METHODS OF PETROGRAPHICAL RESEARCH. 217 



These enable us, for instance, to find at once the extinction- 

 angle and birefringence for a section of known orientation. 

 The actual problem is, in a sense, the converse of this, and 

 the means of solving it in numerous important cases are 

 found to be furnished by these figures, or by the properties 

 which they represent. Certain zones, of which that per- 

 pendicular to the brachypinacoid is the most important, are 

 closely discussed, and it is shown that a section lying only 

 near that zone is sufficient in general to give a result. 

 Further, it is shown that, if a number of random sections of 

 one kind of felspar be examined, the values obtained for their 

 extinction-angles will tend to cluster about certain favourite 

 numbers, which are characteristic for that particular felspar. 

 Thus, for anorthite, the numbers most frequently found will 

 be 32 and 41 , and the chances are three to one that any 

 random section will give an extinction-angle over 30 ; 

 while other felspars have scarcely less characteristic pro- 

 perties. 



In the same work Michel Levy treats more fully of the 

 tests by which a chance section approximately parallel to 

 the brachypinacoid may be recognised, and the measure- 

 ments by which the several felspars can be unequivocally 

 distinguished in such a section ; and he shows in addition 

 that a slight departure from accurate orientation produces 

 in this case very little error. He also considers sections 

 perpendicular to each of the axes of optic elasticity and the 

 optic axes, and shows that their extinction-angles may be 

 utilised with advantage in distinguishing some of the 

 felspars. 



In conclusion he discusses the use of refractive indices 

 for the discrimination of the felspars in rock-slices. A 

 valuable paper by Becke (19) had already appeared, in 

 which this subject is treated with much ingenuity, leading 

 to useful practical results. Briefly his method consists in 

 comparing the refrangibility of the felspar examined with 

 that of quartz. It is applicable when the two minerals are 

 in contact in the slice, along a surface which is cut nearly 

 at right angles by the plane of section. A diaphragm 

 being arranged to give a slightly convergent pencil of light, 



