UPON THE PROPERTIES OF LIGHT. 
251 
not misled by the effect of the small aperture in reversing the action of the edges. 
Thus when viewing the moon or a candle through the interval of two edges, one 
being in advance of the other, we have the coloured images (or fringes) cast on the 
wrong side. But if we are only making the experiment required to illustrate this 
proposition, the edges being to be kept directly opposite, no confusion can arise. 
It is to be noted that the increase of breadth in the fringes is not very rapid in 
any of these experiments ; nor are we led by the calculus to expect it. Thus suppose 
w=l, we find ^because y= a^—x^ point C, when x=Q, the breadth should be 
2 a 200 
proportional to Take x=. Jq, and the breadth is as or the breadth of the one 
fringe is to the other only 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 in- 
crease is more rapid between x—~ and B than between C and Thus between the 
value of x-= | and | the increase is as 4 : 5. But from | to ^ 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 inter- 
ference, 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 
experiments the second body may be placed a foot and a half away from the first, 
and the fringes by disposition are still found, though much narrower than when the 
bending bodies are more near to one another. 
3. The breadth of the interference fringes is said to be in some inverse proportion 
to the difference in length of the interfering rays, It is commonly said to be inversely 
as that difference. 
In fig. 20, A is the first and B the second edge. By interference the fringe at C 
should be broadest and at D narrowest, because AC — BC=AO is less than AD 
— BD=AP; and so as you recede from D, the fringes should become broader and 
broader, because the two rays become more nearly equal. But the very reverse is 
2 K 2 
