2 64 Mr, Brougham's Experiments^ and Observations on 
of the shadows ; these I have found to be, at equal incidences 
and distances, equal to the images on the outside, both in 
breadth, in distance from the edge of the shadow, and in the 
relation which their divisions bear to one another ; wherefore, 
whatever be the ratio of the angle of inflection to that of inci- 
dence, the same is the ratio of the angle of deflection to that 
of incidence ; so that the angle of deflection is equal to the 
angle of inflection. If farther proof of this proposition be 
desired, the following experiment and observations, which 
from the importance of the thing I do not scruple to add, may 
be sufficient. 
Obs. 14. When two knife blades were placed by one ano- 
ther in-a beam of light which entered the dark room, so that 
the one might form and the other distend the images, I made 
in one of the blades (with a file) a small dent, which, on the 
chart, cast an elliptic or semicircular outline ; then I ob- 
served that the images of both blades were disturbed by it, 
and wound round the edges of the semicircle ; and they were 
all affected in precisely the same manner and degree. So then 
the first knife deflected the images formed by the second, in 
precisely the same degree that it inflected those images which 
itself formed, and so of the other knife ; otherwise the effect 
of the dent would have been different upon the two sets of 
images. We may therefore conclude, that the angles or sines 
of inflection and deflection, bear the same ratio to the angle or 
sine of incidence, and that they are equal to one another. My 
next object was to determine this ratio in one of these cases, 
and consequently in both ; and it was very agreeable to find 
data for the solution of this problem in Newton's measure- 
ments of the images and shadow ; since this philosopher's well 
