P. IF. Bridgman — Crystalline Cylinders. 273 



m = c 44«e* 





er = c„e zr 





rO — c sin 40(e r ,. - 



- eee) + [ - 5 --■ + t cos40je,0, 



where 







c n = « - c 





c ia = & + c 





a — b , 



Although tliese equations are characterized by six constants 

 instead of three as are the cubic crystals, we notice that under 

 the conditions of this particular problem the two sets of equa- 

 tions are precisely the same in form. If a solution is assumed 

 independent of z the equations separate into two groups as before, 

 and the value of u s which satisfies the boundary conditions is 

 seen to be identically zero as before. Under these conditions 

 the only stresses left to consider are rr, 00, and r6, and these 

 are precisely the same in form as were the equations for cubic 

 crystals, the only change being the substitution of c 6C for c 14 in 

 the equations for a, b, and c. The solution will then be precisely 

 of the same form as that already written down ; we need not 

 trouble to write it again. The equations for determining zz, the 

 stress to be applied over the ends, will, however, be somewhat 

 differeut. This results only in a term which is to be added to the 

 others and is so simple that it need not be written out explicitly. 



Tetragonal Crystals. (B) Seven Constant Case. This differs 

 from the six constant case only by the appearance of one new 

 elastic constant, c 16 , but the symmetry relations are thereby 

 changed, so that the solution is altered in appearance. The 

 stress-strain relations are the same as before for the zz, rz, and z8 

 stresses; the other three stresses now become 



rr = (a — c cos 40 -4- c 16 sin 40)e„. -\- (b + c cos 40 — c ie sin 40) e^ ' + 



c„e 22 + {<■' si" ±Q + c 16 cos 4=e)e r9 



66 = (b-\- c cos 40 + c 16 sin 40)e,. r + (a — c cos 40 — c ia sin ±6)e 9 Q + 



c 13 e zz — (c sin 40 + c 10 cos A6)e,.g 



rH = (c sin 40 + c ie cos 40) (e,.,.— egg) + ( — — \- c cos 40 — 



e ]6 sin i6je,g. 



An examination shows that just as before the exact solution is 

 one in which there is no warping, but the symmetry conditions 

 on u r and v g no longer hold, and the only condition to be satisfied 



