STUDY OF ORES AND METALS. 423 



refractive index but weak birefringence, such as apatite, do not ex- 

 hibit the required difference in intensity (2 per cent.) of the reflected 

 components ; and that, if the observations were Hmited to this phe- 

 nomenon, the anisotropism of the mineral would escape detection. 

 In other words the sensitiveness of methods based on the relative 

 intensity of the two reflected components is far below that for de- 

 tecting anisotropism in transmitted light. Thus it is not difficult in 

 ordinary thin sections (0.02 mm. thick) to detect a path difference of 

 2/XjU,; this corresponds to a birefringence of o.oooi. For a mineral 

 of refractive index 1.6 the least detectible birefringence by reflected 

 intensities is about 0.070. In other words the methods of trans- 

 mitted light are 50 or more times as sensitive as the methods based 

 on intensity differences of reflected intensities. This follows as a 

 direct result of the lack of sensitiveness of the eye in detecting dif- 

 ferences in intensity of adjacent fields. 



Methods based on equation (34) depend on the ability of the eye 

 to determine the position of complete darkness (intensity of illumi- 

 nation =0) ; the chief factor which limits the degree of precision 

 attainable by this method is the threshold limit of vision or the least 

 quantity of light which the eye can detect. Experience has shown 

 that it is not difficult to detect, under ordinary conditions of illu- 

 mination with the aid of certain devices, a rotation of the plane of 

 polarization through 5'. Substituting this value in equation (34) 

 we obtain 



n„ — n^ = o.oois(>h-\- i)(n.,— i). (36) 



A comparison of this equation with (35) shows that this method is 

 at least three times as sensitive as the first. The precision attain- 

 able by the second method is dependent, moreover, on the sensitive- 

 ness of the device employed to detect a rotation of the plane of 

 polarization. Without any special device an error of >4° is readily 

 possible. In this case the accuracy of this method is considerably 

 less than that of the intensity dift'erence method. In case a device 

 is used which shows a perceptible difference for a rotation oi }i° 

 the precision attainable by the two methods is identical. The ac- 

 curacy of the second method can, however, be increased by using a 

 very intense source of light. The several methods for determining 



