252 



On a method of measuring the Angles of Crystals. 



To measure the angle of inclination 

 of two faces of a crystal, I use a rule 

 h c Avith a straight edge. On one end 

 the crystal is placed on a piece of wax. 

 The eye is then brought near to the 

 crystal until a clear vertical line is 

 seen, such as a vertical bar of a win- 

 dow. The crystal is then moved on 

 the wax until the image reflected be 

 also vertical. The same is then done 



with the other face, and when the reflection of the bar is vertical 

 on both faces, the crystal is adjusted, which is done after a few 

 trials. The rule is then placed on a sheet of white paper, which 

 is placed on the edge of a table. The paper must not be moved 

 during the operation. The eye is again placed near one face of 

 the crystal which is turned until the reflected image is made to 

 coincide with some other vertical line seen directly. Then a 

 pencil is passed along the straight edge and a line made on the 

 paper. Under the edge of the crystal a mark is made to fix the 

 point that is to be the vertex of the angle. The rule is then 

 turned until the reflected line on the other face and the line seen 

 directly coincide. In this second position, the vertical edge of 

 the crystal must be again over the mark made under it in the 

 first position. This is to oblige the eye to place itself in the 

 same position that it had at first. A line is then drawn alon^ 

 the edge and the angle of these two lines is the supplement of 

 the angle between the two faces of the crystal. This needs no 

 proving as the principle is the same as in the case of WoUaston s 

 goniometer. 



The angle on the paper can be measured by a protractor, or 

 in any other convenient way. 



If the operator has no protractor but has a table of natural or 

 logarithmic cosines, the best way is to make a triangle and to 

 measure its three sides. Calling A the angle measured by the 

 two lines, a the sides opposite to it, h and c the adjacent sides. 

 Then a^=b^ +c^-2bc cos A. When the angled is acute the 

 cosine is positive ; when it is obtuse the cosine is negative, li 

 we take h^^^^c^ we have 



a 



and if Z?— 1 



Then when the angle is acute, 



a =2-2 cos A 



and when the angle is obtuse, 



QosA=l{2-a^)=l-ia^j 



cosA=^ 



1. 



