( 621 ) 



in a shorter way, if we start from wliat we kii()\\' already about 

 the forces. 



Indeed, in virtue of the formula (19) and the two eorrespon<linf^ 

 to it, the eoniponeids of the force acting on an element of volume 

 d S may be represented as foUows : 



/dA', dX,, OA'A 1 . 



/dZ, dZ„ dZ.\ 1 ^ 

 Z (IS — -— -f -^ + — : dS e, ,/S 



\ d,r di/ öc 



and these loruiidae give immediately for the components of tlio 

 couple 



({>lZ-zY)dS=z C(;/Z,~^~Y„)<l(j-y /(_.;è.-~è.v)'/^'. . (21) 



§ J 2. Another consequence of the c(piatioJis (20), analogous to 

 the well kjiown virial-theonMU in ordinary kinetic theory, will pei-haps 

 be thought of some interest. In order to find it, we have oidy to 

 add the three equations, multiplied l)y ,/■, //, :, and to integrate the 

 result over the space S, within the surface o. Transforming such 



r dXj. 



terms as I .'; dS by means of jjartial integration, we tind 



J 0,6' 



C{X.c + Yy^ 7.Z) dS = f{X,,r + ¥„>/ + Z,z) da - 



-J{X, + F, + Z^ dS -^^ ji^.'^ + ^v.V + e.c) d.S. . (22) 



For stationary states the last term will \anisli, so that, if we 

 substitute in the term preceding it the values (18), 



C{X,c + Y,/ + Zz) dS ^ ƒ (A,, .f + ]'„ // + Z,, z) do -\- T-\- r. 



Parfiriilrfr ca^ws of ponf/^'roinotirt' ((cf/'oi). 



§ 13. In a lai'ge variety of cases, in which the system of electrons 

 is confined to a space of finite dimensions, the electric and magnetic 

 intensities in the suri-ouudiug field become so feeble at great distances 

 that the surface-integi'als in [[)) and (21) appi-oach the liuiit 0, if 

 the surface o moves to infinite distance. Moreover, the M)lume- 

 integrals will \anish if the state is slaliünary. We then come to 



