44 



University of California. 



[Vol. -i. 



the positive forms pp'o — x' — e' , and for the negative pp ' == 

 x'-\- c'. The symbols pq are simple multiples of the coordinates, 

 p'o f/o of the unit form, therefore the values p ' q ' are readily 

 deduced for each form. Taking fifteen of the best crystals as 

 sufficient for the calculation of the elements, the averages of p „ 

 and q' o were as follows: 



I). 1 4ol 



12 meas. 



./ A r ( j QQ 



(f o U.04:OO 



12 meas 



1 1 



i) ' ' 





Q ' ' 



7441 



4 " 



5435 



9 " 



7425 



7 



5426 



7 



7447 



17 " 



5426 



17 " 



7452 



11 " 



5435 



11 " 



7452 



14 " 



5432 



14 " 



7444 



8 



5429 



8 " 



7449 



10 " 



5417 



10 " 



7435 



14 " 



5424 



9 " 



7450 



16 " 



5436 



16 " 



7447 



13 " 



5423 



13 " 



7453 



6 " 



5437 



6 " 



7446 



8 " 



5425 



8 " 



7448 



16 " 



5431 



16 " 



0.7443 



165 " 



0.5430 



165 " 



The elements for colemanite are therefore 



p'o = 0.7443 ; q'o = 0.5430 ; / = 0.3663 ; m = 69° 53' 



Determination of the Polar Elements po, qo, and e. — The valnes 

 p'o, q'o, and e'o are the elements when h = 1 and ro = ; 



Sill /A 



therefore when ro — 1, these values must be multiplied by sin ^, 

 to obtain the polar elements po, qo, and e. Thus po — p'o sin 

 qo — q'o sin and e = eo sin m = cos p. The elements for 

 colemanite then become 



po = 0.6989 ; qo = 0.5098 ; e = 0.3439. 



.Determination of the Axial Lengths a and c. — In systems with 

 rectilinear axes q'o = tg(001:01l) and p'o = tg(001:10l); there- 

 fore with axis 6 = 1, the formulae for such systems become 



