114. JS. W. Gibbs— Equations of Monochromatic Light 
and intensity of these vibrations in any small part of the 
medium (as measured by a wave-length) are entirely deter- 
mined by the electrical forces and motions in that part of the 
medium. But the equation would not hold in case of molec- 
ular vibrations due to magnetic force. Such vibrations would 
constitute an oscillating magnetization of the medium, which 
has already been excluded from the discussion. 
The supposition which has sometimes been made,* that 
electricity possesses a certain mass or inertia, would not at all 
affect the validity of the equation. 
10. The equation may be reduced to a form in some respects 
more simple by the use of the so-called imaginary quanti- 
ties. We shall write ¢ for y(—1). If we differentiate with 
2 oe 
respect to the time, and substitute — 10) ave for LU }ave: e 
obtain 
47° ° aes * 47° 
p Pot [Ulave — 7[@]ave = ®[U]ave — > YU lave 
If we multiply this equation by ¢, either alone or in connection 
with any real factor, and add it to the preceding, we shall obtain 
an equation which will be equivalent to the two of which it is 
formed. Multiplying by 2 and adding, we have 
. Pot ([Ular Gil Pi) lave) —P([dlave— U f dave) 
4 
Pp 27 27 
9 ° 
= (6628 ») (Uj + 2.t0hn} 
If we set 
W = [Ulave — 7% [U]aver (9) 
Q= [Zlave Be - glass (10) 
O=@+1 di -. (11) 
our equation reduces to 
4 2 
3 Pot W — pQ= OW. (12) 
" * See Weber, Abhandl. d. K. Sachs. Gesellsch. d. Wiss., vol. vi, p. 593-597; 
Lorberg, Crelle’s* Journal, vol. lxi, p. 55. 
