328 APPENDIX CALCULATION OF THE 



OCTAHEDRON WITH A SQUARE BASE. 



Intermediary decrements on the terminal solid angles. 



If we measure the inclination of one of the planes 

 of class c, on P, or of class d on P and P', we may 

 determine its law of decrement by means of formulae 

 similar to those which have been used for the analo- 

 gous modifications of the regular octahedron. 



The calculations relative to decrements on the 

 lateral angles of this form, require a little additional 

 illustration. 



Fig. 342. 



Let the inclination on P of the plane k I m, fig. 342, 

 which represents one of the planes of class/, be de- 

 noted by / 4 . 



A spherical triangle will give the plane angle of 

 the defect a k I, which we may call A & , by means of 

 the formula 



cos. A 5 = cot. |/ t cot. (180 / 4 ). 



R 



whence a k \.al :: p : q may be readily found, and 

 a m =2 r may be thus determined. 



I- ?_- I 



r " q p 



Let n op s represent a plane belonging to class g, 

 whose inclination on P is known and called / 5 . 



