340 APPENDIX CALCULATION OF THE 



RIGHT SQUARE PRISM. 



unit of comparison may be derived. For it would be 

 wholly intercepted by a decrement by 1 row, when 

 the edge a d is so intercepted. And the propriety of 

 adopting this unit will be apparent, if we recollect 

 that the inclination of two planes to each other is 

 measured upon lines perpendicular to their common 

 edge. 



Let the lines i h, h c, be perpendicular to the edge 

 of the secondary plane at the point h. The angle 

 i h c is all that can be known from actual measure- 

 ment of the crystal ; but from this we know the angle 

 i h a, and hence the ratio of a h to a i. The constant 

 relation of a c to a d, may be readily found. 



We are supposed to know the ratio of a m to af', 

 and a m : a f :: R : tang. \/ a m f 

 call \J a mj] A^ ; 



And because a c is perpendicular upon fm, we have 

 a c : a m or a d :: sin A , : R. 



Hence 55! ' becomes the unit of comparison in 

 R 



reference to simple and mixed decrements on the 

 lateral angles of the prism, the symbol representing 

 which would be P A P . 



For decrements on the lateral edges the unit is 

 = 1, and for intermediary decrements, the unit will 

 be the ratios of the particular edges affected by each 

 law of decrement. 



The general methods adopted for determining the 

 laws of decrement on the cube, may be applied to 

 this prism ; observing however the differences in the 

 several units of comparison afforded by the two 

 forms. 



