358 APPENDIX CALCULATION OF THE 



HEXAGONAL PRISM. 



The individual or particular prisms belonging to 

 the seven preceding classes are, as we have seen, 

 distinguishable from each other by the comparative 

 lengths of two or three of their adjacent edges, or by 

 the particular values of some of their plane angles. 



These plane angles may be determined by means 

 of spherical trigonometry from the inclination of the 

 primary planes to each other; and this inclination 

 may be ascertained by measurement with the gonio- 

 meter. 



But the comparative lengths of the edges can be 

 deduced in no other manner than from some second- 

 ary plane, which, for that purpose, must be supposed 

 to have been produced by a given law of decrement. 



If for example we assume that, any known second- 

 ary plane has been produced by a decrement by 1 row 

 of molecules, the ratio of the edges of the defect of 

 the primary form would, as we have already seen, be 

 equal to the ratio of those edges of the primary form 

 of which they are respectively portions. 



If therefore we determine the ratio of the edges 

 of the defect occasioned by the interference of the 

 secondary plane, which we suppose to have been pro- 

 duced by a decrement by 1 row of molecules, we 

 shall, if our supposition be correct, evidently obtain 

 the ratio of the corresponding primary edges. 



But it may happen that the plane which we have 

 supposed to result from a decrement by 1 row of 

 molecules, is really produced by some other law of 

 decrement. 



The only method we possess of discovering whether 

 we have determined the true dimensions of the prism, 

 is to use those dimensions for ascertaining the laws 

 of decrement producing other secondary planes ; and 



