A Uniform Expression for Resistivity

THE need for geophysicists to adopt a uniform mode of expressing the electrical resistivity of geological formations has been stressed by Dr. A. S. Eve.1 The present paper is to emphasize the point he raised, to bring the weight of disinterested authority to bear on the matter, and to urge the adoption henceforth, save in exceptional cases, of a standard expression for resistivity; all in the hope that the needed reform will thus actually be brought about. The general definition of the resistivity of a material is the resistance in ohms between two opposite faces of a unit cube of that, material. No account need be taken here of the cases in which the unit volume is not a cube, and the units of length and cross-section are different, encountered principally when dealing with metallic conductors such as wires. The idea of the resistance of a unit volume of earth or rock has found expres-sion in geophysical literature in a number of forms and with a variety of units. Fortunately, the metric system has been adhered to in most cases, so ordinarily the meter or the centimeter, usually the latter, has been the measure chosen. The resistivity is then the resistance of a cube of the given rock, or soil, one centimeter on, an edge. This is far from always being the same thing, however, as the resistance of a cubic centimeter. A long thin wire could contain a cubic centimeter and have a high resistance, whereas the same volume formed into a flat plate would have an entirely different, and quite low, resistance between faces. Con-sequently, it is not proper to express resistivity in ohms per cubic centi-meter, inch, etc., as has been done occasionally by .some writers. In an effort to emphasize the idea of cubic volume, some geophysicists, the writer among them, have used the phrase, ohms per centimeter cubed. This is a graphic way of picturing the measure, but is not in favor among highly qualified authorities. In this connection, an appeal was made to the U. S. Bureau of Standards for advice, and the Director, George K. Burgess, kindly replied in detail as to the practice adopted by his Bureau: ." . .' such expressions as ohms per centimeter cubed' or any similar expressions are objectionable, because they certainly carry the implica-tion that the resistivity is found by dividing ohms resistance by the volume in cubic centimeters." Actually, of course, resistivity is found