THURSDAY, NOVEMBER 17, 1881 
SYSTEMATIC MINERALOGY 
Text-Book of Systematic Mineralogy. ‘Ysy Hilary Bauer- 
man, F.G.S., Associate of the Royal School of Mines, 
(London : Longmans, Green, and Co., 1831.) 
“+ No text-books of Mineralogy written for English 
readers are so extremely small in number that the 
publication of a new one may be almost looked upon as 
an epoch in the history of the science. The text-books 
already in existence are in many respects very unsatis- 
factory, and in general character fall far below the stan- 
dard of those of France and Germany. The symbols 
adopted in them for the faces of crystals are generally 
those of Naumann, whilst the simple and elegant symbols 
of Miller, if mentioned at all, seem to be regarded as 
intended for ornament rather than for use. As for the 
advances made by theoretic crystallography during the 
last quarter of a century, no account, save that to be 
found in the excellent little work of Mr. Gurney, has 
yet been offered to the English student. 
Mr. Bauerman had thus a clear field and a splendid 
opportunity. It will be interesting to consider how far 
the result of his labour is worthy of the occasion. 
We find, on ‘opening the book, that the Descriptive 
Mineralogy, which the author’s wide experience and ex. 
tensive travel should render highly instructive, has been 
assigned through force of circumstances to a suppleren- 
tary volume; of the 367 pages of the present one, 200 
are given up to the geometrical, 100 to the physical, 
chiefly optical, and the remainder to the chemical and | 
other properties of minerals. One immediately remarks 
with pleasure the numerous figures of crystals distributed 
throughout the work, all well drawn and clearly printed, 
and what is almost as important to the student, having 
wherever practicable the Millerian indices affixed to the 
faces. 
On coming to the letterpress, however, one soon 
finds that there is something wrong; in fact, from the 
first page almost to the last there seems an evident dis- 
position to perplex the reader. The style is very confus- 
ing throughout. On p. 5, for instance, we are informed 
that “quartzite and statuary marbles are aggregates of | 
particles of quartz and calcite into masses of a slaty or 
granular texture.’”” On p. 7 we find the following :— 
“The leading property of crystals, as distinguished 
from mere geometrical solids, is the invariability of the 
angles between corresponding faces in different indivi- 
duals of the same substance. There is usually a very 
marked symmetry to be noticed in the arrangement of 
their plane faces and edges, and occasionally of their 
points also, although the latter symmetry is not essential, 
crystallographic symmetry being one of direction and not 
of position, so that two parallel planes or two parallel 
lines are not distinguished from one another, and on that 
account the invariability of the angles is a paramount 
consideration.” 
Leaving out of sight the fact that the accuracy of the 
above distinction may be very reasonably contested, we 
much doubt the ability of the ordinary mineralogical 
student to master the compound nature of the latter sen- 
tence, On p. 10 we are puzzled on being told that “a poly- 
VoL. Xxv.—-No. 629 
NATURE 
| 
| 
49 
hedron may be turned through an aliquot part of a whole 
revolution without its position in space as a whole being 
changed”; on p, 12 we find that the tetragonal system 
is characterised by the existence of fwo axes of binary 
symmetry, while on p, 112 four are mentioned; on p. 15 
we are informed that if a, 8, y are all different, the mole- 
cular net-work has no symmetry, while on the following 
page it is said that, granted certain relations between these 
different quantities, there will be symmetry ; on p. 19 we 
are told that the values of 4, %, 7 are in no wise altered 
by multiplying them by any numerical co-efficient ; and 
from p. 24 it will be concluded that a crystal with a 
“concave” angle is necessarily a twin. 
On p. 36 it is stated that “ the test of whether we have 
really four faces of one crystal is the rationality of this 
anharmonic sine-ratio when reduced to numbers”’ It is 
a well-known fact that in every zone of the cubic system, 
and in particular zones of the tetragonal and rhombo- 
hedral systems, the anharmonic ratio of any four planes 
belonging to ¢wo twinned crystals will be rational. 
The account of the inter-relations of the various holo- 
hedral forms of each crystallographic system is not such 
as will relieve this branch of the subject from being still 
looked upon by the English student as somewhat dry and 
wearisome, while the attempt to evolve the hemihedral 
forms must cause the learner to despair. Thus the chapter 
on the Tetrazonal System begins as follows :-— 
“The complete symmetry of this system is contained in 
an upright prism upon a square base, which has quater- 
nary symmetry about a principal axis parallel to the 
vertical edges, and binary about four lateral axes.”’ 
Instead of an explanation there is then a statement of 
the fact that only certain permutations of the indices are 
possible: next follows a calculation, one of the principat 
features of which is the use of some spherical triangle 
characterised only by the fact that it is described about 
the pole of the principal axis and has a side represented 
by 7, which symbol has been unfortunately selected to 
represent an arbitrary arc, The hemihedral forms are 
then arrived at by arranging the symbols of the faces of 
a complete form in a particular order, and then halving 
the faces, or the symbols, or the table, it is not clear 
which, in some symmetrical way not easy to discover (see 
pp. 89 and 120). 
On p. 152 we find that, in the case of oblique crystals 
the axis of symmetry is a direction of “physical equiva- 
lence,” while from p. 156 we should conclude that a face 
is “crystallographically possible” when it has a similar 
face parallel to itself. 
In the discussion of twin crystals the relation in which 
the twin axis and the twin plane stand to the lines and 
planes of the crystalloid system is not clearly expressed. 
It may be worth while to point out that on p. 170 the 
somewhat common error is made of considering a face 
of the cube as the twin plane of the two interpenetrant 
tetrahedra, whereas a little reflection will make it clear 
that the twin plane is really a dodecahedral face. On p. 
352 the striations on the cube faces of iron pyrites are, 
strange to say, referred to as ¢win striations. In describ- 
ing a goniometer, of which the picture on p. 192 is no 
doubt very ideal, it is remarked that “the angle through 
which the circle is rotated will be the supplement of the 
dihedral angle required, ¢/ 7¢ was originally set to zero.’’ 
D 
