=235. Rate of transformation of radium D.= It has been observed experimentally that each of the products of radium, which emit α rays, supplies about an equal proportion of the activity of radium when in radio-active equilibrium. Since, when equilibrium is reached, the same number of particles of each of the successive products must break up per second, this is an expression of the fact that every atom of each product breaks up with the expulsion of an equal number (probably one) of α particles. Now radium D is directly derived from radium C, and, since the rate of change of D is very slow compared with that of C, the number of particles of D initially present must be very nearly equal to the number of particles of radium C which break up during the time that radium D is being formed. Now D does not itself give out rays, but the succeeding product E does. The products D and E are practically in radio-active equilibrium one month after D is set aside, and the variation of the β ray activity of E then serves as a measure of the variation of the parent product D. Suppose that a vessel is filled with a large quantity of radium emanation. After several hours, the product radium C, which emits β rays, reaches a maximum value, and then decreases at the same rate as the emanation loses its activity, _i.e._ it falls to half value in 3·8 days. If _N₁_ is the number of β particles expelled from radium C at its maximum value, the total number _Q₁_ of β particles expelled during the life of the emanation is given approximately by $$ Q_1 = \int₀^{\infty} N_1 e^{–λ_1 t} dt = \frac {N_1} {λ_1} $$, where λ₁ is the constant of change of the emanation. After the emanation has disappeared, and the final products D + E are in radio-active equilibrium, suppose that the number of β particles _N₂_ expelled per second by radium E is determined. If _Q₂_ is the total number of particles expelled during the life of D + E, then _Q₂_ as before is approximately given by _Q₂_ = _N₂_/λ₂ where λ₂ is the constant of change of radium D. Now we have seen that if each particle of C and of E gives rise to one β particle, it is to be expected that _Q₁_ = _Q₂_, or λ₂ _N₂_ ---- = ---- . λ₁ _N₁_ The ratio _N₂_/_N₁_ was determined by measuring the activity due to the β rays from C and E in the same testing-vessel. Then, since _N₂_/_N₁_ is known, and also the value of λ₁, the value of the constant of change, λ₂, of radium D is obtained. In this way it was calculated that D is half transformed in about 40 years.