742 



energy per unitj of volume laken with tlie negative sign. Further 

 the coefficients « must be considered as functions of the temperature. 

 To this most general case; in which the number of coeiïicients amounts 

 to 21, answers a crystal of the lowest symmetry. This leads, of course, 

 to very intricate calculations. 



We prefer, therefore, to consider the simplest case, viz. an isotropous 

 body. For this holds, if we use the prevalent notation ^). 



X\ = — 2K [.V,. + 6^ {x, -f i/j, 4- z,)] j 



y~ = -Ky: )■ 



(47) 



from which equations can be derived ; 



1 



2K 



^ (X, + r, + z,) 



l + 3<9 





(48) 



In this the relation : 



E=:2K-—-— (49) 



exists between the coefficients K and 6 on one side and the elasticity 

 coefiicient E on the other side. 



Let us now consider a circular cylinder, the axis of which coin- 

 cides with the Z-axis. Let one end be rigidly fastened, while forces 

 resp. couples act on the other. Let the length in the direction of 

 the Z-axis be /, and the radius of the cylinder R. The conditions 

 of this problem may be satisfied by putting 



X,.z=0 X^ = Y,j = ^ (50) 



If Px, Py. Pz are the components of the force, Qx, Q,j, Qz the com- 

 ponents of the couple acting on the end plane, then for the other 

 tensions hold the expressions : 



_ 2Q,.3/ P. (3 + 8^)(fi--^--)-.v - Py 1 + 4^ ,Jv5n 



P, {3 + S0)iR^-y'')-.v^ \ 



xy + 



:iR' jrPn + 3<9 ' ' 2.tP^ 1 + 3<9 



Further : 



1) Gf. among others G. Kirghroff, Vorlesungen iiber Mechanik. 



