0. Andersen — Aventurine Feldspar. 363 



and r are computed from the readings is easily seen. The 

 formulae for the calculation of p from * and r have been given 

 before (p. 359). 



Direct measurements of the angles p could be made occasion- 

 ally when lamellae were exposed on fracture faces. These 

 measurements were, of course, in no way different from ordi- 

 nary goniometric angle measurements. 



In determining the angles p by measuring the angles * and r 

 we should theoretically obtain two values owing to the double 

 refraction of the feldspar. The deviation between these 

 values is, however, always so small as to be negligible even if 

 a high degree of accuracy were desired. It was, in fact, in 

 most cases, impossible to distinguish two signals in the goni- 

 ometer telescope. 



The color dispersion of the light observed in the same 

 measurements (see p. 361) was also insignificant and it was 

 without noticeable influence on the accuracy of the results 

 when white light was used instead of monochromatic. 



The relative accuracy of the goniometric measurements will, 

 of course, depend on the variable qualities of the cleavage 

 faces and the reflecting lamellae. Owing to the poor cleavage 

 faces after (010) compared with those after (001) (especially 

 in the plagioclases) signals reflected from or passing through 

 (001) were much sharper than signals influenced by (010). 



It should be noticed that the error in the determination of 

 an angle p is much smaller than the actual errors of measure- 

 ments of the angles i and r from which p is calculated, pro- 

 vided that the refractive index is approximately correct. This 

 is plainly inferred from the formulae p. 359. 



We find that the error in the angle determination in general 

 will increase in the order p P , p M , <f> P , <£ M . In the best deter- 

 minations of the angles p the probable error of single measure- 

 ments did not exceed that of ordinary goniometric measurements 

 of medium sharpness (2' — 3'). In the poorest determinations 

 of the angles <p it would reach 1/2° or more. (See Tables 

 2-12.) 



In most of the measurements the goniometer telescope was 

 used with a reducing attachment ; in a few cases with a lense 

 system of low magnifying power. Each angle value listed in 

 the tables (Tables 2-12) is the average of several (generally 5) 

 readings. 



Results of Measurements. 



The results of the microscopic and goniometric measure- 

 ments of the planes of orientation may now be briefly sum- 

 marized. 



