Page:A history of the theories of aether and electricity. Whittacker E.T. (1910).pdf/342

 An interesting application of Hall's discovery was made in the same year by Boltzmann, who remarked that it offered a prospect of determining the absolute velocity of the electric charges which carry the current the strip. For if it is supposed that only one kind (vitreous or resinous) of electricity is in motion, the force on one of the charges tending to drive it to ono side of the strip will be proportional to the vector-product of its velocity and the magnetic intensity. Assuming that Hall's phenomenon is a consequence of this tendency of charges to move to one side of the strip, it is evident that the velocity in question must be proportional to the magnitude of the Hall electromotive force due to a unit magnetic field. On the basis of this reasoning, 1. von Ettingshausen found for the current sent by one or two Daniell's cells through a gold strip a velocity of the order of 0·1 cm. per second. It is clear, however, that, if the current consists of both vitreous and resinous charges in motion in opposite directions, Boltzmann's argument fails; for the two kinds of electricity would give opposite directions to the current in Hall's phenomenon.

In the year following his discovery, Hall extended his researches in another direction, by investigating whether a magnetic field disturbs the distribution of equipotential lines in a dielectric which is in an electric field; but no effect could be observed. Such an effect, indeed, was not to be expected on theoretical grounds; for when, in a material system, all the velocities are reversed, the motion is reversed, it being understood that, in the application of this theorem to electrical theory, an electrostatic state is to be regarded as one of rest, and a current as a phenomenon of motion, and if such a reversal be