CHAP, i.] MIRRORS AND REFLECTING INSTRUMENTS. 211 



FIG. 148. Geometric pr inciple of 

 the goniometer: rotatory angle 

 of the crystal. 



by the second face of the crystal. This latter has then taken the two 

 positions indicated by the figure, and each face has turned through the 

 angle a (Fig. 148). 



The reading of the angle of rotation of the limb gives in degrees 

 and fractions of degrees, not the angle of the crystal itself, but its 

 geometrical supplement, a, from which the 

 first is deduced by a sin] pie calculation. 



Babinet's goniometer consists of a hori- 

 zontal graduated limb, carrying a collimator \ / ' / / 

 always fixed on a radius of the circle. This is 

 a telescope having in the focus of its eye-piece 

 two crossed threads. A second movable tele- 

 scope with an index and vernier turns round 

 the centre, or may be fixed in any position by 

 means of a clamping screw. Lastly, a plat- 

 form placed at the centre of the circle, is made to turn on a ver- 

 tical axis, and is furnished with an index and vernier which serve to 

 measure the angle of rotation. On this platform the crystal is placed, 

 taking care to have the edge of the angle to be measured vertical. 



Let us now see how the angle is measured. 



First, the movable telescope is 

 fixed in a position which makes a 

 certain angle with that of the col- 

 limator ; the zero of the index ver- 

 nier is brought opposite the zero of 

 the graduated arc, and the stand on 

 which the crystal rests is turned 

 until the micrometer-thread in the 

 eye-piece is made to coincide with 

 the image of the micro meter- wire of 

 the collimator seen by reflection by 

 one of the faces of the crystal. 



Now, the crystal is again turned, 

 but this time by the aid of the arm 



attached to the platform, until the same coincidence takes place by a 

 reflection from another surface. 



The angle of rotation measured by the movable arm is that of 

 the normals to the reflecting surfaces, so that by calculating the 



FIG. 149. Babinet'j reflection goniometer. 



