( 262 ) 
— Days). 5. 
Now, according to the definition of mean values (§ 3), division of 
this by 5 will give the mean of g; hence 
GA INA et gl > eee ee eee 
This result may even be extended to a state of the body, in which 
the distribution of the values of g is not the same in neighbouring 
particles. In this case we may again apply to each particle the 
formula (17), but 9 can no longer be calculated by (14). We have 
now to define this vector by 
pes Se Ts = 5 es = beaten 2 (19) 
the sum being taken for all the particles that lie wholly in the space 
5, 
We may express this in words by saying that 9 is the sum of all 
without attending to those that are cut in two by the surface. 
the vectors q, reckoned per umit of volume. 
e. The case still remains that a quantity qg, given for every point, 
has such values that the integral (4) sl gdt, taken for a single par- 
ticle, is not O. If this quantity were constant throughout the space 
occupied by a partiele, it would be unnecessary to take into account 
those which are cut in two by the surface @ and we should have 
g == IN): 
ml A = . ° 2 
The most general case may be reduced in the following way to 
this case and to those that have already been disposed of before. If 
q is distributed in some arbitrary manner, we begin by calculating 
for a single particle the mean value q,=— (q), s being the volume 
5 
of the particle, and we put in every point g — g, — ‚. We shall then have 
I=h ts: 
The problem is therefore reduced to the determination of two 
mean values, one of which may be found by what has just been 
said, and the other by applying the formula (18). 
§ 6. The mean value of each of the quantities gandgv in the 
equations (I), (ID) and (1) may be decomposed into three parts, be- 
longing to the eonduction-electrons, the polarization-electrons and the 
magnetization-electrons. In determining them, we shall suppose the 
ponderable matter to have a visible motion with velocity w, and we 
shall write » for the velocity the charged matter may have in 
addition to this. We have therefore to replace v by w + », and to 
determine separately 9 Wando v. 
