RIGIDITY OF SELENIUM CRYSTALS 
109 
of area of a section of the crystal about an axis perpendicular to 
the section at its center, the length of the crystal, and the moment 
of inertia of the vibrating body, the coefficient of rigidity can be 
calculated. The torsion of a rod of any but a circular section 
creates a very complicated condition, because not only is shearing 
of each section present, but also there is a complicated warping 
of each section. Indeed, this is the celebrated problem of De 
Saint- Venant.^ However, it can be shown ® that for a slender rod 
of any regular section, the torsional couple for a given angle of 
twist, 0, is given with sufficient accuracy by 
(o^n 0 
40IL 
( 8 ) 
where ^ is the torsional couple, w the area of cross-section, n the 
coefficient of simple rigidity,. / the moment of area of the section 
about an axis through its center, and perpendicular to its plane, 
and L the length of the twisted crystal. For unit twist we have, 
letting 0 1 in (8) 
( 0^ n 
- 40/L 
(9) 
For a torsion pendulum we have 
( 10 ) 
where T is the period of vibration, Jo the moment of inertia of the 
suspended mass, and the torsional couple for unit twist. 
Equating the values of ^ from (9) and (10), we have 
160 7r2/o/L 
.( 11 ) 
or, as in the preceding case (section I) the moment of area is not 
constant from section to section over the length L, we can write 
(11) 
160 ir 2 /oLrIl 
72 J 
where the quantity in brackets refers to the mean value of — ^ 
over the length L. To find this we proceed somewhat as before. 
Let P be this mean value. Then 
2 Comptes Rendus 88, pp. 142-147, 1879. 
3 Rove, Treatise on the Theory of Elasticity: Vol. 1, p. 171, Camb. Univ. Press, 
1892. 
