THEORY OF ELECTROMAGNETISM. 
743 
Vd' ( ) d V7'/2 - Sd' ( d V7' + d')/2, 
since for that case d V7' = — 47rK 0 -1 d'. We shall assume that this is the correct 
expression in general, since thereby the stress of equation (29) is rendered identical 
with the pure part of Maxwell’s stress. The pure part of his electromagnetic stress 
is the {< j f} of equation (27) above. Let us then put 
4> m 'oj = Vd'<u d V7'/2 - coSd' ( d VT + dvrE," 1 d')/2 - r ~ wSI'ir/2 (31), 
or )r if we assume that the complete expression for x is — SKTTK 72 [equations (28), 
§ 50 and (20), § 35], 
= - Yd'ojE'o/2 + wSd' (E' 0 - inKp 1 d')/2 - YB'coK/8n - coSl / H / /2 (31a), 
and call cf> m ' Maxwell’s stress. [Of course I do not thereby mean to render Maxwell 
responsible for this form.] If we regard Vd' ( ) d V7'/2 as the correct generalisation of 
Maxwell’s electrostatic stress we may indicate it by calling [<£„/] the second form of 
Maxwell’s stress where 
[</>,/] w = Yd / w d V7 / /2 - YB^H'/Stt - cuSI'H',/2 .... (32), 
which gives, on the assumption that the complete expression for x is — SK'It K'/2, 
[(/.„/] - Vd'wE'o/2 - YB'wH'/Stt - wSI'H'/2 . . . (32a). 
If we now assume that the only variables of l are H and d', equation (28) gives 
2f = - {21' -f S (d' d VT + B'H'/Itt)} + Vd' ( ) d V7' - VB' ( ) H'/47r . (28a), 
of which the following particular cases should be noted :— 
If l' he quadratic in d' and H , 1 
f = Yd' ( ) d V772 -YB'( )H78 ttJ 
If l' he c/iven by (3), S 59, and x by (4), 
f = - Vd' ( ) E 0 /2 - VB' ( ) H'/st + SI 0 'H'/2 
(286), 
(28c). 
from which it follows from equation (32a) that in this case 
f = [M+S(r 0 + r)H72 
(28 d, 326), 
so that this stress differs from the second form of Maxwell’s stress by a hydrostatic 
pressure which is zero for nonmagnetic bodies. 
