210 MINERALOGY 



* 



light RO enters at O, is refracted to O', and is again transmitted, on 

 leaving the prism, in the direction of O'R'. The angle of deviation 

 due to the prism is R'de = R'OV = 8. This will be at a mini- 

 mum, or is the least deviated, when the ray passes through the 

 prism symmetrically as drawn in the figure. 



i = ROn. The angle bac = a; dab = 1/2 a and axO 



~ - 



sin r 



aOl = lO'a = 90. VxOl = xaO = nOP = 1/2 a = r, the angle of 

 refraction. 



Draw O'e' parallel to Re, then from the symmetry of the figure the 

 angle e'O'R' = R'de = B = e'O'P + P'O'R', POR = dOx = e'O'P'; 

 also dox = P'O'R' = POR =1/28, but NOP = xOl = 1/2 a. 



i = NOR = i/ 2 a + i/ 2 8 and n = g^ = sin I/2 (a + S) , where 



sin r sin 1/2 a 



the angle a is carefully measured with the goniometer. 



The angle of least deviation is found as follows : The telescope of 

 the goniometer is set exactly opposite the collimator and the direct 

 ray through the Websky slit is observed and adjusted to the cross 

 hairs, when a reading is taken with everything clamped. 



The graduated circle and telescope remaining clamped, the 

 crystal is mounted and adjusted so that the edge at the angle a 

 is parallel to the vertical hair. It is then pushed in with the screw, 

 between the collimator and the telescope, until the image of the slit 

 disappears on looking in the telescope, the base of the prism 

 being to the left. With the graduated circle still clamped, the 

 telescope is ftow undamped and revolved to the left until the image 

 or signal reappears, then the prism is revolved back and forth 

 through a small arc, at the same time following the signal with the 

 vertical hair of the telescope. It will soon be seen that on revolv- 

 ing the prism there is a maximum position to the right for the sig- 

 nal, and having reached this position, even though the prism is still 

 revolved the same way, the signal moves up to this position then 

 reverses its motion or turns back. This maximum position marks 

 the point where the ray is symmetrical to the prism as drawn in the 

 diagram, Fig. 361. By moving both the telescope and prism at 

 the same time, the vertical hair is brought to this maximum posi- 

 tion of the signal and a reading taken. The difference between the 

 original position of the signal and this of the least deviation will 

 be the angle 8. When white light is used, there will be a series of 

 colored signals, one for each color, due to dispersion, but only one 



