§20 
of Minnesota, which appeared in a recent issue 
of ScIENCE,” opens up again the much dis- 
cussed question of the presentation of the 
subject of crystallography to undergraduate 
classes. 
Professor Bowles apparently takes the view 
that the fundamental laws of this science 
should be studied through their application 
to concrete examples. It has been the experi- 
ence of the writer that, in general, the efforts 
of teachers of crystallography have not been 
directed with sufficient force to the lucid pre- 
sentation of these fundamental laws. In spite 
of the many varieties of models in glass, 
wood, paper and plaster of Paris, now at the 
disposal of the modern teacher of this sci- 
ence, his classes often have only a vague no- 
tion of: 
1. The mechanical relations of the direc- 
tions of particle-attraction. 
2. The all importance of symmetry as a 
basis of erystallographie study. 
3. The application of the above to erystal- 
lographie zones. 
With regard to Professor Bowles’s sugges- 
tion respecting tables for determination of 
axial ratios, the writer desires to point out 
that the use of such tables must of necessity 
presuppose the knowledge on the part of the 
student of which face of the crystal measured 
represents a unit plane. Taking the axial ra- 
tios of a number of common tetragonal min- 
erals such as: 
@ 2c 3c 
Apophyllite ...... 1.2515 
Wernerite ....... 4384 1.3052 
JAIL. cooodeooga$ 6404 1.2808 
1TH Bo gauesoodo 6441 1.2882 
Cassiterite ....... 6723 1.3446 
XenotIMe eee 6187 1.2374 
it will be readily seen that for each of these 
species a pyramid could be selected which 
would give a resulting axial ratio fairly close 
to some pyramid of each of the others. In 
point of fact, in the above series the difference 
in angle, measured from the prism, between 
the pyramid corresponding to 1.2374 (lowest 
value) and 1.3446 (highest value) is only 52° 
1ScmNncE, April 12, 1912, pp. 576-577. 
SCIENCE 
[N.S. Von. XXXV. No. 908 
—a difference not easy of determination with 
a contact goniometer in the hands of an inex- 
pert student. Such instances could be multi- 
plied many times. 
In answer to Professor Bowles’s first ques- 
tion as to whether tables of axial ratios would 
be useful as an aid to crystal determination 
with the reflection goniometer, it has been the 
writer’s experience (and undoubtedly that of 
every crystallographic investigator) that in 
99 cases the name of the species under investi- 
gation is known before it is set up for meas- 
urement. In the rare and much to be desired 
hundredth case (that of a new species) the 
name would obviously not appear in any 
table. 
To the chemical crystallographer, tables of 
the axial ratios of artificial crystals might be 
of use could a work of sufficient size to in- 
clude them all be prepared, but even such a 
collection of tables would have to be very fre- 
quently revised. 
H. P. Warrock 
DEPARTMENT OF MINERALOGY, 
NEw YorK State MUSEUM, 
Aupany, N. Y. 
To THE Epiror oF Sctence: If we may judge 
from the character of most of the text-books 
on erystallography, Mr. Bowles’s suggestion 
in Scrmnoe for April 12, that any phase of 
this subject should be turned into an “ illumi- 
nating and interesting exercise” is certainly 
a novel one. Yet surely the demonstration of 
the “value of the science as a means of min- 
eral determination” is the ideal way to bring 
it before the student, so that crystals shall 
be to him more than, as Goldschmidt has put 
it, “a feared and hated collection of geo- 
metrical figures, of wood, plaster or paste- 
board, with vertices and edges and bad Greek 
names, to be immediately forgotten on leav- 
ing school, and preferably never heard of 
again.” 
The writer has used tables similar to those 
described by Mr. Bowles for several years; 
thus far they have been mimeographed and 
handed around the class, but if elaborated and 
1 Ann. d. Naturphilos., [X., 121. 
