A method of using one or more ground-level air pollution transducers to detect anomalous emission from a fixed point source of air pollution is described. It is assumed a source can be identified by two position variables and three operating parameters. It is possible to spot the source position within a region A ∈ E2if the operating parameters are partially known. The method is based on the principle of source-receptor reciprocity and certain mapping theorems. Mathematical questions arise when finding the set A. One question involves a technique for finding the set A from points on its boundary. Another question deals with the variations in the area of A with the amount of uncertainty in the operating parameters. The questions are resolved by recourse to general characteristics of diffusion patterns. An example is given to illustrate one application of the theory.

A simple scheme of switching triangular waves and measuring the average current through resistors into a low impedance summing point makes possible four-quadrant multiplication with four diodes, precisely adjusted resistors, and a means of measuring the current. A practical circuit utilizes one operational amplifier to obtain -(X+Y)/2 and a second such unit to measure the summing point current. Addition of four auxiliary diodes reduces circuit interactions and makes less stringent requirements on the diodes. A simple operational adjustment procedure is described. Also, a simple means for obtaining the precise resistance balance is outlined. Calibration does not depend upon triangular wave frequency or symmetry. The amplifiers are not required to handle the triangular wave frequencies.