. 38. OF FORMS IN GENERAL. 83 



cipal sections, in particular, allow of many interesting ap- 

 plications, both in Crystallography and in Optics. In Op- 

 tics, however, the term principal section is applied only to 

 those planes, which pass through the principal axis. 



In the hexahedron, Fig. 1., the principal section ACEG 

 passes through the parallel diagonals AC and EG of two 

 opposite faces, and through the edges joining them AE and 

 CG, forming an oblong or rectangle. In the rhombohe- 

 dron, Fig. 7> one principal section ABXC passes through 

 those diagonals of two parallel faces AB and XC, which join 

 different solid angles with each other, and through the in- 

 termediate edges AC and BX, forming a rhomboid. An- 

 other principal section C'C'^'B", passes through the dia- 

 gonals of parallel faces C'C" and B'B", joining equal solid 

 angles with each other, and through the intermediate edges 

 C'B" and C"B', forming a rectangle. Two or more prin- 

 cipal sections, of equal and similar figure, and similarly 

 situated, are accounted as one. Some forms, as the rhom- 

 bohedron, have more than one ; others, as the tetrahedron, 

 no principal section at all. The consideration of these sec- 

 tions is not of equal importance in all forms. 



It is not necessary to carry the distinction of these sec- 

 tions any farther, than to such as yield regular, or at least 

 equiangular or equilateral figures. If, therefore, sections 

 in general are mentioned, only sections of that description 

 are to be understood, 



. 38. HOMOLOGOUS SECTIONS. 



Sections, which either possess similar figures, or 

 which assume them, if reduced to the same distance 

 from the centre of the solid, or in which the junc- 

 tion of certain points, by straight lines, produces si- 

 milar figures, are termed sections of the same 

 kind, or Homologous Sections. 



There are two sets of homologous sections in the hexa- 

 hedron, containing on one side all the squares, as A'B'C'D',, 

 VOL. i. c 



