102 Table 82. 



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 conespoiiaing Elastic Moduli deduced. Tlie symbols 

 a /3 y, 0| /3i y, and ao /3^. y^ represent the direction cosines of llie length, the greater and the less transverse 

 dimensions of the prism wiih 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. 



16.130'+ 18.51)8 + 10.427+4- 2(38.70/3 y- 4 is.2i7'-a- 4- 8-8So"^-) 



10 



,10 



-?|T- = 69.52a' 4- ii7-6Cfi^-\- 116.467' 4- 2(20. 16/8 V" 4" 85.297'V-4- i-7-3S°'"^') 



Beryl (Emerald). 



'-^ = 4.325 sin'.^ 4-4.619 cos''^ -\- 13.328 sin2,^ cos2?. [ ^^^f ^ ^ ^1 ^2 ^'^ ^^^ angles which 

 E ^■^-' ri-ty rioo r r \ the length, breadth, and thickness 



10^'^ ^ .^ . .,^ ., 1 of the specimen make with the 



-^ = 15.00-3.675 COS402 - 17.536 cos-^ cos-n [ principal axis of the crystal. 



Fluorite. 



^' = i3.os-6.26(a++;3'4-y) 



loi"* 



-^ = 5S.04 — 50.08 (j3 7- 4- y^a^ + a&") 



Pyrite. 



i^"==5.o8-2.24(a' + )3'4-7«) 



^-^ = 18.60 — 17.95 (/3 V + 7V -f d'fi'-) 

 Rock salt. 



ig^ =33.48- 9.66 («4 4- ^*+y) 



-^ = 1 54.58 — 77-28 {0Y 4- 7V +a$') 



Sylvite. 



^° = 75.1 -48.2 (a* 4-/3* + 7*) 



ioi'> 



-TyT = 306.0 — 192.8 (j3 72 -f 7V 4- a-fil 



Topaz 



3 







= 14.88a* 4- 16.543* 4- 16.457* + 30.89/3272 4- 40.897202 4- 43.Sia2i82 



-^ = 4.341a* + 3.460/8* + 3.7717* 4- 2 (3.8753V + 2.8567V 4- 2.39a')8-) 



Quartz. 



IqI) 



-^ = 12.734 (i —72)2+ 16.693 (i — 7-)7'^ + 97057* — 8.46C/37 (3a' — ^-) 



-— =z 19.665 -f 9.060722 -f 22.98472712 — 16.920 [(7)8i4- y37i) (3aai — $$i) — 18272)] 



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

 Smithsonian Tables. 



