THE MICROSCOPE BY MEANS OF THEIR OPTICAL CHARACTERS. 613 



retardation. Usually, however, while one of the steps faite to 

 neutralise the section, the next higher will more than do so, and 

 neither will be completely dark. If they are equally bright, 

 the relative retardation of the section must be midway between 

 those of the two steps. If one be darker than the other the 

 relative retardation will be proportionately nearer to that of 

 the darker step. In this way it will be possible to estimate the 

 relative retardation to within twenty or thirty micro-millimetres. 



If a further approximation be desired it may be obtained by 

 employing additional smaller mica steps divided into four portions 

 with twenty, forty, sixty and eighty micro-millimetres relative 

 retardation respectively. If the larger mica steps are inserted in 

 the lower slot, the smaller can be placed in the upper. In this 

 way it is possible to determine relative retardation to within 

 ten micro-millimetres and make estimations to within half that 

 amount. 



Mica steps are one of the many useful pieces of apparatus 

 devised by Fedorov, but the description given above differs 

 from his directions in some details, having reference chiefly to 

 the amount of the relative retardation represented by each step. 



Mica steps may be calibrated by reference to a quartz wedge 

 the errors of which have already been determined. 



In order to obtain the birefringence of the section from the 

 relative retardation it is necessary to determine the thickness. 

 As this will usually involve the movement of the rock-slice it 

 is better postponed till after the " directions-image " has been 

 examined. For the same reason the determination of the 

 refractive index should also be deferred to a later stage. 



The Directions-Image. 



It is frequently desirable to examine simultaneously the 

 optical properties of a number of different directions in a mineral, 

 so that a comprehensive idea of its optical characters may be 

 obtained. For this purpose the microscope is, in the manner 

 which will be described, converted into an optical instrument 

 in which every point in the image corresponds not to a point 

 in the object under examination, but to a direction along which 

 light traverses that object in parallel paths. Such an instrument- 

 may be conveniently described as a hodoscope or path viewer, a 



