442 Transactions of the Society. 



Comparing this with the preceding curves, there are several points 

 which deserve notice. In the first place, the base of the curvilinear 

 area has, as before, a diameter = A. But now the symmetry is not 

 bilateral. On the contrary, the ordinate of the curve at a distance 

 2 tt (= A) from its origin ia double the height of the ordinate at the 

 middle point of the base A'. Furthermore, the two halves, upper and 

 lower, of the curve are now equal and similar. 



Let us now make once more, with this new curve, the experiment 

 illustrated in fig. 101). This is shown in fig. 115. In this diagram the 

 total light-curve, shown by the clotted line, has been removed from the 

 middle of the figure to its natural place on the scale, and it will be 

 observed that owing to the similarity of the lower and upper halves of 

 the curves the total light is now uniform all over. It is to be observed 

 also that the illuminated surfaces (represented by their sections beneath 

 the light-curves in the diagram) are now in contact with one another,, 

 for the point A' stands vertically over the edge of the illuminated area. 

 This case, therefore, in which the light-intensity curves of the adjacent 

 edges of two infinite surfaces bisect and exactly supplement one another,, 



Fig. 115. 



corresponds to a state of things in which the surfaces are in physical 

 contact, and not to a state of things, as supposed by Helmholtz, in which 

 they are separated by an interval of £ A. 



But suppose, further, that the surfaces do not extend for indefinite 

 distances away from the line of contact but are very narrow, that is to 

 say, less in diameter than £ A, the distance for which the fully developed 

 light-intensity curve extends back over the illuminated surface. In 

 that case the area of the fringe-curve which passes over any point in 

 the formation of the surface will be proportionably reduced, with the 

 general result that the final curve will become unsymmetrical, the lower 

 half growing hollower and the upper half being cut short. Fig. 116 



shows the light-intensities across a narrow band assumed to be — in 



o 



breadth. The intersection of two such light-intensity curves is shown, 

 together with the total light curve ; from this it appears that even with 

 such narrow surfaces as these, there is a falling off of illumination in 

 the middle of the half wave-length gap between them which amounts 

 to 25 per cent. Thus, in this extreme case where our finest existing 

 instruments would certainly fail to produce a resolved image, we find 



