UPON THE PROPERTIES OF LIGHT. 
247 
is if it will not reach its full height, whatever that may be, more quickly near its 
source than far from it. This experiment ought above all to be made on radiant 
heat, in which I confidently expect a property will be found similar to the disposi- 
tion of light. It is also plain that we may expect strong analogies in magnetism 
and electro-magnetism. — I throw out these things because my time for such inves 
tigations may not be sufficiently extended to let me undertake them with success. 
Proposition VI. 
The figures made by the inflexion of the second body acting upon the rays de- 
flected by the first, must, according to the calculus applied to the case, be broader 
than those made by the second body deflecting those rays inflected by the first. 
In fig. 14, let Aw' be the violet rays and Ar' the red, inflected by A and deflected 
by B. Let A r be the red and A v the violet deflected by A and inflected by B. The 
action of B must inflect Ar, Av into a broader fringe F, than the action of B deflects 
A v', A r' into the fringe f. 
Let B r=a be the distance at which B acts on A r ; r v=d be the divergence of the 
red and violet ; c be the distance of the two bent pencils, and v' r' the divergence of 
the inflected pencil, equal also to d, because we may take the different inflexibility to 
T 
be as the different deflexibility. B acts on the red of Arw as — ; on the violet as 
(aliy . ; and so on A w' as ; on Ar'as (^a+2d+c)”^ ' evident that the ac- 
tion in bending Ar, Av, or the fringe made by that action, is to the fringe made by 
the action on A r', Av', as ^ - (a + d+c)’‘ ’ ultimately the 
two actions (or sets of fringes) are (supposing a= 1 and d also =1, for simplifying the 
expression) as 
2“xr (3 + c)” (2+cr-v (S+c)™ (2-1-c)’" to 2"r (2-1-c)”*- 2“ w (3-fc)“. 
Now the former of these expressions must always be greater than the latter, because 
(3-}-c)™>l, and also (3-1-c)™— l>(2-l-c)™— 1 ; and this whatever be the value of m 
and of c, and whatever proportion we allow of r to v, the flexibilities. But it is also 
manifest that the excess of the first expression above the second will be greater if the 
flexibility of the red exceed that of the violet, or if r is greater than v, as 2 v. Hence 
we conclude ; Jirst, that in mixed or white light the fringes inflected by B after 
deflexion by A are greater than those deflected by B after inflexion by A ; secondly, 
that they are also greater in homogeneous light ; thirdly, that the excess of the in- 
flected fringes over the deflected is greater in mixed than in homogeneous light. 
The action of flexion after disposition is so much greater than that of simple flexion, 
that I have only taken into the calculation the compound flexion. But the most 
accurate analysis is that which makes the two fringes as 
, r ^ -Tk 1 ^ 
^ — (a + <;)mtOlJ-l- “ (a + «?+c)”*’ 
