40 J. D. Dana on the Homeomorphism 
related in the series of angles, and when so related, the species 
are in a correct sense homeomorphous. Augite and Hornblende 
may be regarded as differing in this way, as we can by no crite- 
rion decide that the lateral molecular axes of Hornblende and 
Augite are identical; we know that they are so related that one 
form might be a secondary to the other,—that the prism of horn- 
blende has its orthodiagoual twice that of augite in length, and 
that the serial relation of the forms is such that they may be said 
to belong to one type. This point will be abundantly illustrated 
beyond. We observe that in all the comparisons made in the fol- 
lowing tables, the only changes from the forms assumed by ate 
thors made on the above principles to exhibit the homcmorph- 
ism of species, are such as depend on the simple ratios, 1:2, 2: 
:2,2:1. No torturing of the forms has been required by em- 
ploying unusual or complex ratios, notwithstanding the hypothet- 
ical manner in which the received fundamental forms have been 
in many cases assumed. 
The preceding are some of the methods that are of importance 
in determining the crystallographic homologies of species. It ap- 
pears that the first point to be determined, is the true vertical axis 
of species under comparison; and _this being ascertained, the 
second is to fix upon the fundamental or unit vertical prism, oF 
that which shall give the relative values of the lateral axes; and 
third, we have to determine upon a unit dome, either a macro- 
dome or brachydome, in a trimetric species, or else the unit octa- 
hedron, in order thereby to ascertain the true value of the verti- 
cal axis; and fourth, to make out the serial relations of forms, 
for a full comparison where the actual relations of the axes may 
be doubtful. = 
While studying forms by the above methods, it is also of in- 
terest to compare them as a whole without reference to which is. 
the vertical prism; and only by viewing them thus in every dif- 
ferent light can we fully understand their actual dimensional re- 
lations. In this point of view, the results of Hausmann respect- 
— 
The position of the vertical axis derives special importance 
lecules. In a trimetric mole- 
cule, if we suppose three crystallogenic axes, a vertical and two 
lateral, while the vertical is at right angles to the lateral, from the 
nature of the form, the lateral may either intersect at right angles,’ 
corresponding to the form of a rectangular prism, or at oblique 
angles, corresponding to the angle of a rhombic prism; that is; 
in other words, they may connect the centres of the lateral faces 
of a rectangular _ or of a rhombic’ prism. Hither condition — 
will express the forces as indicated by the form}and result in the 

