ON THE ELECTRIC RESISTANCE OF SUBSTANCES

Excerpts

ON THE ELECTRIC RESISTANCE OF SUBSTANCES
The resistance of this class of bodies is enormous compared with that of the metals. It diminishes as the temperature rises.
ON THE ELECTRIC RESISTANCE OF SUBSTANCES
The measurement of the electric resistance of electrolytes is rendered difficult on account of the polarization of the electrodes, which causes the observed difference of potentials of the metallic electrodes to be greater than the electromotive force which actually produces the current.
ON THE ELECTRIC RESISTANCE OF SUBSTANCES
In all these substances conduction takes place without any decomposition, or alteration of the chemical nature of the substance, either in its interior or where the current enters and leaves the body. In all of them the resistance increases as the temperature rises.
ON THE ELECTRIC RESISTANCE OF SUBSTANCES
These phenomena seem to be due to a condition of the gutta-percha, which, for want of a better name, we may call polarization, and which we may compare on the one hand with that of a series of Leyden jars charged by cascade, and, on the other, with Ritter’s secondary pile.
ON THE ELECTRIC RESISTANCE OF SUBSTANCES
Hence ordinary resistance coils are made of German silver, on account of its great resistance, and its small variation with temperature.
ON THE ELECTRIC RESISTANCE OF SUBSTANCES
It is of the utmost importance in the electric telegraph that the metal of which the wires are made should have the smallest attainable resistance. Measurements of resistance must therefore be made before selecting the materials.
ON THE ELECTRIC RESISTANCE OF SUBSTANCES
There are three classes in which we may place different substances in relation to the passage of electricity through them.
ON THE ELECTRIC RESISTANCE OF SUBSTANCES
Finally, by making two different experiments, in one of which the path of the current through the electrolyte is much longer than in the other, and so adjusting the electromotive force that the actual current, and the time during which it flows, are nearly the same in each case, we can eliminate the effect of polarization altogether.
ON THE ELECTRIC RESISTANCE OF SUBSTANCES
But even after this current has been allowed to subside the residual current is not constant, and does not indicate the true conductivity of the substance. It is found that the current continues to decrease for at least half an hour, so that a determination of the resistance deduced from the current will give a greater value if a certain time is allowed to elapse than if taken immediately after applying the battery.
ON THE ELECTRIC RESISTANCE OF SUBSTANCES
Thus, with Hooper’s insulating material the apparent resistance at the end of ten minutes was four times, and at the end of nineteen hours twenty-three times that observed at the end of one minute.
ON THE ELECTRIC RESISTANCE OF SUBSTANCES
When the maximum polarization is established, the excess of electromotive force above that of 304 cells is devoted to maintaining the current according to Ohm’s Law.
ON THE ELECTRIC RESISTANCE OF SUBSTANCES
The whole theory of what has been called residual discharge, absorption of electricity, electrification, or polarization, deserves a careful investigation, and will probably lead to important discoveries relating to the internal structure of bodies.
ON THE ELECTRIC RESISTANCE OF SUBSTANCES
‘Multiply each cycle sign (i.e. current) by the sum of all the resistances which bound that cycle, and subtract from it the sign of each neighbouring cycle multiplied by the resistance separating the cycles, and equate the result to the E. M. F. in the cycle.’

Equations

ON THE ELECTRIC RESISTANCE OF SUBSTANCES
r = \alpha T^{\frac{1}{2}} + \beta T + \gamma
Siemens's empirical formula gives the resistance of a metal as a function of absolute temperature, with three constants fitted to the data.
ON THE ELECTRIC RESISTANCE OF SUBSTANCES
\rho = \frac{R_1 - R_2}{{R_1}' - {R_2}'}
Paalzow's ratio: the resistance of an electrolyte divided by that of mercury of the same form at 0°C, found from two siphons of different lengths, with the polarization-cancelling difference taken in each case.
ON THE ELECTRIC RESISTANCE OF SUBSTANCES
r &= 0.039369T^{\frac{1}{2}} + 0.00216407T - 0.2413\text{,}
The fitted resistance formula for platinum, with its numerical constants.
ON THE ELECTRIC RESISTANCE OF SUBSTANCES
r &= 0.026577T^{\frac{1}{2}} + 0.0031443T - 0.22751\text{,}
The fitted resistance formula for copper, with its numerical constants.
ON THE ELECTRIC RESISTANCE OF SUBSTANCES
r &= 0.072545T^{\frac{1}{2}} + 0.0038133T - 1.23971\text{.}
The fitted resistance formula for iron, with its numerical constants.
ON THE ELECTRIC RESISTANCE OF SUBSTANCES
r = \alpha T^{\frac{1}{2}} + \beta T + \gamma\text{,}
Siemens's empirical formula gives a metal's resistance r as a function of absolute temperature T, with constants alpha, beta and gamma fitted to each metal.
ON THE ELECTRIC RESISTANCE OF SUBSTANCES
\rho = \frac{R_1 - R_2}{{R_1}' - {R_2}'}.
The ratio of an electrolyte's resistance to that of mercury of the same form is found from the difference of the two siphon resistances filled with electrolyte divided by the difference of the two filled with mercury.
ON THE ELECTRIC RESISTANCE OF SUBSTANCES
R = r \times 0.8878^t\text{,}
The resistance of gutta-percha at temperature T+t is the resistance r at T multiplied by 0.8878 raised to the power t, an empirical formula found by Bright and Clark.
ON THE ELECTRIC RESISTANCE OF SUBSTANCES
E = E_0 + RC\text{.}
In a rarefied gas the electromotive force is a constant E_0 (the polarization of the electrodes) plus the part that drives the current C through the resistance R according to Ohm's law.
ON THE ELECTRIC RESISTANCE OF SUBSTANCES
( P + G + Q )\overline{ x + y} - Gy - Qz &= 0
First current equation for the bridge: Ohm's law applied to circuit PGQ, with the sum of the resistances around that circuit times its current, minus the neighbouring circuit currents times the shared resistances, equals zero.
ON THE ELECTRIC RESISTANCE OF SUBSTANCES
( R + S + G )y - Sz - G \overline{x + y} &= 0
Second current equation for the bridge: Ohm's law applied to circuit RSG, equal to zero since its electromotive force is zero.
ON THE ELECTRIC RESISTANCE OF SUBSTANCES
( Q + S + B )z - Sy - Q \overline{x + y} &= E
Third current equation for the bridge: Ohm's law applied to circuit QSB, whose total electromotive force is the battery electromotive force E.
ON THE ELECTRIC RESISTANCE OF SUBSTANCES
( P + G + Q )x + ( P + Q )y - Qz &= 0
First current equation of the bridge in solved (rearranged) form, with the currents x, y, z as the unknowns.
ON THE ELECTRIC RESISTANCE OF SUBSTANCES
-Gx + ( R + S )y - Sz &= 0
Second current equation of the bridge in solved form.
ON THE ELECTRIC RESISTANCE OF SUBSTANCES
-Qx - ( S + Q )y + ( Q + S + B )z &= E
Third current equation of the bridge in solved form, equal to the battery electromotive force E.
ON THE ELECTRIC RESISTANCE OF SUBSTANCES
& = \frac{E(QR-PS)}{\Delta}\text{,}
The current x in the galvanometer arm, found by solving the system (II) by determinants, equals E(QR-PS) divided by the determinant Delta of the system.
ON THE ELECTRIC RESISTANCE OF SUBSTANCES
QR - PS = 0 \text{, or } \frac{P}{Q} =\frac{R}{S}\text{.}
The condition for no current in the galvanometer of the bridge: QR - PS = 0, equivalently P/Q = R/S.

Problems

No exercises in this chapter.