of a Crystal according to Boscovich. 



Hence we have 



P = divide ; Q = dw/df ; R = dw/dg 

 S = dw/da ; T = div/db ; U =» div/dc 



;} 



421 



(16) 



Hence, by (14), and taking L, L to denote linear functions, 

 we find 





(17). 



and symmetrical expressions for Q, R, T, U. 



§ 16. Let now our condition of zero strain be one * in 

 which no extraneous force is required to prevent the 

 assemblage from leaving it. We must have P=0, Q = 0, 

 R=0, S = 0, T=0, U = 0, when e = 0, /=0, g=0, a=0, 

 5 = 0, c = 0. Hence, by (17), and the other four symmetrical 

 formulae, we see that 



2*^=0, t*^f=0, 2*^=0, ] 



t m yz=0 , *m„.o, **k*-b 



(18). 



Hence, in the summation for all the points x, y, e, between 

 which and the point there is force, we see that the first 

 term of the summed coefficients in Q, given by (9) above, 

 vanishes in every case, except those of fg and ea, in each of 

 which there is only a single term; and thus from (9) and (14) 

 we find 



w 



— r<j>'(r)-rr 2 <j>"(r)=m . . . 



(19), 



where 



. . . (20). 



The terms given explicitly in (19) suffice to show by 

 symmetry all the remaining terms represented by the u &c." 



§ 17. Thus we see that with no limitation whatever to the 

 number of neighbours acting with sensible force on any one 



* The consideration of the equilibrium of the thin surface-layer, in 

 these circumstances, under the influence of merely their proper mutual 

 forces, is exceedingly interesting, both in its relation to Laplace's theory 

 of capillary attraction, and to the physical condition of the faces of 

 a crystal, and of surfaces of irregular fracture. But it must be deferred. 



