302 APPENDIX CALCULATION OF THE 



As it will not be necessary to repeat even the for- 

 mulaB in all the cases which are to follow, it may not 

 be useless again to observe that when a law of decre- 

 ment producing any plane is to be determined, the 

 general symbol of that plane is to be first discovered, 

 and then the particular values of its indices to be 

 found. 



In simple or mixed decrements^ these values are 

 deduced from the ratio of radius to tangent a, or of 

 sin. a to sin. &, as we have already seen ; a and b 

 representing the particular angles in each particular 

 case. 



The following may be regarded as the general pro- 

 cess for determining the law of an intermediary decre~ 

 ment. 



1st. To measure the inclination of one of the 

 secondary planes on two of the adjacent 

 primary planes. 



2d. To determine the two plane angles at the ter- 

 mination of the greater edge of the defect 

 of the primary form occasioned by the plane 

 we have measured. 



3d. From a knowledge of these plane angles, and 

 of the plane angles of the primary planes, to 

 deduce the ratios of the edges of the defect. 



4th. When the primary edges are unequal, to divide 

 these ratios by the ratios of the correspond- 

 ing edges of the primary form, and thus to 

 deduce the law of decrement. 



5th. If the intermediary decrement has taken place 

 on an octahedron, to determine the fourth 

 edge of the defect by a method which will 

 be described when we apply our calculations 

 to the regular octahedron. 



