LAWS OF DECREMENT. 327 



OCTAHEDRON WITH A SQUARE BASE. 



then use of the triangle ; and hence results 



the relation we have given. 



From which, if any two of these angles be known, 

 the third may be immediately found. 

 Hence it is apparent that the angle /, being 

 known, all the other elements of the form may be 

 known also. 



Its units of comparison. 



The unit of comparison is zz 1 in reference to the 

 following decrements. 



1st. Those which affect the terminal angles, the 



four edges of the pyramid being equal. 

 2d. Simple and mixed decrements on the lateral 

 angles ; these being measured by the pro- 

 portions intercepted of the equal lines h *, 

 h i. drawn from the angle h perpendicularly 

 on the edges afand d c. 



3d. All decrements on the terminal edges, which 

 are measured by the proportions intercepted 

 of the equal lines b a, b e. 

 4th. Those on the edges of the base, which are 



measured on the lines c d, ef. 



But in relation to intermediary decrements on the 

 lateral solid angles, the unit is constituted of the 

 ratio of the terminal and lateral edges ; which is evi- 

 dently that of sin. A v : sin. A z . 



Simple and mixed decrements on tht terminal angles. 



If we measure the inclination of P to the adjacent 

 plane belonging to class &, and call the angle / 3 , we 

 have 



sin. (180 /J 



