10 



CRYSTALLOGRAPHY. 



figure, it reads 45°. The arms have slits at g h, n p, by which the parti 

 a o, co, may be shortened so as to make them more convenient foi 

 measuring small crystals. 



In the best form of the common goniometer the arc is a complete 



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 IHtle ingenuity the student may construct a goniometer for 

 himself thac 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 side*. For example : in a square, the four angles are 

 each 90% and hence the supplements are 90°, and 4x90=360 ; again, 

 in a regular hexagon the six angles are each 120, the supplements are 

 60°, and 6 x 60=300. 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 abeve, 360° 

 and if this result is not obtained there is error somewhere. 



