LAWS OF DECREMENT, 375 



Fig. 361. 



Let fig. 361 represent a section of any crystal whose 

 planes af, a g', are perpendicular to each other, and 

 let the lines b c, b d, b e^ be sections of planes modify- 

 ing the edge or angle g a f. 



Thus let us suppose that we have the law of decre- 

 ment given by which the plane b c has been produced ; 

 and let the required angle g c b be called /. 



Let the ascertained ratio of the edges a g, a f, be 

 as 5 : 4, and the law of decrement producing the 

 plane b c, be 1 row of molecules. 



It follows that a c : a b :: 5 : 4 :: 1 : -. 



5 



But we also have a c : a b :: R : tang. (180 /) 



therefore - = '8 = tang. (ISO /) 

 5 



and &, in the table of natural tangents, is the tang, 

 of angle 38 40' nearly, = ISO /; 

 therefore / ISO (38 40') = 141 20'. 



If we suppose b d the section of a plane resulting 

 from a decrement by 2 rows in breadth, we should 

 obviously have 



adiab :: 10:4 :: 5 : 2 :: 1 : -. 



5 



And if we call the angle g d b, /', we must have 

 a d : a b :: R. tang. (180 /') 



