LAWS OF DECREMENT. 323 



RHOMBIC DODECAHEDRON. 



gh.g t, h i, in fig. 340, may be regarded as edges of 

 the base of an irregular tetrahedron, of which the 

 obtuse solid angle would be the summit. 



Simple and mixed decrements on the acute angles. 



An analogy similar to that which subsists between 

 the obtuse solid angle of this form and the solid angle 

 of the regular tetrahedron, will be found to subsist 

 between its acute solid angle and the terminal solid 

 angle of an octahedron. For the lines da, af, may 

 be regarded as edges of the base of an irregular octa- 

 hedron, and obviously of one with a square base. 



Let the inclination of P on an adjacent plane of 

 class &, be known and called I 5 

 The inclination of P on P' is 90. 



whence %L 



R 



q tang. (180"-/ 5 ) 



Intermediary decrements on the acute solid angles. 



These, like those on the octahedron, are of two 

 kinds, and produce the planes of mod. c and d. 



Let P on one of the planes belonging to mod. a be 

 measured, and its angle called I 6 . 



Its symbol might be (B P B' q b' q br), and those 

 indices may be determined by the method adapted to 

 the corresponding plane on the regular octahedron ; 

 observing, however, that as the plane angles, and the 

 mutual inclination of the primary planes, vary from 

 those of the regular octahedron, there will be a cor- 

 responding variation in the terms of the ratios which 

 give the values of/?, <?, a "d r. 



2 s 2 



