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THE TOESION PEOBLEM FOE BODIES OF EEYOLUTION. 
By E. T. Stegmann. 
(Thesis approved for the Degree of Doctor of Science i7i the University of the 
Cape of Good Hope.) 
(With Plates A, B, Ylll-XVIII.j 
Introduction. 
The problem which we are to consider deals with the distribution of 
stresses and strains in an isotropic body of revolution of infinite length 
under the action of terminal couples and free from body forces. 
As far as I am aware, an analytical solution of the problem has been 
given only in the case of a circular cylinder, the solution following from 
Saint- Venant's general theory of the torsion of cylinders.* 
The general theory of the torsion of such bodies has been worked out 
by Foppl t and Williers.:]: They have shown that in such a body, where 
the stresses and strains are obviously independent of 0, we have the 
equation, 
where rd = — 
or 
and further that 
rr = tid = zz = rz = 0, 
where rr, - - rz - - - are the stress-components referred to cylindrical 
co-ordinates r, Q, z. 
* Love, "Theory of Elasticity," § 86, a ; § 221, a. See also Webster, "Dynamics," 
§ 184, /3. 
t Foppl, 'Miinch. Ber.' 35 (1905), p. 249. ' Zeitsch. tier Ver. der Inq.' 50 (1906), 
p. 1032. 
X Williers, "Diss.," Gottingen (1908). ' L. f. Math. u. Physik; 55 (1907), p. 225. 
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