. 4$. 43. 44. OF FORMS IN GENERAL. 37 



. 42. UPRIGHT POSITION. 



A form is said to be in its Uprigfit Position 

 when one of its principal axes is vertical. 



Forms that have only one principal axis are upright but 

 in a single one ; such as have more than one are upright 

 in several positions. If a form contains only axes of the 

 third kind, it is upright, when that axis is in the vertical 

 position, which is considered as its principal axis. 



In the subsequent inquiries, all forms, simple and com- 

 pound, are supposed to have been previously brought into 

 an upright position. 



. 43. PARALLEL POSITION. 



Two or several forms are in Parallel Position, 

 if the axes of the one are parallel to the homolo- 

 gous axes of the other. 



Two or several forms are in parallel position, if of the 

 axes of the one, only two are parallel to two homologous 

 axes of the other. For all the homologous axes intersect 

 each other in the centre of the form, at equal angles (. 39.) 



The parallel position cannot in general be perfectly de- 

 termined in forms which possess only one axis. Several 

 forms, moreover, may be considered in different positions. 

 It will be pointed out hereafter by what means, in these 

 cases, the parallel position must be determined. The diffe- 

 rent positions of forms are of great importance in all crys- 

 tallographic researches, if the object of these be more than 

 the consideration of one form at a time. 



Similar forms in parallel position, have their faces pa- 

 rallel. 



. 44. HORIZONTAL PROJECTION. 



Place any given form in its upright position. 



