the Inflection, Reflection, and Colours of Light. 263 
of the shadow, and pass precisely through its middle, I marked 
on one side 6 or 8 points of the shadow's outline, in each set 
of rays ; and this being often repeated, at different distances 
and in different shadows, the position of the axis remaining 
the same, the curves formed by joining the points were all pa- 
rallel ; which shows that each sine of inflection taken apart has 
a given ratio to the sine of incidence. I afterwards divided 
the axis according to the musical intervals, and thus found 
where each colour of the spectrum had terminated, in what 
colour each part of the shadows had been, and by what rays 
formed. Then I joined the parts that I had marked, and ob- 
tained a curve, which I took to be, either nearly or accurately, 
an hyperbola of the 4th order. I next measured the ordinates 
(the axis of the spectrum and shadow being the axis of the 
curve) at the confines of each colour ; first, the ordinate at 
the extremity of the rectilinear red, then that at the confine of 
the red and orange, and so on to that at the extreme rectili- 
near violet; to each of these ordinates I added the greatest one, 
or that in the violet, which (in fig. 10.) is VV' ; that is, I pro- 
duced v\ to V', so that vW is equal to vN ; and through V' I 
drew V'R' parallel to the axis VR, and produced gG to G', 
and rR to R' ; then from V' I set off Y'g' equal to G'^, and 
VV' equal to R'r, and the other ordinates in like manner ; and 
I found, according to the method before described,* that 
VV' was divided inversely, after the manner of the musical 
intervals. It is therefore evident that the inflexibilities of the 
rays are directly as their deflexibilities, and reflexibilities, but 
inversely as their refrangibilities. The same may be proved, 
by measuring and dividing the images made in the inside 
* Page 247. 
