$$ R = 4 (\cdot195e \frac{−3\cdot66KZ}{a^2V} + \cdot0243e \frac{22\cdot3KZ}{a^2V} + &c.) $$ where _a_ = radius of the tube, _Z_ = length of the tube, _V_ = mean velocity of the gas in the tube. Only the first two terms of the series need be taken into account when narrow tubes are used. In this equation _R_, _V_, and _a_ are determined experimentally, and _K_ can thus be deduced. The following table shows the results obtained by Townsend when X rays were used. Almost identical results were obtained later, when the radiations from active substances replaced the X rays. _Coefficients of diffusion of ions into gases._ Gas _K_ _K_ Mean Ratio for + for − value of ions ions of _K_ values of _K_ Air, dry ·028 ·043 ·0347 1·54 „ moist ·032 ·035 ·0335 1·09 Oxygen, dry ·025 ·0396 ·0323 1·58 „ moist ·0288 ·0358 ·0323 1·24 Carbonic acid, ·023 ·026 ·0245 1·13 dry „ „ ·0245 ·0255 ·025 1·04 moist Hydrogen, dry ·123 ·190 ·156 1·54 „ moist ·128 ·142 ·135 1·11 The moist gases were saturated with water vapour at a temperature of 15° C. It is seen that the negative ion in all cases diffuses faster than the positive. Theory shows that the coefficients of diffusion should be directly proportional to the velocities of the ions, so that this result is in agreement with the observations on the greater velocity of the negative ion. This difference in the rate of diffusion of the ions at once explains an interesting experimental result. If ionized gases are blown through a metal tube, the tube gains a negative charge while the gas itself retains a positive charge. The number of positive and negative ions present in the gas is originally the same, but, in consequence of the more rapid diffusion of the negative ions, more of the negative ions than of the positive give up their charges to the tube. The tube consequently gains a negative and the gas a positive charge. =38.= A very important result can be deduced at once when the velocities and coefficients of diffusion of the ions are known. Townsend (_loc. cit._) has shown that the equation of their motion is expressed by the formula 1 _dp_ --- _pu_ = − ---- + _nXe_, _K_ _dx_ where _e_ is the charge on an ion, _n_ = number of ions per c.c., _p_ = their partial pressure, and _u_ is the velocity due to the electric force _X_ in the direction of the axis of _x_. When a steady state is reached,