LAWS OF DECREMENT. 367 



RHOMBOID. 



parallel to its diagonal, to be called / 4 , the ratio of 

 the edges of the defect will be as 



sin. (/ 4 A & ) : *in. (ISO 1 7 4 ). 



This being divided as before by cos. \A l : R, will 

 give the law of decrement producing the plane we 



have measured. 







Simple and mixed decrements on the lateral angles. 



Let us suppose the inclination known of the pri- 

 mary plane P, to one of the adjacent planes of mod. A, 

 and let this be called 1 5 . The angle measured, 

 would be in the plane e b w, fig. 358. And as e b is 

 perpendicular to b n, the ratio of the edges of the 

 defect would be as radius to tang, of the supplement 

 of the measured angle; and this beii g divided by 

 cos. \Ai : R, will give the required law of decrement. 



Intermediary decrements on the terminal solid angles. 



The general symbol representing a single plane of 

 mod. d is (B P B' q B"r). 



The values of the indices /?, q, and r may be dis- 

 covered from the inclination of the particular plane 

 represented by that symbol, on the two adjacent pri- 

 mary planes, by means of a spherical triangle, and 

 the plane triangles, adapted in the manner already 

 described. 



Intermediary decrements on the lateral solid angles* 



These, as we have already seen in our account of 

 the symbols representing the planes produced by 

 them, may be referred to the angle at O, or to that 

 at E. Let the plane from which we are about to 



