ft ee ee ee 
Burl. Ate eae ek So ig ee 
Sod eV? Rope eer oe eS Bee 
de ea eS ee ee 
and the electric force f, i.e. the force acting on the charged matter 
per unit charge, will be given by 
f=] far? 8 le hv os. Toe 
§ 3. If it were possible, by means of our observations, to pene- 
trate into the molecular structure of a ponderable body, containing 
an immense number of charged particles, we should: perceive within 
and between these an electromagnetic field, changing very rapidiy 
and in most cases very irregularly from one point to another. This 
is the field to which the equations (D—{(V) must be applied, but it 
is not the field our observations reveal to us. Indeed, all observed 
phenomena depend on the mean state of things in spaces containing 
a very large number of particles; the proper mathematical expressions 
for such phenomena will therefore not contain the quantities themselves 
appearing in the formulae (I)—(V) but only their mean values. Of 
course, the dimensions of the space for which these values are to 
be taken, though very large as compared with the mutual distance 
of neighbouring particles, must at the same time be very much smaller 
than the distance over which one must travel in the body in order 
to observe a-perceptible change in its state. We may express this by 
saying that the dimensions must be physically infinitely small. 
Let ? be any point in the body and @ a physically infinitely small 
closed surface of which it is the centre. Then we shall define the 
mean value at the point 2? of a scalar or vectorial quantity A by 
the equation 
xe jr 
zn PK EE PE 
A= il Z (2) 
in which the integration has to be extended to all elements dr of 
the space 5, enclosed by 6. It is to be understood that, if we wish 
to calculate the mean value for different points P?, P’, the corre- 
sponding spaces S, S' are taken equal, of the same form and 
in. the same position relatively to P, P'. The result A will depend 
on the coordinates of the point considered; however, the above 
mentioned rapid changes will have disappeaed from it; it is only 
the slow changes from point to point, corresponding to the perceptible 
changes in the state of the body, that will have been preserved in 
the mean value. 
