Thus de-emanation does not permanently destroy the power of thorium of giving out an emanation, but merely produces an alteration of the amount of the emanation which escapes from the compound. =152. Rate of production of the emanation.= The emanating power of thorium compounds, then, is a very variable quantity, much affected by moisture, heat, and solution. Speaking generally, increased temperatures and solution greatly increase the emanating power of both thorium and radium. The wide differences between the emanating powers of these substances in the solid state and in solution pointed to the conclusion that the differences were probably due to the rate of escape of the emanation into the surrounding gas, and not to a variation of the rate of reaction which gave rise to the emanation. It is obvious that a very slight retardation in the rate of escape of the thorium emanation from the compound into the gas, will, on account of the rapid decay of activity of the emanation, produce great changes in emanating power. The regeneration of the emanating power of de-emanated thoria and radium by solution and chemical treatment made it evident that the original power of thorium and radium of producing the emanation still persisted in an unaltered degree. The question whether the emanation was produced at the same rate in emanating as in non-emanating compounds can be put to a sharp quantitative test. If the rate of production of emanation goes on at the same rate in the solid compound where very little escapes, as in the solution where probably all escapes, the emanation must be _occluded_ in the compound, and consequently there must be a sudden release of this emanation on solution of the compound. On account of the very slow decay of the activity of the emanation of radium, the effects should be far more marked in that compound than in thorium. From the point of view developed in section 133, the exponential law of decay of the emanation expresses the result that _N_{t}_ the number of particles remaining unchanged at the time _t_ is given by $$ \frac {N_t} {N₀} = e^{–λt} $$ (1). where _N₀_ is the initial number of particles present. When a steady state is reached, the rate of production _q₀_ of fresh emanation particles is exactly balanced by the rate of change of the particles _N₀_ already present, _i.e._ _q₀_ = λ_N₀_, _N₀_ in this case represents the amount of emanation “occluded” in the compound. Substituting the value of λ found for the radium emanation in section 145, _N₀_ ----- = 1/λ = 463,000. _q₀_ The amount of emanation stored in a non-emanating radium compound should therefore be nearly 500,000 times the amount produced per second by the compound. This result was tested in the following way[247].