Prof. Chapman's Mineralogical Notes. 



117 



The following simplified formulae for the determination of the 

 relative length of the principal axis in rhombohedrons, from the 

 angle over a polar edge, will be found, I believe, more expeditious 

 in the working than any that have been hitherto proposed. 

 They are adapted to the ordinary logarithmic tables, and are so 

 arranged as to be conveniently employed by persons but little 

 accustomed to crystallographic calculations. 



Let a = half the given angle over a polar edge ; b the incli- 

 nation of a face of the rhombohedron on the principal axis ; and 

 p the principal or vertical axis required, the other axes being 

 unity. Then 



log cos b = log cos a + 0*0624694 ; 1 



log/? =log cot b - 10*0624694. f 



Or, let a and p stand as above, and let c = the inclination of 

 a polar edge on the principal axis. Then 



I. 



log cos c=log cot a-0-2385606 ; 

 log/? =log cot c-9-7614394 



.'} 



11. 



If the rhombohedron under investigation be not assumed as 

 the protaxial form, the value of/?, thus found, must be compared 

 with the protaxial value. Thus, in calcite, p in the form R = 

 0-854, and in the form 4R, 3-416. 



The accompanying figures may serve to illustrate the con- 

 struction of these equations ; but it should be remarked, that 

 the letters in the figures have no reference to those given above. 



I. 



[Fig. 4.] 



A = 60°; B=5^?; C = 90°. 



Here A and B are given to find b. 

 cosB 



Fig. 4. 



cos 6 = 



sin A* 



Fig. 5. 



[Fig. 5.] 



A = 30°;C = 90°; b = b found 

 by the first equation. 



Here A and b are given to find c. 



cos A 

 cotc= - — r-. 

 tano 



