the surface AI, that is to say when the piece G shall have reached I, it will be the curves HF, FI, generated as evolutes of the curves FA, FE, both beginning at F, which together constitute the propagation of the part AG.  And a little afterwards, when the part AK has met the surface AM, the piece K having come to M, then the curves LN, NM, will together constitute the propagation of that part.  And thus this folded wave will continue to advance until the point N has reached the focus E. The curve AFE can be seen in smoke, or in flying dust, when a concave mirror is held opposite the sun.  And it should be known that it is none other than that curve which is described by the point E on the circumference of the circle EB, when that circle is made to roll within another whose semi-diameter is ED and whose centre is D. So that it is a kind of Cycloid, of which, however, the points can be found geometrically.

Its length is exactly equal to 3/4 of the diameter of the sphere, as can be found and demonstrated by means of these waves, nearly in the same way as the mensuration of the preceding curve; though it may also be demonstrated in other ways, which I omit as outside the subject.  The area AOBEFA, comprised between the arc of the quarter-circle, the straight line BE, and the curve EFA, is equal to the fourth part of the quadrant DAB.

INDEX

Archimedes, 104.

Atmospheric refraction, 45.

Barrow, Isaac, 126.

Bartholinus, Erasmus, 53, 54, 57, 60, 97, 99.

Boyle, Hon. Robert, 11.

Cassini, Jacques, iii.

Caustic Curves, 123.

Crystals, see Iceland Crystal, Rock Crystal.

Crystals, configuration of, 95.

Descartes, Rene, 3, 5, 7, 14, 22, 42, 43, 109, 113.

Double Refraction, discovery of, 54, 81, 93.

Elasticity, 12, 14.

Ether, the, or Ethereal matter, 11, 14, 16, 28.

Extraordinary refraction, 55, 56.

Fermat, principle of, 42.

Figures of transparent bodies, 105.

Hooke, Robert, 20.

Iceland Crystal, 2, 52 sqq.

Iceland Crystal, Cutting and Polishing of, 91, 92, 98.

Leibnitz, G.W., vi.

Light, nature of, 3.

Light, velocity of, 4, 15.

Molecular texture of bodies, 27, 95.

Newton, Sir Isaac, vi, 106.

Opacity, 34.

Ovals, Cartesian, 107, 113.

Pardies, Rev. Father, 20.

Rays, definition of, 38, 49.

Reflexion, 22.

Refraction, 28, 34.

Rock Crystal, 54, 57, 62, 95.

Roemer, Olaf, v, 7.

Roughness of surfaces, 27.

Sines, law of, 1, 35, 38, 43.

Spheres, elasticity of, 15.

Spheroidal waves in crystals, 63.

Spheroids, lemma about, 103.

Sound, speed of, 7, 10, 12.