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And so, by our hypothesis, we explain perfectly the phenomenon mentioned above; to wit, that when there are two rays equally inclined, but coming from opposite sides, as here the rays RC, rc, their refractions diverge equally from the line followed by the refraction of the ray perpendicular to the surface, by considering these divergences in the direction parallel to the surface of the crystal.
By these two refractions, and this single reflection, the light is sent to the eye of an observer facing the drop, and with his back to the sun. Conceive a line drawn from the sun, through the back of his head, to the observer's eye and prolonged beyond it. Conceive a second line drawn from the shower to the eye, and enclosing an angle of 42½° with the line drawn from the sun.
The noble qualities of Johnson have been well discerned by Carlyle, and his obvious peculiarities and prejudices somewhat magnified and distorted in Macaulay's brilliant refractions. One quality only shall I dwell upon, though that may be the sum of all the rest. Johnson had a supreme capacity for human relationship. In him this capacity amounted to genius.
Ricarda Huch in her "Blütezeit der Romantik" makes the striking statement that from this poet's figures one must "tear away the labels stuck upon them and name them altogether Ludwig Tieck, for in truth they are only refractions of this one beam." One may hear for example how Sternbald felt: "The orb of the moon stood exactly opposite the window of his room."
Now the finding and construction of this second oval is the same as that of the first, and the demonstration of its effect likewise. But it is worthy of remark that in one case this oval becomes a perfect circle, namely when the ratio of AD to DB is the same as the ratio of the refractions, here as 3 to 2, as I observed a long time ago.
But the refractions which appertain to every other section of this crystal have this strange property that the refracted ray always quits the plane of the incident ray perpendicular to the surface, and turns away towards the side of the slope of the crystal.
But I saw that if the plane NN was almost perpendicular to the plane GG, making the angle NCG, which is on the side A, an angle of 90 degrees 40 minutes, the hemi-spheroids NGN would become similar to the hemi-spheroids GNG, since the planes NN and GG were equally inclined by an angle of 45 degrees 20 minutes to the axis SS. In consequence it must needs be, if our theory is true, that the surfaces which the section through NN produces should effect the same refractions as the surfaces of the section through GG. And not only the surfaces of the section NN but all other sections produced by planes which might be inclined to the axis at an angle equal to 45 degrees 20 minutes.
Moreover, apart from illusory refractions, of which there is no question here, the indications of light are precise; one goes straight to the object seen. But the butterfly was sometimes mistaken: not in the general direction, but concerning the precise position of the attractive object.
But everybody is drugged with his own dream, and the pageant marches at all hours, with music and banner and badge. Amid the joyous troop who give in to the charivari, comes now and then a sad-eyed boy, whose eyes lack the requisite refractions to clothe the show in due glory, and who is afflicted with a tendency to trace home the glittering miscellany of fruits and flowers to one root.
We employed our time in completing the Flora of Cumana, geologically examining the eastern part of the peninsula of Araya, and observing many eclipses of satellites, which confirmed the longitude of the place already obtained by other means. We also made experiments on the extraordinary refractions, on evaporation and on atmospheric electricity.
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