(1) Simplified formulae are given by means of which the maximum electric stress between equal spherical elctrodes can be readily found.(2)Experimental results on sparkling voltages when the potentials of the equal spherical electrodes are equals and opposite are analysed. It is found that it a be the length of the radius of each electrodes in centimetres, the maximum potential gradient Rmaxat the instant of discharge is given by the Rmax. = 27.4 + 14.1/√ Kilovolts per cm. very approximately when the temperature of the air is 25° C. and the height of the barometer is 76 cm.(3) The sparking voltage E between two spherical electrodes, the radius of each beinga, andxbeing the distance between them, is given by E =x/f(21.4 + 14.1/√a) Kilovolts at 25° C. and 76 cm. pressure, wherefis a factor which can be easily calculated from the geometrical dimensions.It has to be remembered that these formulae do not apply to air-gaps less than 1 mm. or air-gaps so great that brush discharges take place.(4)It follows from the formulae given above that in general for a fixed spark-gap there are certain sized spherical electrodes which offer the maximum resistance to sparking. Increasing or diminishing the size of the electrodes from this value makes the spark take place more readilly.(5) The results when one electrode is earthed given in the “Standardization Rules” of the American Institute are analysed. From the results it appears that the potentials of the electrodes were not E and o, but were 0.57 E and — 0.43 E. These values of the potentials make the values of Rmax. deduced the same as the values found when the potentials are equals and opposite.