LAWS OF DECREMENT. 361 



RHOMBOID. 



This angle is supposed generally to be 

 measurable by the goniometer; but it may 

 sometimes require to be deduced from the 

 inclination of secondary planes to each other 

 or to the primary. If two planes modifying 

 the edge itself be used to determine the 

 angle / we must know the inclination of 

 those planes to each other, and that of one 

 of them on the adjacent primary plane ; and 

 hence the inclination of the primary planes 

 is known. 



If we know the inclination of the plane a 

 of the modification of the rhomboid, to the 

 plane P, and call it /, we may determine /, 

 from the following equation, 



, j j . _ cos. 30. sin. (ISO /) 



" ~ll~ 



It is apparent from the above fig. that if 

 (180 /) and | I, be taken as two angles 

 of a spherical triangle, the third angle must 

 be 90, and the side subtending the angle 

 | /, must be 30. and hence the given equa- 

 tion is derived. 



If we know the inclination to the plane 

 P, of that plane of mod. e which replaces 

 the inferior angle of the plane P, we may 

 still deduce /, from that inclination, by the 

 preceding formula. For plane e on P is 

 obviously 270 /, and consequently 

 1 270 (e on P). 



The inclination of the adjacent planes at the in- 

 ferior edges will consequently be (180 / t ) 

 and may be called J 2 , 



