LAWS OF DECREMENT. 

 REGULAR OCTAHEDRON. 



this purpose let us imagine the defect of the primary 

 form to be divided by a plane passing through the 

 edges a h, af, and let a hfg represent one half of this 

 defect. 



The inclination is known of P on P' 5 and called /,, 

 and of the new plane on P', which we shall call 1 5 . 

 Hence from a spherical triangle whose angles are 

 90, I /!, and (180 / 5 ), we may deduce the plane 

 angles afg, af h, which we shall call^ 2 and^ 3 . 



The formulae for this purpose are the following : 







sin. i , 



we know the angle fa g n: 60 

 fah=:90 



whence we deduce 



af: a g :: sin. (120 A z ) sin. A 



sin A 



. _ 



sin. (120 A z ) 



and af: a h :: R : tang.^ 3 



:: p : 



:: P ' r 



and by substituting for p, q, and r, in the general 

 symbol of the class of modifications to which this 

 plane belongs, these particular values, we shall obtain 

 the symbol of the particular plane we have observed. 



