LAWS OF DECREMENT. 295 



of the cube or regular octahedron, or g, or i, of the 

 right rhombic prism, &c. the lines whose ratio con- 

 stitutes the unit of comparison in such cases, will 

 always be equal. 



And the units of comparison for determining any 

 law of intermediary decrement, will always be the ratios 

 of the edges which meet at the solid angle on which the 

 decrement has taken place. 



Fig. 326. 



To ascertain the ratio of the edges of the defect of 

 the primary form, when a decrement takes place 

 on an edge of any parallelepiped, fig. 326, we must 

 suppose the inclination of the primary planes to each 

 other to be known, and the inclination of the modi- 

 fying plane a b cf, to the primary planes P and T. 



Fig. 327. 



Now to determine the ratio which the line i , 

 bears to i c, we require the angles of the plane tri- 

 angle i b c. These may be obtained by means of a 

 spherical triangle, fig, 327, whose angle A is the 



