!LAWS OF DECREMENT. 387 



and . . df: d g :: sin.45 39' 22" : sin. 32 25' 38" 

 .: 7152 : 5360 



:: 4 : 3 



If we again dispense with the use of natural sines, 

 we may still derive the same result by means of the 

 logarithms of those sines. 

 For log. sin. 54 10' 4" = 9-9088794 

 log. sin. 23 54' 56" = 9-6078695 



0-3010099 



The natural number corresponding to this result- 

 ing log. is 2 very nearly, which may be represented 



2 4 

 by the fraction zz 



And log. sin. 45 39' 22" = 9-8544077 

 log. sin. 32 25' SS" =: 9*7293493 



0-1250584 



The natural number corresponding to this resulting 

 log. is 1-3337 =. ]l 3337 = i, which gives the same 



law of decrement as that already found. 



The general symbol to represent the plane e f g, 

 would be (B'r B P B" q ), and its particular symbol 

 will be found by substituting in this general symbol, 

 for the letters p, q, and r, the particular values of 

 the indices as we have just found them. We shall 

 then have the symbol (B'2 B4 B"3), which repre- 

 sents this particular plane, and signifies that the 

 compound molecule abstracted in the production of 

 this plane belongs to a treble plate, or is 3 molecules 

 in height, 2 in the direction of the edge B', and 4 in 

 the direction of the edge B. 



3 c 2 



