378 THE AMERICAN NATURALIST. [VoL. XXXII. 
(5) Apparatus for recording rotations 
(6) Apparatus for locking and celdai beam. 
(7) Apparatus for recording depth. 
After giving detailed descriptions of the various parts of the in- 
strument and the method of use and calibration, the results are given 
of a preliminary series of tests on the minerals of the Mohs scale of 
hardness, and the following table shows the values obtained, together 
with those of two other investigators for comparison : 
PFAFF, 1884. RosIWAL, 1892. JAGGAR, 1897. 
9.< OU e ee a T000 1000 1000 
S PIDA eee ace ha oO 138 152 
T OUa e eerie ANA 149 40 
Ge Orthoclase: =: 40 TOT 28.7 25 
Be Apan eg 53-5 6.20 1.23 
A PROME a es 39.3 4-70 75 
3. Calcite . et 15.3 2.68 .26 
Be GPU se ae 12.03 34 04 
The possibility is suggested of using the instrument for other ends 
than the determination of hardness; the extreme exactness of the 
appliance for measuring the vertical movement of the diamond point 
makes it possible to determine the thickness of a mineral section, 
and of the thickness of a mineral necessary to produce in polarized 
light a given interference color, whence the double refraction may 
be calculated. The borings from very minute crystals in thin sec- 
tion might also be subjected to chemical tests, —a novel method of 
isolation. 
Tables of Crystal Angles. — Goldschmidt, continuing his valu- 
able work on the use of the goniometer with two circles, has pub- 
lished a table t of angles for the forms of all crystallized minerals. 
The construction of such a table is first made possible by the new 
method of measurement of crystals involved in this goniometer. In 
the old method of measurement of interfacial angles, such a table 
involved the presentation of the angles which each form makes with 
every other, and the number of values would be so great that its very 
bulk would render it impracticable or even useless. Monographs on 
individual mineral species contain approximations to such complete 
tables of angles, but these were widely scattered through the litera- 
ture. But with the two-circle goniometer, each face is determined 
independently, once the crystal is oriented on the instrument, by the 
measurement of two angles which suffice, the crystallographic ele- 
1 Goldschmidt, V. Arystallographische Winkeltabellen. Berlin, J. Springer, 1897- 
