APPLICATION TO AUGITE, ETC. 375 



A = D = F=0; B=(n-\-m)cota; C=~2cota; mid E = m — n. 

 Hence, from § 6 — 



, — ^ ■ r, — ^ cos (p 



Since siii^ 6 -f cos' <^ = 1, we have — 



B' cof <p + E' cos' <f r= C\ 



Now we can put a = [^ and b = (^-^' , and we may call cos' <f 

 i. e., coC (f = Y 2^ Accordingly— 



(-t) 



ax 



-=^ + ^=6; To) 



whence- 



"^ ^ 2—) - ^- ^6) 



2 - V 



-D , , 1 + COS 2 cT 



i3utasa;== cos-c^= v> 'equation (1) follows at once from (6). We 



may develop it into a rapidly converging series. Moreover, putting h in 



-• /o\ 1 • •> COS' 



equation {6) we have sur 6 = —-. Substituting 2 ^ and 2 c> for 6 and <f, 

 we obtain (2). 



In number* 909, for example, there is an augite twin, quite obliquely 

 cut, which is sketched in figure 2a. From it we have the following data : 

 The trace of twinning (100) is parallel to the vertical cross-hair when the 

 rotating stage is at 7°.l. Similarly for the trace of (iTO) we have 340.°9 ; 

 for (110), 63°.l. Hence n = cot 26°.2 = — 2.0323, and m = cot 56°.0 =' 

 0.67-45, and we have the following solution : 



cot a = cot 46° 27' ; log. cot a = 9.97S0 

 771 — 71 = 2.7068 ; log. m — n = 0.4324 



Subtract 9.5456 X 2 = 9.0912 ; 

 7/1 4- 71 = — 1.3578 ; log. m -\-n = n 0.1328 



Add to the above : n 9.6784 X 2 = 9.3568. 



Log.-i 9.0912 = 0.1234 ; log.-^ 9.3568 = 0.2274 = a. 

 Multiply 0.1234 by 4, and we have 0.4936 = h. 



The numbers refer to sectioas in the collections of the Michigan State Geological Survey. 



