With the apparatus described above, it has been shown that the positive and negative ions are equal in number. If the expansion is large enough to ensure condensation on both ions, the drops formed on the right and left of the vessel in [Fig. 7] are equal in number and fall at the same rate, i.e. are equal in size.
Since the ions are produced in equal numbers from a gas electrically neutral, this experiment shows that the charges on positive and negative ions are equal in value but opposite in sign.
36. Charge carried by an ion. For a known sudden expansion of a gas saturated with water vapour, the amount of water precipitated on the ions can be calculated readily. The size of the drops can be determined by observing the rate at which the cloud settles under the action of gravity. From Stokes’ equation, the terminal velocity u of a small sphere of radius r and density d falling through a gas of which the coefficient of viscosity is μ is given by
2 dgr2
u = --------
9 μ
where g is the acceleration due to gravity. The radius of the drop and consequently the weight of water in each drop can thus be determined. Since the total weight of water precipitated is known, the number of drops present is obtained at once.
This method has been used by J. J. Thomson[[69]] to determine the charge carried by an ion. If the expansion exceeds the value 1·31, both positive and negative ions become centres of condensation. From the rate of fall it can be shown that approximately the drops are all of the same size.
The condensation vessel was similar to that employed by C. T. R. Wilson. Two parallel horizontal plates were fitted in the vessel and the radiation from an X ray tube or radio-active substance ionized the gas between them. A difference of potential V, small compared with that required to saturate the gas, was applied between the parallel plates distant l cms. from each other. The small current i through the gas is given ([section 28]) by
NuVe