by the _Cartesian Hypothesis_ it is possible to give any plausible reason
of the nature of the Colours generated in the thin _laminæ_ of these our
_Microscopical Observations_; for in many of these, the refracting and
reflecting surfaces are parallel to each other, and consequently no
_rotation_ can be generated, nor is there any necessity of a shadow or
termination of the bright Rays, such as is suppos'd (_Chap._ 8. §. 5. _Et
præterea observavi umbram quoque, aut limitationem luminis requiri:_ and
_Chap._ 8. §. 9.) to be necessary to the generation of any distinct
colours; Besides that, here is oftentimes one colour generated without any
of the other appendant ones, which cannot be by the _Cartesian Hypothesis_.

There must be therefore some other propriety of refraction that causes
colour. And upon the examination of the thing, I cannot conceive any one
more general, inseparable, and sufficient, than that which I have before
assign'd. That we may therefore see how exactly our _Hypothesis_ agrees
also with the _Phænomena_ of the refracting round body, whether _Globe_ or
_Cylinder_, we shall next subjoyn our _Calculation_ or _Examen_ of it.

And to this end, we will calculate any two Rays: as for instance;[10] let
EF be a Ray cutting the _Radius_ CD (divided into 20. parts) in G 16. parts
distant from C, and ef another Ray, which cuts the same _Radius_ in g 17.
parts distant, these will be refracted to K and k, and from thence
reflected to N and n, and from thence refracted toward P and p; therefore
the Arch Ff will be 5.d 5'. The Arch FK 106.d 30'. the Arch fk 101.d 2'.
The line FG 6000. and fg 5267. therefore hf. 733. therefore Fc 980, almost.
The line FK 16024. and fk 15436. therefore Nd 196. and no 147 almost, the
line Nn 1019 the Arch Nn 5.d 51'. therefore the Angle Nno is 34.d 43'.
therefore the Angle Non is 139.d 56'. which is almost 50.d more than a
right Angle.