248 LORD brougham’s experiments and observations 
D being the breadth of the fringes on the chart by simple flexion in case the rays 
had passed on without disposition and without a second flexion. If it be carefully 
kept in mind that D is much less than — , or even ^ 
than D, then it will always be certain that the first quantity is larger than the second. 
Cor . — It is a corollary to this proposition that the difference of the two sets of 
fringes is increased by the disposition communicated by the rays in passing by the 
first body. For the excess of the value of r over that of v being increased, the differ- 
ence between the two expressions is increased. 
Proposition VII. 
When one body only acts upon the rays, it must, by deflexion, form them into fringes 
or images decreasing as the distance from the bending body increases. But when 
(he rays deflected and disposed by one body are afterwards inflected by a second 
body, the fringes will increase as they recede from the direct rays. Also when the 
fringes made by the inflexion of one body, and which increase with the distance from 
the direct rays, are deflected by a second body, the effect of the disposition and of 
the distances is such as to correct the effect of the first flexion, and the fringes by 
deflexion of the second body are made to decrease as they recede from the direct 
rays. 
In fig. 15, A P is the pencil inflected by A and forming the first and narrower 
fringe p A r is the pencil inflected nearer to A and forming the broader fringe r. 
Such are the relative breadths, because they are inversely as some power of the di- 
stance at which A acts on them. But if B afterwards acts, it is shown by the same 
reasoning which was applied to the last proposition that r will be less than p ; and so 
in like manner will r' be made less than o', though o' was greater than r', until B’s 
action, and the effects of disposition with the greater proximity of the smaller fringe, 
altered the proportions. 
Proposition VIII. 
It is proved by experiment that the inflexion of the second body makes broader 
fringes or images than its deflexion after the inflexion of the first body ; and also that 
the inflecto-deflexion fringes decrease, and the deflecto-inflexion fringes increase 
with the distance from the direct rays. 
Exp. 1. It must be observed that when we examine the fringes (or images) made 
by the second edge deflecting the rays which the first had inflected, we can see the 
effects of the disposition communicated to the rays at a much greater distance of the 
second edge from the first, than we can perceive the effects of that disposition upon 
the inflexion by the second edge of the rays deflected by the first. Indeed w^e only 
lose the fringes thus made by deflexion, in consequence of their becoming so minute 
as to be imperceptible to our senses. But it is otherwise with the fringes or images 
