_dp_ ---- = -λ_p_, _dt_ and _d²p_ K ----- = λ_p_. _dx²_ Thus $$ p = Ae^{-\sqrt {\frac {λ} {K} x}} + Be^{\sqrt {\frac {λ} {K} x}} $$ . Since _p_ = 0 when _x_ = infinity, _B_ = 0. If _p_ = _p₀_ when _x_ = 0, _A_ = _p₀_. Thus $$ p = p₀ e^{-\sqrt {\frac {λ} {K} x}} $$ . It was not found convenient in the experiments to determine the activity of the emanation along the cylinder, but an equivalent method was used which depends upon measuring the distribution of “excited activity,” produced along a central rod _AB_, which is charged negatively. It will be shown later (section 177) that the amount of excited activity at any point is always proportional to the amount of emanation at that point. The distribution of “excited activity” along the central rod from the plate _C_ upwards thus gives the variation of _p_ for the emanation along the tube. In the experiments, the cylinder was filled with dry air at atmospheric pressure and was kept at a constant temperature. The central rod was charged negatively and exposed from one to two days in the presence of the emanation. The rod was then removed, and the distribution of the excited activity along it determined by the electric method. It was found that the amount of excited activity fell off with the distance _x_ according to an exponential law, falling to half value in about 1·9 cms. This is in agreement with the above theory. Since the activity of the emanation falls to half value in 1 minute, λ = ·0115. The value _K_ = ·09 was deduced from the average of a number of experiments. This is a slightly greater value than _K_ = ·07, obtained for the radium emanation, but the results show that the two emanations do not differ much from one another in molecular weight. Makower (_loc. cit._) compared the rates of diffusion of the thorium and radium emanation through a porous plate, and concluded that the two emanations were of about the same molecular weight, thus confirming the results obtained by the above method. Diffusion of the Emanation into Liquids. =164.= Experiments have been made by Wallstabe[259] on the coefficient of diffusion of the radium emanation into various liquids. The radium emanation was allowed to diffuse into a closed reservoir, containing a cylinder of the liquid under observation. The cylinder was provided with a tube and a stop-cock extending beyond the closed vessel, so that different layers of the liquid could be removed. The liquid was then placed in a closed testing vessel, where the ionization current due to the escape of the emanation from the liquid was observed to rise to a maximum after several hours, and then to decay. This maximum value of the current was taken as a measure of the amount of emanation absorbed in the liquid.