10 CRYSTALLOGRAPHY. 
figure, it reads 45°. The arms have slits at g h, 2 », by which the parts 
@ 0, €0, may be shortened so as to make them more convenient for 
measuring small crystals. ; 
In the best form of the common goniometer the are is a complete 






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circle, of larger diameter than in the above figure, and the arms are 
separate from it. After making the measurement, the arms are laid 
upon the circle, with the pivot at the centre of motion inserted in a 
socket at the centre of the circle. The inner edge of one of the arms 
is then brought to zero on the circle, and the angle is read off as before. 
With a little ingenuity the student may construct a goniometer for 
himself that will answer a good purpose. A semicircle may be de- 
scribed on mica or a glazed card, and graduated. The arms might also 
be made of stiff card for temporary use; but mica, bone, or metal is 
better. The arms should have the edges straight and accurately paral - 
lel, and be pivoted together. The instrument may be used like that last 
described, and will give approximate results, sufficiently near for dis- 
tinguishing most minerals. The ivory rule accompanying boxes of 
mathematical instruments, having upon it a scale of sines for measuring 
angles, will answer an excellent purpose, and is as convenient as the arc. 
In making such measurements it is important to have in mind the 
fact that— 
1. The sum of the angles about a centre is 360°. 
2. In a rhomb, as in a square, the sum of the plane angles is 360°. 
In any polygon, the supplements of the angles equals 360°, whatever 
the number of sides. For example: in a square, the four angles are 
each 90°, and hence the supplements are 90°, and 4x 90=360 ; again, 
in a regular hexagon the six angles are each 120, the supplements are 
60°, and 6 x 60=360. So for all polygons, whether regular or irregular. 
In measuring the angles it is therefore convenient to take down the 
supplements of the angles. This principle is conveniently applied in 
the measurement of all the angles of a zone of planes around the 
crystal; for the sum of all the supplements should be, as abc ve, 360° ; 
and if this result is not obtained there is error somewhere. 
