In the figure, OA is an optic axial direction in the crystal, OB is
the direction of optic axial emergence into air, and OC is the direction of emergence into a liquid of refractive index g; ON is the
normal to the crystal plate. Then a, the angle of emergence into air,
is NOB, whilst 9,the angle of emergence into the liquid is NOC
and sin « / sin 9 — g ;it is required to calculate the angle «, from
the observed value of a. — 9.
Then, since sin a/sin 9 — g, 1 sin {a — (a —#)} g ~~ sin a sin cl cos (a—(?) — cos cl sin (a—(?) sin a = cos (a — (?) — cot clsin ( ) and . co U = “ * ( * - 0 - „ sin(a- r g ) ........................ (!) Or again, since sin a/sin 9 = «, g +1 _ sin a 4- sin 9 g —1 sin cl— sin whence sin-|(a + (?) cos -§(a —(?) sin |( a —(?) cos-|(a + (?) ’ a + 9 tan ------ 2 tan JLL--1 OC— 9 2 (2)
a form more convenient than (1) for logarithmic calculation.
To test the accuracy of the method, measurements have been made on biaxial plates of different optical properties, liquids of various refractive indices being used. The index of refraction of the liquid employed is conveniently determined with the Pulfrich refractometer ; the refraction is so affected by differences of temperature and of purity that it is necessary to determine it for the liquid as actually used; the liquid does not need to be specially purified. The measurements given in the two appended tables were made on plates of topaz, each of them cut perpendicularly to the acute bisectrix. By measurement of the optic axial angles, the apparent emergences into air for sodium light were found to be 53° 24' and 54° 42', respectively.
These two sets of measurements suffice to show that the method possesses very considerable accuracy, although the values of <x.—9 measured are not very larg e; the numbers also seem to indicate
