ON ELECTRICAL THEORIES. 107 
On the theories which eaplain the action of currents by assuming that the 
forces between two electrified bodies depend upon the velocities and ac- 
celerations of ihe bodies. 
According to these theories a body conveying an electric current con- 
tains equal quantities of positive and negative electricity, so that it will 
not exert any ordinary electrostatic effect: the positive electricity is sup- 
posed, however, to be moving differently from the negative. In some of 
the theories (Weber’s, Gauss’s, Riemann’s) Fechner’s hypothesis, that the 
electric current consists of positive electricity moving in one direction 
(the direction of the current), and an equal quantity of negative elec- 
tricity moving at the same speed in the opposite direction, is assumed ; 
in other theories (Clausius’) only one of the electricities is supposed to 
move, the other remains at rest. We can see in a general way how the 
assumption that the forces between two electrified particles depend on 
the velocities and the accelerations of the particles can explain the effects 
produced by an electric current. 
Let us take first the mechanical action between two circuits A and B, 
and let us consider the action of an element (a) of A on an element (b) 
of B. Weshall consider first the action of the two electricities which are 
flowing through a on the positive electricity which is flowing through 6. 
Since the motion of the positive electricity in a relative to that of the 
positive electricity in b is not the same as the motion of the negative 
electricity in a relative to that of the positive in b, the forces due to the 
positive and negative electricities in a will not counterbalance, so that 
there will be a resultant force on the positive electricity in b depending 
on the inequality between the motion of the positive and negative 
electricities in a relative to that of the positive in 6. Similarly there 
will be a force on the negative electricity in b depending on the in- 
equality between the velocities of the positive and negative electricities 
in @ relative to that of the negative in b, and, except for special laws of 
force and special values of the velocities of the electricities in b, this force 
will not be equal and opposite to the force on the positive electricity in ), 
80 that a mechanical force on b will be produced by the currents through a. 
Let us now consider how inductive forces can be explained by this 
hypothesis: let us suppose that the element a is moving, and that the 
element bis at rest. The velocity of the electricity in a will be the 
resultant of the velocity with which the electricity flows through a and 
the velocity of translation of a itself, so that since the velocities of flow 
of the positive and negative electricities are different, the actual velocity 
of the positive electricity will differ in magnitude from the velocity of 
the negative (unless, assuming Fechner’s hypothesis, the element a is 
moving at right angles to itself); thus the force due to the positive 
electricity in a on a unit of positive electricity at b will not be equal and 
Opposite to that due to the negative electricity in a, and thus there will 
be an E.M.F. at } due to the motion of a. This explains induction due to 
the motion of the primary circuit. 
Let us now consider induction due to the variation of the intensity of 
the current in the primary circuit. According to all the theories there 
is a force produced by a moving electrified body proportional to the first 
power of the acceleration of that body. Let us consider the elements a 
and 6 again, and suppose that a variable current is flowing through a and 
no current through b ; then if we suppose that a variation in the intensity 
