MEASUREMENT OK CRYSTALS. 



49 



a< 



grees. The arms are so applied to the scale, that the center 

 of motion is exactly at the extremity of the middle line, 

 marked 90 ; and the leg crossing the scale (or, mat edge of it 

 in the line of the center of motion) will then indicate by its 

 position over the graduated margin, the angle desired.* 



In making such measurements it is important to remember 

 that— 



1. An angle A D (figure 87) and A C, together, 

 equal 180° ; so that if A O C be measured, A O D is ascer- 

 tained by subtracting A O C from 180°. 



2. In a rhomb or rhomboid, b a b and a b a, to- 

 gether, equal 180° ; and one may be ascertained 

 by subtracting the other from 180°. If an obtuse 

 angle of a rhombic prism has been measured and 

 found to be 110°, and the acute angle on measurement is as 

 certained to be 60°, the student should add the two together 

 to find whether the sum is 180° ; for if not, there is somr 

 error in the measurement, and it should be repeated. 110 

 added to 60° makes 170°, showing in this case an erroi 

 of 10°. 



3. In any polygon, the sum of the angles is equal to twice 

 as many right angles qs there are sides less two. Let the 

 number of sides, for example, be 6 : 6 less two is 4 ; and 

 the angles together equal twice 4, (or 8,) right angles, which 

 is equivalent to 8 X 90° =720°. If we have a prism of six 

 sides, and wish to ascertain the angles between these sides 

 the angles should be measured successively, and the whol< 

 added together to ascertain whether the measurements ar( 

 correct. If the sum is 720°, there is good reason to confidt 

 in them. Crystals are at times a little irregular ; and thii 

 should be looked to, as part of the apparent error may at 

 times be thus accounted for. This general principle and the 



What three points must be observed in making measurements ? 



* Another mode for approximate results consists in holding the crys- 

 tal with the two faces (whose inclination is to be measured) in an 

 exactly vertical position over a piece of paper : then place a small rule 

 parallel, as near as the eye can judge, to one face, and draw a line ; next 

 do the same for the other face. The angle between the two lines, 

 measured either by an arc or the ivory rule just mentioned, is the 

 desired inclination. With practice, much skill may be acquired in 

 euch trials. Thf-y may be made with micro? opic crystals under 

 microscope. 



