The variation of activity with time is shown graphically in Fig. 76. The activity rises from zero to a maximum in 220 minutes and then decays, finally decreasing, according to an exponential law, with the time, falling to half value in 11 hours. This theoretical curve is seen to agree closely in shape with the experimental curve (Fig. 65), which shows the variation of the activity of the active deposit of thorium, produced by a short exposure in presence of the emanation. There are several points of interest in connection with an activity curve of this character. The activity, some hours after removal, decays according to an exponential law, not at the rate of the product _B_, from which the activity rises, but at the same rate as the first rayless transformation. This will also be the case if the rayless product has a slower rate of change than the succeeding active product. Given an activity curve of the character of Fig. 76, we can deduce from it that the first change is not accompanied by rays and also the period of the two changes in question. We are, however, unable to determine from the curve which of the periods of change refers to the rayless product. It is seen that the activity curve is unaltered if the values of λ₁, λ₂, that is, if the periods of the products are interchanged, for the equation is symmetrical in λ₁, λ₂. For example, in the case of the active deposit of thorium, without further data it is impossible to decide whether the period of the first change has a value of 55 minutes or 11 hours. In such cases the question can only be settled by using some physical or chemical means in order to separate the product _A_ from _B_, and then testing the rate of decay of their activity separately. In practice, this can often be effected by electrolysis or by utilizing the difference in volatility of the two products. If now a product is separated from the mixture of _A_ and _B_ which loses its activity according to an exponential law, falling to half value in 55 minutes (and such is experimentally observed), we can at once conclude that the active product _B_ has the period of 55 minutes. The characteristic features of the activity curve shown in Fig. 76 becomes less marked with increase of the time of exposure of a body to the emanation, that is, when more and more of _B_ is mixed with _A_ at the time of removal. For a long time of exposure, when the products _A_ and _B_ are in radio-active equilibrium, the activity after removal is proportional to _Q_, where $$ Q = \frac {n₀} {λ_1 − λ_2} (\frac {λ_1} {λ_2} e^{–λ_2 t} − e^{λ_1 t}) $$, (see equation 8, section 198). The value of _Q_, in this case, does not increase after removal, but at once commences to diminish. The activity, in consequence, decreases from the moment of removal, but more slowly than would be given by an exponential law. The activity finally decays exponentially, as in the previous case, falling to half value in 11 hours.