THE MICROSCOPE, AND ITS CRYSTALLOGRAPHIC APPLICATION. 175 
One preliminary observation only need be borne in mind, viz. that every 
crystal, of whatever system it may be, is always derived from some primary 
form. Thus, for instance, the elegant crystals of calcite and quartzite are 
secondary modifications of a rhomb. The irregular crystals of tartaric acid and 
sulphate of soda are derived from an oblique rhombic prism ; while sulphates of 
zinc and potash are two in a long list that owe their several forms to the right 
rhombic prism. 
But, while all these sets of geometric forms have apparently the same general 
shape, each has its own peculiar angles. For instance, the rhombs of calcite 
and quartzite to the eye seem identical; but when measured the rhomb of calcite 
measures 74° 55' and 105° 5 - 0'; whilst that of quartzite measures 94° 15' and 
85° 45'. The measurements of the secondary forms are quite as constant. It 
therefore follows that the angles of a crystal being known, the name may be 
known also. On reference to the drawings, it will be observed that the predo¬ 
minating angles are identical with certain angles as measured on a large crystal. 
Sometimes, when the two lines meet, it is difficult with plain light to say 
whether they are two crystals meeting, or two lines belonging to one crystal. 
The application of polarized light will at once decide the question. 
A singular fact may now be mentioned, that often when polarized light is 
used, a number of lines start into view, which also are coincident with the lines 
on irregular forms of crystals. On referring to the drawing of tartaric acid, 
for example (Plate I.), the line marked A is one which starts up. As a general 
rule, the author prefers a solution containing about eighteen or twenty grains 
to the ounce, because, if stronger, the crystals will be too thick and inclined 
to admit of horizontal measurement. 
The goniometers used by the author are that made by Ross and that in¬ 
vented by Dr. Leeson ; the latter being more correct, while the former is more 
easily used. 
Ross’s goniometer is a positive eye-piece, across the field of which is a very 
fine line, the whole being made to revolve in a circle very finely graduated. 
Wh en used, the engraved line is placed over or parallel to one side of the angle 
to be measured. The line is then revolved by means of the rackwork till it coin¬ 
cides with the other side of the angles, when that portion of the graduated arc 
traversed by the vernier gives a very correct measurement of the angle required. 
The beautiful instrument of Dr. Leeson is an ingenious application of the 
phenomena of double refraction. It is equally adapted for measuring opaque or 
transparent crystals, microscopic or the largest crystals. It consists of a doubly 
refracting prism of Iceland spar, which is mounted over the eye-piece, and the 
whole fitted into a very finely-divided circle. When, therefore, the crystal is 
viewed through this prism two angles are produced, which revolve round each 
other as the prism is revolved. The amount of rotation, when applied to the 
angle, gives the measurement required. 
For instance, let A, B, C be the angle to be measured. Place the crystal 
perfectly in a plane perpendicular to the axis of vision, which is easily accom¬ 
plished by seeing that every part is in focus. Then revolve the prisms till the 
lines A B and a b coincide; then revolve the vernier till B C and b c also 
coincide. The length passed over by the vernier of course gives the measure¬ 
ment of the angle. 
