l)ii observations in parallel light. 55 



Let two BectionB, both perpendicular to the plane of sym- 

 metry, and^respectively parallel and perpendicular to the elon- 

 gation, have indices of refraction (yfi) and (a'f$) respectively, 

 be the angle from c to the prismatic axis and tet V also 

 be measured from c. Then 6 and 0' will become (^+90°— V), 



and (p+90°+V) or (f— Y) and (f+V) respectively. Then 

 substituting in (3)we may transform it into the following forms : 

 •_'\ is the value of 2"V that would he obtained by treating a'ft 

 and y ' .i as principal sections. 



f ,A^ *(«' — P) , 



£.- cos 2\ =9 -- ^4-cos lq> / 1A x 



= 2. A / ~ cos 2 </; / , , % 



>(r-o) F 00 



= f^""^ + i/ a !" ff cos2a>=coB2V'cosgg> (12) 

 i(y-a)cos 2<p=:+d(y'-0)-d(a t -/3) (13) 



In a slide of even thickness d is constant and cancels out. 

 (y — a) and c will be determined in the same slide. Eq. (13) 

 being an equation of condition controls the observations. 



The character of (y' — ,i) and (a'—j3) whether + or— must be de- 

 termined by mica plate or otherwise. Eq. (12) is the best one to 

 use. It is easy to make a diagram for its graphical solution. 



See figure. Throwing (12) into the (j^j- 1) Q~^~~ *) = 2, 



y' — (i cos 2V 



we see that we may consider -. — — the ordinate y. — the 



J a - fi J cos 2<p 



abscissa x of a rectangular hyperbola whose asymptotes are 



./ = -f 1 and y=-\-l and intercepts on ox and oy are (!,<>) and ( ,I). 



cos 2 V" 



This hyperbola once constructed we can find for any 



1/1 cos 2cp 



value of y' — [i and a!— ft at once. Then will any point on the 

 line through {0,0) and ( 1) have its abscissa propor- 

 tional to 2 V if its ordinates is proportional to —cos 2<p. Hence 

 by drawing a set of Hues diverging from and by marking the 

 values of ip against the corresponding lengths of — COS 2^ on 

 ON and the values of v against the length- of cos2Y on the 

 same scale (i. e. to the same radius) on NP we can read off V for 

 a given c. (See example below). We need only to construct 

 the hyperbola for one quadrant if we remember that x for y is 



equal to — x for -, but we must be careful about the signs. 



if 



§ -L Formula (12) etc. may be applied to the hornblendes by 

 seeking out three kinds of sections : 1) Plasmatic, with only 



