LAWS OF DECREMENT. 545 



RIGHT RHOMBIC PRISM. 



Fig. 349. 



The unit of comparison for decrements on the 

 terminal edges, is the ratio of the line fg, fig. 349, 

 toy/; fg being perpendicular to i k, and conse- 

 quently to a b. For the law of decrement is to be 

 determined from the inclination of the plane abed, 

 to one of the primary planes, let us suppose to JP, 

 which inclination would be measured on the lines 



P* fi fi f[ t 



& * 



It is evident that the line fg falls within the de- 

 scription already given of the lines from which the 

 unit of comparison may be derived ; for, whatever 

 the law of decrement may be which produces the 

 new plane abed, we must have 



fh :Jb :: fg : fk. 



The ratio offg to f I may be thus discovered. We 

 are supposed to have found 



fk : fl :: m : n .: 1 : - 



and knowing the angle efk, which we have called 

 A,, we known the angle gf k =^4 l 90. 

 hence fk:fg::R: cos. (^,90) 

 1 cos. (^,-90). 



~TT~ 



wherefore fg:fl :: cos. (^,-90") . n 



:: m cos. (A , 90 n ) : n R. 



