368 
POPULAR SCIENCE REVIEW. 
assigned. Tlie classical memoir of Mallard (Ann. des Mines, Vol. X. 1876) 
had a strong influence in this direction. In it he sustained this change for 
some of the best-known species, and some of those which had been accepted 
as types of the systems to which they were referred, — such as garnet, vesu- 
vianite, fluorite, apophyllite, zirkon, apatite, beryl, tourmaline, &c. In 
explanation of cases like those of just named, Mallard suggested the hypo- 
thesis that such crystals were to be considered as twins or compound-crystals, 
so made up as to have a pseudo-symmetry corresponding to a higher grade 
than that belonging to the individuals themselves. 
The question as to the sharpness of the line dividing the crystalline 
systems from each other, and in many cases as to the system to which a 
given crystal really belongs, cannot be said to be decided at the present 
time. It is certainly possible to exaggerate the ‘ optical anomalies/ and to 
attribute to them a morphological significance, when they are, in fact, due 
simply to accidental causes, such as the internal tension produced at the 
time the crystal was formed. For example, the species boracite, long 
regarded as a typical hemihedral form in the isometric system, although 
with an anomalous optical character, which was variously explained, has 
been referred, by Mallard and others, to the orthorhombic system. Recently, 
however, Klein (Neues Jahrb. 1881) has shown, by the effect produced upon 
the optical character by heating sections of the crystals, that the peculiarities 
are probably due to internal tension simply, and that there is nothing which 
really conflicts with its being referred to the isometric system. Similarly 
analcite, the common form of which was long held to be a typical example 
of an isometric trapezohedron, was afterwards referred to other systems by 
Schrauf, Mallard, Lasaulx, and others, and finally referred back to the 
isometric system by several mineralogists, who have arrived at the same 
result by somewhat different methods. Other similar examples might be 
given. 
M. Bertrand, working from the standpoint of M. Mallard, has recently 
published some interesting contributions to this subject. He shows that the 
apparently isometric octahedrons of ralstonite exhibit two optic axes, with 
an angle of about 90°. He has also examined a series of minerals, ranging* 
from the pure lead phosphate, pyromorphite, to the lead arsenate, mimetite ; 
and his conclusion is that while the first is truly hexagonal, and has a 
negative optic axis, the other is really orthorhombic, and owes its apparent 
hexagonal form to twinning. A section of mimetite from Johanngeorgen- 
stadt, cut normal to the vertical axis, was seen in polarized light to be made 
up of six triangles, each having as base the side of the hexagon ; the two 
optic axes make an angle of 64° in air. Between the two extremes there 
are various intermediate compoimds containing both P 2 0 5 and As 2 0 5 , and it 
is found that as the proportion of As 2 0 5 diminishes, the angle of the optic axes 
also diminishes. Similar results have been obtained by M. Jannettaz. 
These facts recall the results obtained with crystals of iodide of antimony by 
Cooke, who proved the existence of a uniaxial (hexagonal) and a biaxial 
(orthorhombic) variety, of which the latter changes into the former on a 
slight elevation of temperature. M. Bertrand has also studied several 
varieties of garnet, and arrived at essentially the same results as M. Mallard. 
Sections of crystals of aplome, ouvarovite and topazolite show two optic 
