148 EXPERIMENTS AND INVESTIGATIONS 



2 a 



should be proportional to . Take x = , and the breadth 



a 10 



is as , or the breadth of the one fringe is to the other only 

 *} y 



as 200 to 198 or 100 : 99. We need not wonder therefore if 

 there is only a gradual increase of breadth from C to B and 



from C to A. The increase is more rapid between x - - 



a 



and B than between C and -. Thus between the value oi 



2. 



a a , . . K -n j. * a 3a 



x = and the increase is as 4 : 5. But from -- to - 

 42 24 



the increase is as 7 : 12 ; and this too agrees exactly with the 

 experiments ; for as the edges are approached the increase of 

 the fringes becomes more apparent. 



PROPOSITION XI. 



The phenomena described in the foregoing propositions are 

 wholly unconnected with interference, and incapable of being 

 referred to it. 



1. When the fringes in the shadow are formed by what is 

 supposed to be interference, there are also formed other 

 fringes outside the shadow and in the white light. If the 

 rays passing -on one side the bending body (as a pin or 

 needle) are stopped, the internal fringes on the opposite side 

 of the shadow are no longer seen. But no effect whatever is 

 produced on the external fringes. These continue as long as 

 the rays passing on the same side of the body on which they 

 are formed, continue to pass. The external fringes have 

 many other properties which wholly distinguish them from 

 the internal or interference fringes. 



2. Interference is said to be in proportion to the different 

 lengths of the interfering rays, and not to operate unless 

 those lengths are somewhat near an equality. In my experi- 

 ments the second body may be placed a foot and a half away 

 from the first, and the fringes by disposition are still formed, 



