This second nicol, called the analyzer, is so constructed as to revolve freely about its longitudinal axis, and is attached to a graduated circle in such a way that the degree of rotation can be accurately read. If the planes of polarization of the two nicols are coincident when prolonged, the ray of light passing from the first nicol will pass through the second practically unchanged in character or intensity. If, however, the analyzing nicol be turned until the plane of polarization is at right angles to that of the polarizer the immergent ray will suffer refraction in such a manner as to be totally reflected when reaching the film of balsam and will be thus entirely lost. In making a complete revolution of the analyzer, therefore, two positions of maximum intensity of light and two of darkness will be observed. In intermediate positions the ray immergent to the analyzer will be separated as in the first instance into two rays _g p_ varying intensities, one of which will be always totally reflected. [Illustration: FIGURE 32. THEORY OF THE NICOL.] In Fig. 32 is given a more detailed illustration of the action of the rays of light. The film of balsam is represented as enlarged and of the thickness _bb_. Draw the perpendiculars represented by the dotted lines _n_₁ _n_ʹ₁, _n_₂ _n_ʹ₂, _n_₃ _n_ʹ₃ and _n_₄ _n_ʹ₄. In passing into the prism at _m_ both refracted rays are bent towards the normal _m n_ʹ₁. The degree of deflection depends on the refractive index of the two rays 1.52 and 1.66 respectively. The refractive index of the extraordinary ray in calcspar being 1.52, and in Canada balsam 1.54, it suffers but little disturbance in passing from one to the other. On the other hand the balsam, being considerably less refractive for the ordinary ray than the calcspar, causes that ray to diverge outwards from the normal _o n_ʹ₂, and to such a degree as to suffer total reflection. The critical angle, that is the angle at which a ray issuing from a more refractive into a less refractive medium, emerges just parallel to the bounding surfaces, depends on the relative index of refraction. In the case under consideration the ratio for balsam and spar is 1.54/1.66 = 0.928 = sin 68°. Therefore the limiting value of _m o_ _n_₃ so that _m o_ may just emerge in the direction _od_ is 68°. If now _mo_ were parallel to _o d_ the angle _m o n_, would be just 68°, being opposite _b a d_. which has been ground to 68° in the construction of the prism. But in passing into the prism, _m o_ is refracted so that the angle _m o n_₃ is greater than _b a d_. It is therefore always certain that by grinding _b a d_ to 68° the ordinary ray _m o_ will be with certainty entirely thrown out in every case. In respect of the analyzing nicol the following additional observations will be found useful. In all uniaxial crystals there are two directions at right angles to each other, one of greatest and one of least resistance to the propagation of luminous vibrations. These planes are