VII. Experiments, by the method of Lorentz, for the further determination the absolute value of the British Association Unit of Resistance, with an appendix on the determination of the pitch of a standard tuning-fork

Abstract

In this method, which was employed by Lorentz in 1873, a circular disc of metal is maintained in rotation at a uniform and known rate about an axis passing through its centre, and is placed in the magnetic field due to a battery current which circulates through a coaxal coil of many turns. The revolving disc is touched at its centre and circumference by two wires. If the circuit were simply closed through a galvanometer, the instrument would indicate the current due to the electromotive force of induction acting against the resistance of the circuit. The electromotive force corresponding to each revolution is the same as would be generated in a single turn of wire coincident with the circumference of the disc by the formation or cessation of the battery current. If this be called γ , and M be the coefficient of induction between the coil and the circumference, m the number of revolutions per second, the electromotive force is m M γ . In the actual arrangement, however, the circuit is not simply closed, but its terminals are connected with the extremities of a resistance R, traversed by the battery current, and the variable quantities are so adjusted that the electromotive force R γ exactly balances that of induction. When the galvanometer indicates no current, the following relation, independent, it will be observed, of the magnitude of the battery current, must be satisfied— R = m M; and from this, M being known from the data of construction, the absolute resistance R of the conductor is determined. One of the principal difficulties to be overcome arises from the smallness of the resistance R, necessary for a balance, even when m and M are both increased as far as possible. Lorentz employed three resistances, ranging from ·0008 to ·002 of a mercury unit, and he evaded the necessity of comparing these small resistances with ordinary standards by constructing them of actual columns of mercury. His result was accordingly obtained directly in terms of mercury, and was to the effect that 1 mercury unit = ·9337 x 10 9 C. G. S. differing nearly 1 per cent. from the value (·941) obtained by ourselves.