LAWS OF DECREMENT. 307 



CUBE. 

 Tir i IT i. & COS. (180 / 2 ) 



We shall have cos. A, = : i =-? 



sin. (180 / 3 ) 



A R. COP. (180 /,) 



and cos. A 2 = _ -A ^ 



sin. (180 / 2 ) 



The plane angles being thus found, we have 

 a i : i c : : p : q : : R : tang. A l 

 a i : i b : : p : r : : R : tang. -4 2 . 

 We may determine these particular values of the 

 ratios of p : q, and p : r, by means of the tables of 

 natural tangents, or by logarithms. 



Decrements on the edges of the cube. 



Let the inclination of the plane P on the plane/, 

 or &, adjacent to it, be called / 4 . 



?= *- 



q tang. (180/ 4 ). 



Throughout the remainder of this appendix, when 

 the law of a simple or mixed decrement is expressed by 



^, the letter p will always be understood to denote the 

 decrement in breadth, and q the decrement in height. 



