Use of uniform-field values of Townsend´s ¿ to predict current multiplication in nonuniform fields

Some earlier investigations had indicated that the amount of ionisation observed in nonuniform fields was more than that predicted by the use of uniform-field values of ¿/p to evaluate current multiplication. The reasons for this discrepancy between theory and experiment were attributed to the variation (> 2%) of electric-field intensity over an electron mean free path or to the nonequilibrium of electrons with fields at high E/p. The results and methods of previous investigators are considered and analysed in the paper, and the reasons for the apparent discrepancy are found to be due to the use of inappropriate values of ¿/p to evaluate the quantity exp ¿ ¿dx and due to invalid methods of analysis. A new method of analysis for nonuniform fields is proposed.