_I_{t}_ ------ = λ_t_. _I₀_ Since the activity of Th X falls to half value in 4 days, the value of λ expressed in hours = ·0072. After standing a period of 1 hour about ¹⁄₁₄₀, after 1 day ⅙, after 4 days ½ of the maximum should be obtained. The experimental results obtained showed an agreement, as good as could be expected, with the equation expressing the result that the Th X was being produced at a constant rate. The thorium-nitrate which had been freed from Th X was allowed to stand for one month, and then it was again subjected to the same process. The activity of the Th X was found to be the same as that obtained from an equal amount of the original thorium-nitrate. In one month, therefore, the Th X had been regenerated, and had reached a maximum value. By leaving the thorium time to recover fully its activity, this process can be repeated indefinitely, and equal amounts of Th X are obtained at each precipitation. Ordinary commercial thorium-nitrate and the purest nitrate obtainable showed exactly the same action, and equal amounts of Th X could be obtained from equal weights. These processes thus appear to be independent of the chemical purity of the substance[229]. The process of the production of Th X is continuous, and no alteration has been observed in the amount produced in the given time after repeated separations. After 23 precipitations extending over 9 days, the amount produced in a given interval was about the same as at the beginning of the process. These results are all in agreement with the view that the Th X is being continuously produced from the thorium compound at a constant rate. The amount of active matter produced from 1 gram of thorium is probably extremely minute, but the electrical effects due to its activity are so large that the process of production can be followed after extremely short intervals. With a sensitive electrometer the amount of Th X produced per minute in 10 grams of thorium-nitrate gives a rapid movement to the electrometer needle. For larger intervals it is necessary to add additional capacity to the system to bring the effects within range of the instrument. =133. Rate of decay of activity.= It has been shown that the activity of Ur X and Th X decays according to an exponential law with the time. This, we shall see later, is the general law of decay of activity in any type of active matter, obtained by itself, and freed from any secondary active products which it may, itself, produce. In any case, when this law is not fulfilled, it can be shown that the activity is due to the superposition of two or more effects, each of which decays in an exponential law with the time. The physical interpretation of this law still remains to be discussed.