LAWS OF DECREMENT. 311 



REGULAR TETRAHEDRON. 



The plane representing class d, on the figure in 

 the tables of modifications, which corresponds to the 

 plane e fg of fig. 333, is that which rests on the edge 

 between P and P' and inclines on F'. 



Let the inclination of this plane on P be called / 4 . 



........ V . . .1,. 



and let the plane angle afe be called A 5 . 

 ....... afg . . . A 6 . 



we shall have sin. | A, == 



L O 



V 



- J 4 )+(180-/ 5 ) ]cos4[ I 



sin. /n sin. / 4 



and sin. A 6 =z 



^ / 



I/ 



sin. /, sin. 1 5 



Having from these formula deduced the angles 

 A 5 and A 6 , we have 



/: a g :: p : q :: sin, (120 A 6 ) : sin. A 6 



sin. A 6 



sin. (120 A 6 ) 

 a f: a e :: p : r :: sin. (120 yl/ 5 ) : sin. A 5 

 .. I . sin.^ 5 



* sin. (120" J 5 ) 



Hence the particular values of p, <y, and r, being 

 found, and substituted for those letters in the general 

 symbol (B P B' q B"r), 



we shall obtain a symbol representing the particular 

 plane we have observed. 



