34fi The American Geologist. May, 1894 
These mirrors consist of hollow triangular pyramids of defin- 
ite angles, lined with looking-glass and held firmly by their 
apices in an inverted position by a universal joint, so that 
they can be inclined at any angle. If into such a pyramid 
some opaque liquid be poured its surface can be successively 
given any inclination to the three reflecting surfaces by alter- 
ing the position of the mirror. The multiple reflection of 
this surface reproduces some form of that crystal class for 
which the particular mirror has been made, divided by all of 
its planes of symmetry, and this form may be made to pass 
by every intermediate stage, into any other form having the 
same grade of symmetry by suitably altering the inclination 
of the mirror. As a guide to the proper positions of the mir- 
ror, one of its edges may be prolonged as a needle to a gnomic 
projection of the forms desired and any one of these may then 
be produced by placing the point of the needle at the corres- 
ponding projection pole. One mirror may be made for each 
crystal class having a different grade of symmetry and all may 
fit into the same standard. They are, however, only of especial 
advantage for those of the higher grades of symnietrj^, like the 
holohedral and hemihedral divisions of the isometric, hexagonal, 
tetragonal systems. From practical experience the writer can 
say that it would be difficult to imagine a more beautiful or 
satisfactory piece of apparatus for the demonstration of the 
symmetry and relationships of crystal-forms than these 
mirrors.* 
In the New South Wales exhibit in the same gallery, Prof. 
Liversidge of Sidney had two ingenious sets of crystallograph- 
ic axes to illustrate the relationships of the pyramidal and 
prismatic forms in different systems. These were of brass 
and sufficiently large to be seen by a large class. Each was 
fixed to a solid standard, and by means of a movable rod in- 
side of the exterior hollow one, each axis was extensible by 
rational increments. By a joint at the center these axes could 
also be given any inclination to one another, and, as their ex- 
tremities were united by a white elastic cord, they admirably 
*Within the past lew months the writer lias had a set of these mirrors 
made i>\ Chas. Willms, surgical instrument maker of No. 300 North 
Howard St., Baltimore, which has proved in all respects most satisfac- 
tory. The workmanship is admirable, and the instrument is one alto- 
gether fitted for class demonstration. 
