The theory as given by J. J. Thomson for the drop of potential at plane electrodes has been modified by allowing for recombination in the layer and a similar theory for cylindrical electrodes has been worked out. The equation for plane cathodes is V2=32pi 75k1 12x32 2 , and for cylindrical cathodes is V2=2i 3k1&parl0;r22-r2 0&parr0;2 12 r32 logr2+r 22-r20 r0-r2 2&parl0;r22-r20 &parr0;12-&parl0; r22-r20&parr0; 323 , where V2 = the potential drop across the sheath, i = the current density, x2 = the sheath thickness at the plane cathode, r0 = the radius of the cylindrical cathode, r2 = the radius of the cylindrical sheath about the cathode, and k1 = the velocity of the positive ions for a gradient of 1.0 volt per cm. The experimental results for platinum electrodes immersed in pure NaCl flames agree well with the theoretical equations given. It is found that the drop in potential at the cathode occurs in a sheath of uniform thickness, which completely surrounds the electrode. By plotting the gas potential at various points in the flame against distance from the cathode it is possible to estimate the thickness of the sheath. Over 95% of the potential drop takes place across the sheath at the cathode provided it is of clean platinum. If the cathode is not clean electrons are emitted which partially neutralize the accumulation of positive ions and thus reduce the sheath thickness. By measuring v2, i, x2 or r0 and r2, and making the proper substitutions in the above equations, the mobility k 1 of the positive ions is found to average 12.4 for a pure flame and 8.1 cms per sec. for one volt per cm for a NaCl flame.
A study of the characteristic current-voltage curve for a wire probe in a flame makes it possible to measure the voltage correction to be applied to the measured probe potential in order to obtain the true gas potential adjacent to the test probe. The correction is of the order of +1.0 volts.
It is found that the current density at the surface of the cylindrical sheath is constant for any given flame conditions, and size of cathode. Thus one can measure the current density existing in the small uniform gradient just outside the sheath. The current density at the sheath surface in a pure flame varies from 1.0 to 2.5 microamperes and for the NaCl flame from 5.0 to 11.0 microamperes.