'732 



Physics. — ''On the lowerim/ of the freeziiui point In consequence 

 of an elastic deformation.'' By Dr. G. J. Elias. (Communicated 

 by Prof. H. A. LoRENTz). 



(Communicated in the meeting of May 30, 1914). 



A iHiiiiber of years ago E. Rieckk ^) derived from tiierinodynamic 

 considerations that a solid body subjected to forces wliieh bring 

 about an extension or compression, will in general exhibit a h^wering 

 of the freezing point, also at those places of the surface where no 

 deformative forces are directly active. 



This case may be extended to that of an arbitrarily deformed body. 



J. Let the free energy per unily of mass be U', and tlie density (>, 

 then the total free energy of a certain system will amount to 



=ƒ- 



i^j.dr (1) 



in which the integration must be extended over all the material 

 elements Q.ch. Further we make no suppositions at all on the state 

 of the system. 



Let us suppose the system to undergo an intinitely small deform- 

 ation at constant temperature. We can always assume this deform- 

 ation to consist of the intinitely small dilatations .iv, y>,, z~, and the 

 distortions Vz,Zx,^v,,, for which the well-known relations hold: 



"■'^a;. y'-'^Yy "'-^ 



Zy ==?/,= - 1- — - Xz = 2'2- = s ^- T" y^: = '^''Z — ^ T ^ 



y ^ de Ö// ö.^• Ö^ • Öy Ox 



(2) 



when ^, i], S denote the infinitely small displacements of the poiuts 

 of the system. 



In consequence of this deformation the free energy of the material 

 element qcIx will increase by the amount 



/dip öip öi|^ öif' öq. M^ \ 



\dx:, dy,j dzz dyz Oz^ Ox,, ) 



On the other hand work has been done by the external forces. 

 When the components of the joint volume forces which act on the 



1) E. RiEGKE, Wied. Ann. 54 p. 731. 1895. 



