microscope through two holes in the cylinder, covered with thin mica. In cases where the natural ionization due to the enclosed air in the cylinder is to he measured accurately, it is advisable to enclose the supporting and charging rod and sulphur bead inside a small metal cylinder M connected to earth, so that only the charged gold-leaf system is exposed in the main volume of the air.
In an apparatus of this kind the small leakage over the sulphur bead can be eliminated almost completely by keeping the rod P charged to the average potential of the gold-leaf system during the observation. This method has been used with great success by C. T. R. Wilson (loc. cit.). Such refinements, however, are generally unnecessary, except in investigations of the natural ionization of gases at low pressures, when the conduction leak over the sulphur bead is comparable with the discharge due to the ionized gas.
57. The electric capacity C of a gold-leaf system about 4 cms.
long is usually about 1 electrostatic unit. If V is the decrease of
potential of the gold-leaf system in t seconds, the current i through
the gas is given by
i = CV/t.
With a well cleaned brass electroscope of volume 1 litre, the fall of potential due to the natural ionization of the air was found to be about 6 volts per hour. Since the capacity of the gold-leaf system was about 1 electrostatic unit
i = 1 × 6/(3600 × 300) = 5·6 × 10^{-6} E.S. units = 1·9 × 10^{-15} amperes.
With special precautions a rate of discharge of 1/10 or even 1/100 of this amount can be measured accurately.
The number of ions produced in the gas can be calculated if the charge on an ion is known. J. J. Thomson has shown that the charge e on an ion is equal to 3·4 × 10^{-10} electrostatic units or 1·13 × 10^{-19} coulombs.
Let q = number of ions produced per second per cubic centimetre
throughout the volume of the electroscope,
S = volume of electroscope in cubic centimetres.
If the ionization be uniform, the saturation current i is given by i = qSe.
