Fig. 5. Is the Experimentum Crucis, or determining Experiment. Where B F is the Hole that lets in a large Ray of Light: whose middle Part, after it has pass'd through the Prism A B C, is let through a lesser Hole at G, and forms an oblong colour'd Image at d e: where another small Hole lets thro' one Colour only; which passing through the Second Prism a b c it is refracted again, and cast upon N M. And here it is most remarkable, that the two Holes and second Prism are kept immoveable; and so the Rays G g fall upon the second Prism in the very same Angle, whatever Colour they are of, and that by the Motion of the first Prism, all the Colours may successfully pass through the same Holes. Yet is the Refraction by the second Prism never then able to produce any Variety of Colours; but exhibits the Image always of that Colour alone, which falls upon it before the second Refraction.
Fig. 6. Is a Figure for the Explication of the several Refractions and Reflections of Light, which cause the Phænomena of the Rainbow. Thus if the greatest Crowd of Rays enter in Parallel to B Q along or near to A N, the round Drop of Water L B G Q will refract Part of those Rays to F, whence Part of them will be reflected to G: And going there out of the Drop, will be thereby refracted to R, which double Refraction will so separate the several Colours, and make them go out in Angles so sensibly different, that as the Eye is placed a little higher or lower, it will see a different Colour; and that in Angles as A X R, of about 41 Degrees; and this is the Case of the primary Rainbow, which appears in about that Angle from the Axis B Q, or its Parallel A X. Thus also, if the same Line A N be now suppos'd to represent another Drop, and that some of the Rays at G are reflected a second time, and so pass out at H, and are there refracted to S; here will be a weaker Impression, but a like Refraction and Separation of the Colours as before; and the Eye placed a little higher or lower will also see different Colours, tho' in a contrary Order to the former; and that in an Angle, as A Y S, of about 52 Degrees and a half; which is the Case of the secondary Rainbow.
Fig. 7. Are the two Rainbows themselves, r presented as they appear in Nature. Where A E B F represents the Air full of spherical Drops of Rain, in such Parts as the Angles E O P, F O P are about 41 Degrees from the Axis O P, which Axis is the Line from the Sun's Center, through the Eye of the Spectator, to the Center of the Rainbow: And where C G D H represents the same Air, full of the like Drops, in such Parts where the Angles G O P, H O P are about 52 Degr. and a half. Where also the Rays S E, S F, S G, S H, coming from the Sun's Center, are represented as parallel, by reason of its vast Distance. These Rays, when they fall upon the higher Quadrant of the Drop, as at S E, S F, come to the Eye at O in about an Angle of 41 Degrees, after two Refractions, and one Reflection; and so cause the primary Rainbow: the Red is without, by the least refrangible Rays at F: and the blue within, by the more refrangible Rays at E. But when they fall upon the lower Quadrant of the Drop, as at S G, S H, they come to the same Eye at O, but in an Angle of about 52 Degrees and a half, after two Refractions, and two Reflections, and so cause the secondary Rainbow. Which is Blue without, by the more refrangible Rays at H; and Red within by the least at G. Where note, that because the Angles F O P, E O P, as well as those H O P, G O P, are ever the same, the same Colours must still be circular, or appear in the Surface of a right Cone, whose Axis is O P, and whose Sides are the Lines turned round thereon, as O E O F, and O G O H.
12
HYDROSTATICKS.
An Explication of the First Plate.
Figure 1. Is a Balance, to weigh Water in its own Element, and in the Air; and to prove that its Weight is the very same in the former Case as in the latter. For when the Glass Bottle F is exhausted of Air, it will indeed require much more Weight to counterpoise it in the Air, than in the Water; by Reason of the much greater Weight of the Water thrust out by it, than of the Air; yet when upon the Admission of Water within, you weigh it again in the Air, and then in the Water, the additional Counterpoise now necessary is the very same; and shews that the real Weight of the Water admitted, is the same in both Elements. This Figure does also shew how Trials may be made to shew the respective Weight of those Bodies in Fluids that sink in them.