of Maxwell's Electrical Theory. 177 



where p is put for the ordinary pressure given by 



;> = (D^/3D'-l)(D^=D'^WaD'; . . (3) 



and p e is an additional pressure due to the variation of K' and 

 \x! with D f given by 



p e = D'd/3D'. ( - 27rK'" 1 D' a + ^H ,2 /8tt) ... (4) 



Now in equation (26), § 50, put 



F=<jy=<s>'=o. 



Thus 



D'^-DyW + ^'A' 



= -DVW-v'CjtJ + Pe) - i(D'A'E' + B'A'H'/4ir), 



where we have substituted E' for 47rK'~ I D / and B' for /i/H'. 

 From these connexions and the equations 



Sy'B' = Sv'D' = (5) 



it is quite easy to prove that 



B' A'H' = 2 YB'Y y'H' - H' 2 y V, 

 D'A'E'= 2YD'Yy'E' -E'VK'/^tt, 

 and therefore that 



- V'/>e- i (D' A'E' + B' A'H'/4tt) 



= -Y(D'Yy'E' + B'Yy'H'/47r) -D'y'P*, 

 where 



87rP e =E' 2 BKVdD' + H' 2 B/x'/BD'. ... (6) 



Hence, putting as usual 



P=$(dpfD>), (7) 



we obtain 

 p> = - y ' (W + P + P e ) - V (D'V y'E' + B'Yy'H'/47r)/D', . (8) 



which, when the electrical terms are omitted, is the usual 

 hydrodynamical equation of motion. 

 Put now 



P' = <r', (9) 



and let cr be an intensity. Noting that D', Yy'E', B' and 

 Yy'H' are all fluxes, and therefore, by § 2 above, that 



V (D' Y y'E' + B'Yy 'H'/4tt)/D' 

 is an intensity, we obtain from equation (8) 



% 'a'=-v(W + P + P e )-Y(DYvE + BYvH/47r)/D. (10) 

 Now 



