Relation of Mass to Energy. 9 
Thus we may take 
X y = -^(E^ y + H,H,)-r 1 ™ WiE + U ^ mdy 
i v r p 
X = - r L (B x E,+H x HJ-» 1 niii r +| : J m<fe (12) 
Similar values are of course to be found for the other six 
components of stress in the constraint Y x , Y 1Jy Y z , Z J; Z y , Z z . 
8. The values for these nine stress-components are now to 
be substituted in equation (5). In doing this it is to be 
noticed that the last term in each of equations (12) will, after 
substitution, furnish a term of the type 
U^f v^m/lv^ichi vdhndx,. . (13) 
and this, being a time derivative, gives an average value of 
zero when the time is allowed to increase indefinitely, since 
all quantities in the system remain finite. Also 
P + m 2 + n 2 = l. 
Making the substitution in (5) and simplifying, we have as 
the value for («iW) 
fiW^M-t;, j'|^(E/-f E/ + E/) + ^(H/ + H/ + H/)}rfT 
+ l 'l ^_ ) { ( /E r + m ^j + >* E ~~) 2 + ( m * + mB -y + " H ,) 2 1 dT 
-f i\ 2 \ (/»*> + mm y + mnj)dr : . . (14) 
Xow the first integral represents the total included energy, 
the two parts of the second integral represent the squares of 
the components of the electric and magnetic forces in the 
direction of the motion of the system, and the last integral 
represents the momentum in the direction of motion, which 
in this case is the whole momentum M, since we have 
assumed that M and r, are in the same direction. 
Calling 
i- j ((lE x +mV y +nEj 2 + (lH x + mtt s + nH. z ) 2 \ th = ~W L 
