666 Mr. H. Hargreaves on the Difference between 



Flux of energy and work done by pressure are shown very 

 simply by interpreting 



E 1 (Y^~^)(1-^ 1 /V) =V 2 (Vn 2 + w)(l + wn 2 /V), (14) 



which is an immediate consequence of (10) and (9), as 

 difference of two fluxes giving work done by pressure. 



§ 3. To deal with a conductor in a general electromagnetic 

 field, the properties of the ideal conductor in virtue of which 

 its interior is an electromagnetic blank need consideration. 

 For this purpose the field equations are integrated through 

 a layer in which a rapid transition is made from finite to zero 

 values, and the volume of integration has a cross-section dB 

 with thickness small in comparison with the linear dimensions 

 of dS. Such integration gives 



fl^r = fl^dS =fdS, and I ^df = lfd%, . (15a) 



I a direction-cosine of the normal, and /a value just outside 

 the surface. 



To deal with *' we note that in respect to / or 

 B* r dt 



B/' B/' B/ , 3/ .{ , . T . , , , 



~-\-uzr + v ^r- -{• w^r- rapid chancre is obviated because 

 dt B^ oy B~ 

 the motion of an element is followed, and accordingly a 



zero value is given for the integral of -~ in consequence 



of the small thickness of the layer. Thus 



fB/ 7 (V B/, B/\ ~df\ 7 n . \_ , wa 



J d* J V B^ By W 



= -iyfl3, say. (15 6) 



Applying these to the volume-integrals of p = %^-~ . 

 1 BX o. f Be -db 1B« BY BZ , :. ° lC 



V W*-Y-=T^Tz> VBT^BZ "By ' we have resnlts : 



ir'=7X+wT + nZ, •.. . . (16) 



— v v X/Y-\-.au e /'V=-mc—nb, (17) 



,/Y = mZ-nY. . . . ,. . (18.) 



a i\ 



It is not assumed that the velocity (it e v e w e ) attributed jo 

 charge at the surface agrees with the velocity (uvw) of the 

 material surface. But (16) and (17) demand the condition 



