336 PHYSICS: H. A. LORENTZ Proc. N. A. S. 
where we may write for the first term J^{Fi.^)dS because Fi is constant 
and tdt - D(D being 0 for ^ = 0). 
From (10) and (9): 
A -W = J(Fi.D)JS + £ dtj(¥2. {C -C})dS (11) 
In v^irtue of (8): 
f(Fi.B)dS = 2U - f(E.5)dS, 
and by (2), applied to the final state, F2 = C/a — E. Substituting 
these values in (11) we find 
A -W = 2U + £ dt j(^^C.{C -C})dS- 
- j'{E.D)dS - £ dt J(E. { C - C } ) J5 (12) 
Now, we may write 
and we can therefore combine the two last terms of (12) into 
- £dt J(E. {D + C - C})dS 
We have by (5) and (6) 
curl E = 0, div (D + C) = 0, div C = 0; 
hence (13) vanishes^ and (12) reduces to 
A -W = 2U + £ ^^/Q^- {C-C}^(iS 
Transformation of the last term: Substitute C = c curl H (form. (4) 
applied to final state), C — C = ^(E — E) (form. (2) combined with 
corresponding equation for final state), integrate by parts, and finally 
replace curl E by — B/c and curl E by 0. 
J^' J/ J^ic.jC -C}^dS = £dtj (c curl H.{E - e}) 6/5'' 
= £ dt J (cM.. curl {E - E})dS = - £ dt £ (H..B) dS 
= - £ dS £ {E.B)dt (15) 
(13) 
(14) 
