of the shaded area, on the contrary, x = 0, for it corresponds to 
a point on the central axis of the original line. If therefore H is the height of the 
curve, 
T _ T .9 —pH tan a 
± c - L 0 C ' ? 
where a is the angle of the wedge, for >7 = H tan a for the point Z. If y is the 
distance of any other point P, on the boundary of the area, from the line AB, and x 
its distance from the axis OZ of the curve, then x is also the distance from the centre 
in the original line, of the light affecting P, and y tan a is the thickness of wedge it 
has passed through, so that if ( x , y) are the co-ordinates of P, referred to an origin 
at the intersection of base and axis, 
T — T p -lc ! x--Py tana 
-*-c - L 0 C ' ) 
or 
whence, eliminating k 2 , 
— T ,-OT _ T -pH tan a 
-*-0° - L 0 C ' ? 
h 2 x 2 + py tan a = ZrD 2 = pH tan a, 
Ha? 2 + D“ (y— H) = 0, 
and the curve on the plate should be parabolic. An obvious change of axes reduces 
this to 
y*!x = D 3 /H. 
But we have already seen that, if the curve is y n cc x with this choice of axes, n is 
less than unity from all the plates. We must conclude that the law of intensity for 
