1885.] TJie Force Function in Crystals, 65 



It will be seen at once that this is an extension of Poisson's solu- 

 tion of the equation —zzza 2 *^-. There is only one arbitrary function 



dt dx 2 



in my solution, and only one in Poisson's, as thus treated. But he 

 has given one with two arbitrary functions, and I believe a similar 

 investigation would apply to my general equations if the equation, 



an v + bn v ~ l + . . . 



t 1 = m > 



+ . . . 



were solved with regard to (n), and thus n found in terms of (wi). 



III. " The Force Function in Crystals." By Alfred Einhorn, 

 Ph.D. Communicated by G. Matthey, F.R.S. Received 

 November 27, 1884. 



(Abstract.) 



The first part of the paper which appears at present restricts 

 itself to the consideration of the Tesseral, Tetragonal, and Rhombic 

 systems. By means of a well founded assumption in regard to the 

 stress-distribution in crystals of the above systems, the equilibrium 

 conditions are deduced which further involve that the boundary of 

 the configuration must either be plane or spherical. 



It also appears that the statical conditions of the agency which 

 causes crystallisation are the same as those so well investigated for 

 gravitation and electricity. 



The paper is divided into three chapters. The first chapter treats 

 of the " Foundation of the Assumption." The assumption is that 

 the stress upon any particle can only be transmitted in six direction- 

 lines respectively at right angles in pairs to the three crystallogra- 

 phic axes — it is a consequence of the internal structure which is 

 shown to be analogous to that of an ordinary cannon-ball pile by 

 means of the cleavage properties, the external form and inertia 

 relations of crystals. 



The second chapter — " Derivation of the Force Function" — applies 

 the three general differential equilibrium equations of an elastic solid 

 subject to internal forces to the stated stress-distribution. In order 

 to effect this it was necessary to deduce some peculiarities of the 

 force function in a system of uniform density in equilibrium, and 

 subject to internal forces when referred to the three principal axes of 

 inertia through the mass centre. The character of the attracting 

 agency here becomes evident. 



The third heading, " Determination of the Boundary." Under this 



VOL. XXXVIII. F 



