458 



Transactions of the Society. 



In cases (i.) and (iii.) the resultant amplitude is symmetrical with 

 respect to the point u = — \tt midway between the two geo- 

 metrical images ; in case (ii.) the sign is reversed, but this of 

 course has no effect upon the intensity. Graphs of the three 

 functions are given in fig. 120, the geometrical images being at the 

 points marked — it and 0. It will be seen that while in case iii., 

 relating to self-luminous points or lines, there is an approach to 

 separation, nothing but an accurate comparison with the curve due 

 to a single source would reveal the duplicity in case i. On the 



Fig. 120. 



other hand, in case ii., where there is a phase-difference of half a 

 period between the radiations, the separation may be regarded as 

 complete. 



In a certain sense the last conclusion remains undisturbed even 

 when the double point is still closer, and also when the aperture 

 is of any other symmetrical form, e.g. circular. Tor at the point of 

 symmetry in the image, midway between the two geometrical 

 images of the radiant points, the component amplitudes are neces- 

 sarily equal in numerical value and opposite in sign, so that the 

 resultant amplitude or illumination vanishes. For example, sup- 



