LAWS OF DECREMENT. 333 



OCTAHEDRON, RECTANGULAR BASE. 



Its units of comparison. 



The unit is z= 1 in reference to all decrements on 

 the terminal angles, and to decrements on the edges 

 of the base. 



For simple or nvxed decrements on the lateral 

 angles, the unit will be the ratio of the perpendiculars 

 b 7t, b /, drawn from the angle at b perpendicularly 

 on the edges fd and e m. The ratio of those lines 

 may be thus determined. 



fb : k b :: R : sin. V kfb = A, 

 b m fb i b I :: R : sin. \J b m I zz A t 

 whence . . . k b : b I :: sin. A , : sin. A a 



When the decrement is conceived to proceed along 



the plane P. the unit of comparison will be ?3- L 



sin. A % 



but when the decrement proceeds along the plane M, 

 the decrement in breadth will evidently be measured 



by the line b I, and the unit will then become sin 3 



sin. A t . 



Fig. 344. 



The laws of decrement on the terminal edges may 

 be determined from the lines b a, b c, drawn perpen- 

 dicular to the edge f 6, on which a decrement is sup- 

 posed to have taken place, and meeting the edges 



