Scholium. If this Experiment and the former be conjoined and made one by applying a fourth Prism VXY [in Fig. 22.] to refract the reflected beam MN towards tp, the Conclusion will be clearer. For then the Light Np which in the fourth Prism is more refracted, will become fuller and stronger when the Light OP, which in the third Prism HJK is more refracted, vanishes at P; and afterwards when the less refracted Light OT vanishes at T, the less refracted Light Nt will become increased whilst the more refracted Light at p receives no farther increase. And as the trajected beam MO in vanishing is always of such a Colour as ought to result from the mixture of the Colours which fall upon the Paper PT, so is the reflected beam MN always of such a Colour as ought to result from the mixture of the Colours which fall upon the Paper pt. For when the most refrangible Rays are by a total Reflexion taken out of the beam MO, and leave that beam of an orange Colour, the Excess of those Rays in the reflected Light, does not only make the violet, indigo and blue at p more full, but also makes the beam MN change from the yellowish Colour of the Sun's Light, to a pale white inclining to blue, and afterward recover its yellowish Colour again, so soon as all the rest of the transmitted Light MOT is reflected.
Now seeing that in all this variety of Experiments, whether the Trial be made in Light reflected, and that either from natural Bodies, as in the first and second Experiment, or specular, as in the ninth; or in Light refracted, and that either before the unequally refracted Rays are by diverging separated from one another, and losing their whiteness which they have altogether, appear severally of several Colours, as in the fifth Experiment; or after they are separated from one another, and appear colour'd as in the sixth, seventh, and eighth Experiments; or in Light trajected through parallel Superficies, destroying each others Effects, as in the tenth Experiment; there are always found Rays, which at equal Incidences on the same Medium suffer unequal Refractions, and that without any splitting or dilating of single Rays, or contingence in the inequality of the Refractions, as is proved in the fifth and sixth Experiments. And seeing the Rays which differ in Refrangibility may be parted and sorted from one another, and that either by Refraction as in the third Experiment, or by Reflexion as in the tenth, and then the several sorts apart at equal Incidences suffer unequal Refractions, and those sorts are more refracted than others after Separation, which were more refracted before it, as in the sixth and following Experiments, and if the Sun's Light be trajected through three or more cross Prisms successively, those Rays which in the first Prism are refracted more than others, are in all the following Prisms refracted more than others in the same Rate and Proportion, as appears by the fifth Experiment; it's manifest that the Sun's Light is an heterogeneous Mixture of Rays, some of which are constantly more refrangible than others, as was proposed.
PROP. III. Theor. III.
The Sun's Light consists of Rays differing in Reflexibility, and those Rays are more reflexible than others which are more refrangible.
This is manifest by the ninth and tenth Experiments: For in the ninth Experiment, by turning the Prism about its Axis, until the Rays within it which in going out into the Air were refracted by its Base, became so oblique to that Base, as to begin to be totally reflected thereby; those Rays became first of all totally reflected, which before at equal Incidences with the rest had suffered the greatest Refraction. And the same thing happens in the Reflexion made by the common Base of the two Prisms in the tenth Experiment.
PROP. IV. Prob. I.
To separate from one another the heterogeneous Rays of compound Light.
Fig. 23.
The heterogeneous Rays are in some measure separated from one another by the Refraction of the Prism in the third Experiment, and in the fifth Experiment, by taking away the Penumbra from the rectilinear sides of the coloured Image, that Separation in those very rectilinear sides or straight edges of the Image becomes perfect. But in all places between those rectilinear edges, those innumerable Circles there described, which are severally illuminated by homogeneal Rays, by interfering with one another, and being every where commix'd, do render the Light sufficiently compound. But if these Circles, whilst their Centers keep their Distances and Positions, could be made less in Diameter, their interfering one with another, and by Consequence the Mixture of the heterogeneous Rays would be proportionally diminish'd. In the twenty third Figure let AG, BH, CJ, DK, EL, FM be the Circles which so many sorts of Rays flowing from the same disque of the Sun, do in the third Experiment illuminate; of all which and innumerable other intermediate ones lying in a continual Series between the two rectilinear and parallel edges of the Sun's oblong Image PT, that Image is compos'd, as was explained in the fifth Experiment. And let ag, bh, ci, dk, el, fm be so many less Circles lying in a like continual Series between two parallel right Lines af and gm with the same distances between their Centers, and illuminated by the same sorts of Rays, that is the Circle ag with the same sort by which the corresponding Circle AG was illuminated, and the Circle bh with the same sort by which the corresponding Circle BH was illuminated, and the rest of the Circles ci, dk, el, fm respectively, with the same sorts of Rays by which the several corresponding Circles CJ, DK, EL, FM were illuminated. In the Figure PT composed of the greater Circles, three of those Circles AG, BH, CJ, are so expanded into one another, that the three sorts of Rays by which those Circles are illuminated, together with other innumerable sorts of intermediate Rays, are mixed at QR in the middle of the Circle BH. And the like Mixture happens throughout almost the whole length of the Figure PT. But in the Figure pt composed of the less Circles, the three less Circles ag, bh, ci, which answer to those three greater, do not extend into one another; nor are there any where mingled so much as any two of the three sorts of Rays by which those Circles are illuminated, and which in the Figure PT are all of them intermingled at BH.
Now he that shall thus consider it, will easily understand that the Mixture is diminished in the same Proportion with the Diameters of the Circles. If the Diameters of the Circles whilst their Centers remain the same, be made three times less than before, the Mixture will be also three times less; if ten times less, the Mixture will be ten times less, and so of other Proportions. That is, the Mixture of the Rays in the greater Figure PT will be to their Mixture in the less pt, as the Latitude of the greater Figure is to the Latitude of the less. For the Latitudes of these Figures are equal to the Diameters of their Circles. And hence it easily follows, that the Mixture of the Rays in the refracted Spectrum pt is to the Mixture of the Rays in the direct and immediate Light of the Sun, as the breadth of that Spectrum is to the difference between the length and breadth of the same Spectrum.