310 



APPENDIX- 



CALCULATION OF THE 



REGULAR TETRAHEDRON. 



back plane of the figure, be known and called J 3 , the 

 preceding formula will give the law of decrement 

 producing that particular modification. 



Intermediary decrements. 

 Fig. 333. 



The law of an intermediary decrement on an angle 

 of the tetrahedron, is determined by the ratios of the 

 defect or intercepted portions ae, af, a g, of the three 

 primary edges a b, a c, a d. 



Let efg, fig. 333, be one of the six planes pro- 

 duced by a modification of the tetrahedron belonging 

 to class d. 



The general symbol representing a single plane 

 belonging to this class is (B P B' q B"r), p representing 

 the number of molecules contained in af, q the num- 

 ber contained in a g, and r the number contained 

 in ae. 



To determine the ratios of a e : af : a g, we re- 

 quire the plane angles af e, afg; from which, as we 

 know the angles e af, f a g, we may deduce the 

 angles a ef, a gf. 



To obtain the plane angles afe, afg, we may 

 have recourse to a spherical triangle. 



