the rate of heat emission of the radium and the emanation together, was at any time found to be equal to that of the original radium. The maximum heating effect of the tube containing the emanation from 30 milligrams of radium bromide was 1·26 gram-calories per hour. The emanation together with the secondary products which arise from it, obtained from one gram of radium, would thus give out 42 gram-calories per hour. The emanation stored up in the radium is thus responsible for more than two-thirds of the total heat emission from radium. It will be seen later that the decrease to a minimum of the heating effect of radium, after removal of the emanation, is connected with the decay of the excited activity. In a similar way, the increase of the heating effect of the emanation to a maximum some hours after removal is also a result of the excited activity produced by the emanation on the walls of the containing vessel. Disregarding for the moment these rapid initial changes in heat emission, it is seen that the heating effect of the emanation and its further products, after reaching a maximum, decreases at the same rate as that at which the emanation loses its activity, that is, it falls to half value in four days. If Q_{max.} is the maximum heating effect and Q_{t} the heating effect at any time t later, then Q_{t}/Q_{max.} = e^{-λt} where λ is the constant of change of the emanation.
The curve of recovery of the heating effect of radium from its minimum value is identical with the curve of recovery of its activity measured by the α rays. Since the minimum heating effect is 25 per cent. of the total, the heat emission Q_{t} at any time t after reaching a minimum is given by
Q_{t}/Q_{max.} = ·25 + ·75(1 - e^{-λt}),
where Q_{max.} is the maximum rate of heat emission and λ, as before, is the constant of change of the emanation.
The identity of the curves of recovery and fall of the heating effect of radium and its emanation respectively with the corresponding curves for the rise and fall of radio-activity shows that the heat emission of radium and its products is directly connected with their radio-activity. The variation in the heat emission of both radium and its emanation is approximately proportional to their activity measured by the α rays. It is not proportional to
