138 Table 86 



ELASTICITY OF CRYSTALS * 



The formulae were deduced from experiments made on rectangular prismatic bars cut from the crystal. These bars 

 were subjected to cross bending and twisting and ihe corresponding Elastic Moduli deduced. The symbol 

 a (3 y, a, |3j y, and a 2 /3, y 2 represent the direction cosines of the length, the greater and the less transverse 

 dimensions of the prism with reference to the principal axis of the crystal. E is the modulus for extension or 

 compression, and T is the modulus for torsional rigidity. The moduli are in grams per square centimeter. 



Barite. 



^°= 16.13a 4 + 18.51/3'+ 10.427* + 2 (38.79j8V+ I5-2I7V + 8.88a ? * 2 ) 



TO 10 -, , „ -, 



- 7 p = 6t).52a 4 4- 1 17.660'+ 116.467* + 2(20.i6/8-y 2 + 85- 2 97' ? «' 2 + 127.350-18-) 



Beryl (Emerald). 



^- U = 4 .325sin> + 4.6i 9 cos>+ 13-328 sin^cos^ f wh " e , ^A, are j!\, e an f!f l Mch 

 E J D y tijj t t \ t j ie i en gth, breadth, and thickness 



io 10 , , , ,, ',. of the specimen make with the 



tjj- = 1 5.00 — 3.67 5 ccs 4 2 — 1 7- 536 costy cos 2 9>i [ principal axis of the crystal. 



Fluorite. 



= 13.05— 6.26 (a 4 +0 l + 7 4 ) 



1. 

 to 1 

 T 



Pyrite. 



io 1 ' 



-=- = 58.04 — 50.08 (j8"V + 7' 2 «' 2 + <*' 2 * 2 ) 



i^ = 5.o8-2.2 4 (a 4 + /3' + 7«) 



i|r- = 18.60 - 17.95 (*V + 7"«' 2 + a 2 * 2 ) 



Rock salt. 



^ = 33.48 -9.66 (a 4 + 4 + 7 4 ) 



T0l° « „ 



i5_ = , 54.58 - 77.28 (*V + 7 2 « 2 + « 2 * 2 ) 



Sylvite. 



lg-° = 75.,_ 4 S.2(a 4 + 4 + 7 4 ) 



IO 10 



-=■ = 306.0 — 192.8 (3-7 2 + 7-0- + a 2 *-) 



Topaz 



1 

 = 14.88a 4 + 16.54/8* + 16.457 4 + 30.89/3-7 2 + 40.897 2 o' 2 + 43.51a 2 * 2 



■^H = 4.341 a 4 + 3.460/3 4 + 3.77 17 1 + 2 (3.879IBV + 2.8567V + 2.39a 2 * 2 ) 

 io 10 



Quartz. 



^- = 1 2.734 (1 — 7 2 ) 2 + 16.693 (I — 7 2 )7 2 + 97057 4 — 8.460*7 (3a 2 — * 2 ) 



-^- = 19.665 + 9.06072 2 + 22.9847V 2 — 16.920 [(7*1+ *7i) (3 a «i — **l) — *272)] 



* These formulas are taken from Voigt's papers (Wied. Ann. vols. 31, 34, and 35). 

 Smithsonian Tables. 



