366 APPENDIX CALCULATION OF THE 



RHOMBOID. 



various relations between that primary form and its 

 numerous secondary forms, occupy a considerable 

 portion of the Abbe H ally's crystallographical re- 

 searches. Some, however, of the relations he has 

 demonstrated, though curious in themselves, are not 

 immediately useful to the mineralogist for deter- 

 mining the mineral species to which a given crystal 

 belongs. 



Little more will be attempted here than to give an 

 outline of a method of determining the laws of decre- 

 ment, similar to that which has been applied to the 

 other classes of primary forms; and it is hoped that 

 this will supply the mineralogist with as much assist- 

 ance as his purposes will generally require. 



Simple and mixed decrements on the superior and 

 inferior angles. 



The planes produced by these are contained in the 

 classes b, c, e g, and k. 



Let us be supposed to have measured the incli- 

 nation of one of the planes b on an adjacent primary 

 plane, or of one of the planes c, over the summit on 

 a primary plane, and if we call the measured angle 

 / 3 , the ratio of the portions of the oblique diagonal 

 and edge contained in the defect, would be as 

 sin. (I 3 A & ) : sin. (180 / 3 ), 



and if we divide this ratio by c __fLj L, we shall 



R 



obtain the law of decrement producing the plane we 

 have measured. 



Let us suppose the inclination of one of the planes 

 belonging to the classes e, g-, or k 9 on that primary 

 plane which i&. intersected by the modifying plane 



