Makower[258] has recently attacked the question of the molecular weight of the radium emanation by another method. The rate of diffusion of the emanation through a porous plug of plaster-of-Paris was compared with that of the gases oxygen, carbon dioxide, and sulphur dioxide. It was found that Graham’s law, viz. that the coefficient of diffusion _K_ is inversely proportional to the square root of its molecular weight _M_, was not strictly applicable. The value of _K_ √_M_ was not found to be constant for these gases, but decreased with increase of molecular weight of the gas. If, however, a curve was plotted with _K_ √_M_ as ordinate and _K_ as abscissa, the points corresponding to the values of O, CO₂ and SO₂ were found to lie on a straight line. By linear extrapolation, the molecular weight of the emanation was estimated. The value obtained from experiments on three different porous plugs was 85·5, 97, and 99 respectively. This method indicates that the molecular weight of the radium emanation is about 100; but in all the experiments on diffusion, it must be remembered that the emanation, whose rate of inter-diffusion is being examined, exists in minute quantity mixed with the gas, and is compared with the rate of inter-diffusion of gases which are present in large quantity. For this reason, deductions of the molecular weight of the emanation may be subject to comparatively large errors, for which it is difficult to make correction. Diffusion of the Thorium Emanation. =163.= On account of the rapid decay of the activity of the thorium emanation, it is not possible to determine the value of _K_ its coefficient of diffusion into air by the methods employed for the radium emanation. The value of _K_ has been determined by the writer in the following way. A plate _C_, Fig. 57, covered with thorium hydroxide, was placed horizontally near the base of a long vertical brass cylinder _P_. The emanation released from the thorium compound diffuses upwards in the cylinder. [Illustration: Fig. 57.] Let _p_ be the partial pressure of the emanation at a distance _x_ from the source _C_. This will be approximately uniform over the cross section of the cylinder. From the general principles of diffusion we get the equation _d²p_ _dp_ _K_ ----- = − ---- . _dx²_ _dt_ The emanation is continuously breaking up and expelling α particles. The emanation-residue gains a positive charge, and, in an electric field, is removed at once from the gas to the negative electrode. Since the activity of the emanation at any time is always proportional to the number of particles which have not broken up, and since the activity decays with the time according to an exponential law, $$ p = p_1 e^{–λt} $$, where _p₁_ is the value of _p_ when _t_ = 0 and λ is the _radio-active constant_ of the emanation. Then